Quizbank/University Physics Semester 2/T9

University Physics Semester 2/T9 ID153341821922

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Exams:  A0  A1  A2   B0  B1  B2   C0  C1  C2   D0  D1  D2   E0  E1  E2   F0  F1  F2   G0  G1  G2   H0  H1  H2   I0  I1  I2   J0  J1  J2   K0  K1  K2   L0  L1  L2   M0  M1  M2   N0  N1  N2   O0  O1  O2   P0  P1  P2   Q0  Q1  Q2   R0  R1  R2   S0  S1  S2   T0  T1  T2   U0  U1  U2   V0  V1  V2   W0  W1  W2   X0  X1  X2   Y0  Y1  Y2   Z0  Z1  Z2

Answers:  A0  A1  A2   B0  B1  B2   C0  C1  C2   D0  D1  D2   E0  E1  E2   F0  F1  F2   G0  G1  G2   H0  H1  H2   I0  I1  I2   J0  J1  J2   K0  K1  K2   L0  L1  L2   M0  M1  M2   N0  N1  N2   O0  O1  O2   P0  P1  P2   Q0  Q1  Q2   R0  R1  R2   S0  S1  S2   T0  T1  T2   U0  U1  U2   V0  V1  V2   W0  W1  W2   X0  X1  X2   Y0  Y1  Y2   Z0  Z1  Z2

78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the |study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take  version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

Links:  Quizbank/Instructions   |Study guide    file:QB-University Physics Semester 2-T9.pdf

Contact me at User talk:Guy vandegrift if you need any help.

T9 A0
1) A circular current loop of radius 2.1 cm carries a current of 5.02 mA. What is the magnitude of the torque if the dipole is oriented at 26 &deg; to a uniform magnetic fied of 0.184 T?


 * a) 5.610E-07 N m
 * b) 6.171E-07 N m
 * c) 6.788E-07 N m
 * d) 7.467E-07 N m
 * e) 8.213E-07 N m

2) The silver ribbon shown are a=3.68 cm, b=2.66 cm, and c= 0.505 cm. The current carries a current of 113 A and it lies in a uniform magnetic field of 3.12 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 6.104E-06 V
 * b) 6.714E-06 V
 * c) 7.385E-06 V
 * d) 8.124E-06 V
 * e) 8.936E-06 V

3) Two loops of wire carry the same current of 66 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.485 m while the other has a radius of 1.27 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.507 m from the first (smaller) loopif the disance between the loops is 1.76 m?


 * a) 2.733E-02 T
 * b) 3.007E-02 T
 * c) 3.307E-02 T
 * d) 3.638E-02 T
 * e) 4.002E-02 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * e) $$\chi \text{ (chi) }=$$ 1.907E+03

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.29 T and $$\omega=$$4.720E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 6.420E+04 V
 * b) 7.062E+04 V
 * c) 7.768E+04 V
 * d) 8.545E+04 V
 * e) 9.400E+04 V

6) A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds  coil of radius 6.01 meters and 10turns.  If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?


 * a) 1.463E-02 V
 * b) 1.609E-02 V
 * c) 1.770E-02 V
 * d) 1.947E-02 V
 * e) 2.142E-02 V

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.82 V. The resistance, inductance, and capacitance are R =3 &Omega;, L= 6.20E-03H, and C=6.70E-04 F, respectively. What is the amplitude of the current?


 * a) 2.259E-01 A
 * b) 2.485E-01 A
 * c) 2.733E-01 A
 * d) 3.007E-01 A
 * e) 3.307E-01 A

8) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 23 &Omega; resistor and a battery of voltage V0=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?


 * a) 2.877E+00 V
 * b) 3.165E+00 V
 * c) 3.481E+00 V
 * d) 3.829E+00 V
 * e) 4.212E+00 V

9) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.253E-05 N/m2
 * b) 1.378E-05 N/m2
 * c) 1.516E-05 N/m2
 * d) 1.667E-05 N/m2
 * e) 1.834E-05 N/m2

10) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.87E-11 Vs2m-1
 * b) 7.11E-11 Vs2m-1
 * c) 8.61E-11 Vs2m-1
 * d) 1.04E-10 Vs2m-1
 * e) 1.26E-10 Vs2m-1

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * a) 2.80E+04 N/C (or V/m)
 * b) 3.40E+04 N/C (or V/m)
 * c) 4.12E+04 N/C (or V/m)
 * d) 4.99E+04 N/C (or V/m)
 * e) 6.04E+04 N/C (or V/m)

T9 A1
1) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.253E-05 N/m2
 * b) 1.378E-05 N/m2
 * c) 1.516E-05 N/m2
 * d) 1.667E-05 N/m2
 * e) 1.834E-05 N/m2

2) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 &deg; to a uniform magnetic fied of 0.402 T?


 * a) 1.022E-06 N m
 * b) 1.124E-06 N m
 * c) 1.236E-06 N m
 * d) 1.360E-06 N m
 * e) 1.496E-06 N m

3) Two loops of wire carry the same current of 24 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.53 m while the other has a radius of 1.38 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.485 m from the first (smaller) loopif the disance between the loops is 1.78 m?


 * a) 1.294E-02 T
 * b) 1.424E-02 T
 * c) 1.566E-02 T
 * d) 1.723E-02 T
 * e) 1.895E-02 T

4) The silver ribbon shown are a=3.6 cm, b=2.68 cm, and c= 1.13 cm. The current carries a current of 97 A and it lies in a uniform magnetic field of 1.89 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.560E-06 V
 * b) 1.716E-06 V
 * c) 1.888E-06 V
 * d) 2.077E-06 V
 * e) 2.284E-06 V

5) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.188E+03
 * b) $$\chi \text{ (chi) }=$$ 1.307E+03
 * c) $$\chi \text{ (chi) }=$$ 1.438E+03
 * d) $$\chi \text{ (chi) }=$$ 1.582E+03
 * e) $$\chi \text{ (chi) }=$$ 1.740E+03

6) A circlular capactitor of radius 4.4 m has a gap of 8 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 4.96E-11 Vs2m-1
 * b) 6.01E-11 Vs2m-1
 * c) 7.28E-11 Vs2m-1
 * d) 8.82E-11 Vs2m-1
 * e) 1.07E-10 Vs2m-1

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =9 &Omega;, L= 8.50E-03H, and C=7.20E-04 F, respectively. What is the amplitude of the current?


 * a) 8.384E-02 A
 * b) 9.222E-02 A
 * c) 1.014E-01 A
 * d) 1.116E-01 A
 * e) 1.227E-01 A

8) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 84 &mu;C.  What is the electric field between the plates?


 * a) 1.37E+05 N/C (or V/m)
 * b) 1.66E+05 N/C (or V/m)
 * c) 2.01E+05 N/C (or V/m)
 * d) 2.43E+05 N/C (or V/m)
 * e) 2.95E+05 N/C (or V/m)

9) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.7 T and $$\omega=$$8.100E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.827 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 1.416E+05 V
 * b) 1.557E+05 V
 * c) 1.713E+05 V
 * d) 1.884E+05 V
 * e) 2.073E+05 V

10) A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds  coil of radius 6.86 meters and 14turns.  If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?


 * a) 1.894E-02 V
 * b) 2.083E-02 V
 * c) 2.291E-02 V
 * d) 2.520E-02 V
 * e) 2.772E-02 V

11) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * a) 7.693E+01 V
 * b) 8.463E+01 V
 * c) 9.309E+01 V
 * d) 1.024E+02 V
 * e) 1.126E+02 V

T9 A2
1) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 6.669E-07 N/m2
 * b) 7.336E-07 N/m2
 * c) 8.069E-07 N/m2
 * d) 8.876E-07 N/m2
 * e) 9.764E-07 N/m2

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * e) $$\chi \text{ (chi) }=$$ 1.907E+03

3) A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?


 * a) 5.131E+01 V
 * b) 5.644E+01 V
 * c) 6.209E+01 V
 * d) 6.830E+01 V
 * e) 7.513E+01 V

4) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 &deg; to a uniform magnetic fied of 0.402 T?


 * a) 1.022E-06 N m
 * b) 1.124E-06 N m
 * c) 1.236E-06 N m
 * d) 1.360E-06 N m
 * e) 1.496E-06 N m

5) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.3 V. The resistance, inductance, and capacitance are R =2 &Omega;, L= 8.10E-03H, and C=9.40E-04 F, respectively. What is the amplitude of the current?


 * a) 1.364E-01 A
 * b) 1.500E-01 A
 * c) 1.650E-01 A
 * d) 1.815E-01 A
 * e) 1.997E-01 A

6) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.49 m while the other has a radius of 1.11 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * a) 1.564E-02 T
 * b) 1.720E-02 T
 * c) 1.892E-02 T
 * d) 2.081E-02 T
 * e) 2.289E-02 T

7) The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.648E-06 V
 * b) 1.813E-06 V
 * c) 1.994E-06 V
 * d) 2.194E-06 V
 * e) 2.413E-06 V

8) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 2.05E-11 Vs2m-1
 * b) 2.48E-11 Vs2m-1
 * c) 3.01E-11 Vs2m-1
 * d) 3.64E-11 Vs2m-1
 * e) 4.42E-11 Vs2m-1

9) A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds  coil of radius 6.86 meters and 14turns.  If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?


 * a) 1.894E-02 V
 * b) 2.083E-02 V
 * c) 2.291E-02 V
 * d) 2.520E-02 V
 * e) 2.772E-02 V

10) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.7 T and $$\omega=$$8.100E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.827 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 1.416E+05 V
 * b) 1.557E+05 V
 * c) 1.713E+05 V
 * d) 1.884E+05 V
 * e) 2.073E+05 V

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * a) 2.80E+04 N/C (or V/m)
 * b) 3.40E+04 N/C (or V/m)
 * c) 4.12E+04 N/C (or V/m)
 * d) 4.99E+04 N/C (or V/m)
 * e) 6.04E+04 N/C (or V/m)

T9 B0
1) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.449 m and a magneticfield of 0.81 T. What is their maximum kinetic energy?


 * a) 5.795E+00 MeV
 * b) 6.374E+00 MeV
 * c) 7.012E+00 MeV
 * d) 7.713E+00 MeV
 * e) 8.484E+00 MeV

2) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?


 * a) 1.174E+00 A
 * b) 1.291E+00 A
 * c) 1.420E+00 A
 * d) 1.562E+00 A
 * e) 1.719E+00 A

3) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.776 m while the other has a radius of 1.2 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?


 * a) 1.127E-02 T
 * b) 1.240E-02 T
 * c) 1.364E-02 T
 * d) 1.500E-02 T
 * e) 1.650E-02 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.86 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.488E-05 T
 * b) 1.637E-05 T
 * c) 1.800E-05 T
 * d) 1.981E-05 T
 * e) 2.179E-05 T

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * a) 1.605E-04 V/m
 * b) 1.766E-04 V/m
 * c) 1.942E-04 V/m
 * d) 2.136E-04 V/m
 * e) 2.350E-04 V/m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.23% of its maximum value if &epsilon; = 3.13 V, R = 3.59 &Omega;, and L = 3.38 H?


 * a) -1.345E+00 s
 * b) -1.480E+00 s
 * c) -1.628E+00 s
 * d) -1.790E+00 s
 * e) -1.969E+00 s

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.64 V. The resistance, inductance, and capacitance are R =2 &Omega;, L= 4.00E-03H, and C=8.30E-04 F, respectively. What is the amplitude of the current?


 * a) 3.200E-01 A
 * b) 3.520E-01 A
 * c) 3.872E-01 A
 * d) 4.259E-01 A
 * e) 4.685E-01 A

8) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.673E-07 N
 * b) 2.940E-07 N
 * c) 3.234E-07 N
 * d) 3.558E-07 N
 * e) 3.913E-07 N

9) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * a) 7.315E-02 A
 * b) 8.047E-02 A
 * c) 8.851E-02 A
 * d) 9.737E-02 A
 * e) 1.071E-01 A

10) A circlular capactitor of radius 4.4 m has a gap of 12 mm, and a charge of 72 &mu;C.  What is the electric field between the plates?


 * a) 6.21E+04 N/C (or V/m)
 * b) 7.52E+04 N/C (or V/m)
 * c) 9.11E+04 N/C (or V/m)
 * d) 1.10E+05 N/C (or V/m)
 * e) 1.34E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is the decay time?


 * a) 2.57E-04 s
 * b) 3.11E-04 s
 * c) 3.77E-04 s
 * d) 4.57E-04 s
 * e) 5.53E-04 s

T9 B1
1) A parallel plate capacitor with a capicatnce C=6.80E-06 F whose plates have an area A=6.60E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 62 &Omega; resistor and a battery of voltage V0=36 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * a) 8.288E-02 A
 * b) 9.117E-02 A
 * c) 1.003E-01 A
 * d) 1.103E-01 A
 * e) 1.213E-01 A

2) What is the radiation force on an object that is 1.70E+11 m away from the sun and has cross-sectional area of 0.033 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.904E-07 N
 * b) 2.094E-07 N
 * c) 2.303E-07 N
 * d) 2.534E-07 N
 * e) 2.787E-07 N

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.098E-05 T
 * b) 1.208E-05 T
 * c) 1.329E-05 T
 * d) 1.462E-05 T
 * e) 1.608E-05 T

4) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.54% of its maximum value if &epsilon; = 2.46 V, R = 2.8 &Omega;, and L = 5.67 H?


 * a) -2.540E+00 s
 * b) -2.794E+00 s
 * c) -3.073E+00 s
 * d) -3.381E+00 s
 * e) -3.719E+00 s

5) Two loops of wire carry the same current of 97 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.595 m while the other has a radius of 1.1 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.63 m from the first (smaller) loopif the disance between the loops is 1.72 m?


 * a) 5.302E-02 T
 * b) 5.832E-02 T
 * c) 6.415E-02 T
 * d) 7.056E-02 T
 * e) 7.762E-02 T

6) A circlular capactitor of radius 3.4 m has a gap of 15 mm, and a charge of 63 &mu;C.  What is the electric field between the plates?


 * a) 1.62E+05 N/C (or V/m)
 * b) 1.96E+05 N/C (or V/m)
 * c) 2.37E+05 N/C (or V/m)
 * d) 2.88E+05 N/C (or V/m)
 * e) 3.48E+05 N/C (or V/m)

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.355 m and a magneticfield of 1.28 T. What is their maximum kinetic energy?


 * a) 7.476E+00 MeV
 * b) 8.224E+00 MeV
 * c) 9.046E+00 MeV
 * d) 9.951E+00 MeV
 * e) 1.095E+01 MeV

8) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 3.62E-04 s
 * b) 4.38E-04 s
 * c) 5.31E-04 s
 * d) 6.43E-04 s
 * e) 7.79E-04 s

9) A 33 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.869 T. What current is required to maintain this balance?


 * a) 2.259E-01 A
 * b) 2.485E-01 A
 * c) 2.734E-01 A
 * d) 3.007E-01 A
 * e) 3.308E-01 A

10) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.31 V. The resistance, inductance, and capacitance are R =5 &Omega;, L= 9.00E-03H, and C=5.10E-04 F, respectively. What is the amplitude of the current?


 * a) 4.235E-02 A
 * b) 4.658E-02 A
 * c) 5.124E-02 A
 * d) 5.636E-02 A
 * e) 6.200E-02 A

11) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * a) 6.040E-05 V/m
 * b) 6.644E-05 V/m
 * c) 7.309E-05 V/m
 * d) 8.039E-05 V/m
 * e) 8.843E-05 V/m

T9 B2
1) A 24 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.706 T. What current is required to maintain this balance?


 * a) 5.258E-01 A
 * b) 5.784E-01 A
 * c) 6.362E-01 A
 * d) 6.998E-01 A
 * e) 7.698E-01 A

2) Two loops of wire carry the same current of 21 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.753 m while the other has a radius of 1.47 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.406 m from the first (smaller) loopif the disance between the loops is 1.38 m?


 * a) 1.559E-02 T
 * b) 1.715E-02 T
 * c) 1.886E-02 T
 * d) 2.075E-02 T
 * e) 2.283E-02 T

3) A long solenoid has a radius of 0.624 m and 84 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$20 s&minus;1.What is the induced electric fied at a distance 1.78 m from the axis at time t=0.0579 s ?


 * a) 3.597E-04 V/m
 * b) 3.956E-04 V/m
 * c) 4.352E-04 V/m
 * d) 4.787E-04 V/m
 * e) 5.266E-04 V/m

4) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.65E-04 s
 * b) 2.00E-04 s
 * c) 2.43E-04 s
 * d) 2.94E-04 s
 * e) 3.56E-04 s

5) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 7.396E-08 N
 * b) 8.136E-08 N
 * c) 8.950E-08 N
 * d) 9.845E-08 N
 * e) 1.083E-07 N

6) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.944E-05 T
 * b) 2.138E-05 T
 * c) 2.352E-05 T
 * d) 2.587E-05 T
 * e) 2.846E-05 T

7) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 24 &mu;C.  What is the electric field between the plates?


 * a) 4.24E+04 N/C (or V/m)
 * b) 5.13E+04 N/C (or V/m)
 * c) 6.22E+04 N/C (or V/m)
 * d) 7.53E+04 N/C (or V/m)
 * e) 9.13E+04 N/C (or V/m)

8) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if &epsilon; = 5.95 V, R = 7.26 &Omega;, and L = 1.29 H?


 * a) -3.114E-01 s
 * b) -3.425E-01 s
 * c) -3.767E-01 s
 * d) -4.144E-01 s
 * e) -4.559E-01 s

9) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.157 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?


 * a) 8.608E-01 MeV
 * b) 9.468E-01 MeV
 * c) 1.042E+00 MeV
 * d) 1.146E+00 MeV
 * e) 1.260E+00 MeV

10) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.25 V. The resistance, inductance, and capacitance are R =7 &Omega;, L= 5.00E-03H, and C=7.70E-04 F, respectively. What is the amplitude of the current?


 * a) 2.439E-02 A
 * b) 2.683E-02 A
 * c) 2.952E-02 A
 * d) 3.247E-02 A
 * e) 3.571E-02 A

11) A parallel plate capacitor with a capicatnce C=6.80E-06 F whose plates have an area A=6.60E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 62 &Omega; resistor and a battery of voltage V0=36 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * a) 8.288E-02 A
 * b) 9.117E-02 A
 * c) 1.003E-01 A
 * d) 1.103E-01 A
 * e) 1.213E-01 A

T9 C0
1) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 3.43 mT and 4.670E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 1.362E+06 m/s
 * b) 1.498E+06 m/s
 * c) 1.647E+06 m/s
 * d) 1.812E+06 m/s
 * e) 1.993E+06 m/s

2) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23&deg; away from the wire?


 * a) 5.205E-01 N/m
 * b) 5.725E-01 N/m
 * c) 6.297E-01 N/m
 * d) 6.927E-01 N/m
 * e) 7.620E-01 N/m

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * e) $$\chi \text{ (chi) }=$$ 1.907E+03

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.549 m and $$B_{max}=\,$$ 0.599 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.29 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 5.581E+05 A
 * b) 6.139E+05 A
 * c) 6.752E+05 A
 * d) 7.428E+05 A
 * e) 8.170E+05 A

5) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1 A and $$\alpha=$$30 s&minus;1.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?


 * a) 6.618E-05 V/m
 * b) 7.280E-05 V/m
 * c) 8.008E-05 V/m
 * d) 8.809E-05 V/m
 * e) 9.689E-05 V/m

6) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.230E-04 s
 * b) 6.853E-04 s
 * c) 7.538E-04 s
 * d) 8.292E-04 s
 * e) 9.121E-04 s

7) A step-down transformer steps 19 kV down to 220 V. The high-voltage input is provided by a 230 &Omega; power line that carries 5 A of currentWhat is the output current (at the 220 V side ?)


 * a) 3.244E+02 A
 * b) 3.569E+02 A
 * c) 3.926E+02 A
 * d) 4.318E+02 A
 * e) 4.750E+02 A

8) A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.10E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 18 &Omega; resistor and a battery of voltage V0=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?


 * a) 6.259E-02 A
 * b) 6.885E-02 A
 * c) 7.573E-02 A
 * d) 8.331E-02 A
 * e) 9.164E-02 A

9) A parallel plate capacitor with a capicatnce C=7.40E-06 F whose plates have an area A=5.30E+03 m2 and separation d=6.30E-03 m is connected via a swith to a 5 &Omega; resistor and a battery of voltage V0=58 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.10E-04?


 * a) 4.548E+01 V
 * b) 5.003E+01 V
 * c) 5.503E+01 V
 * d) 6.054E+01 V
 * e) 6.659E+01 V

10) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is the decay time?


 * a) 2.57E-04 s
 * b) 3.11E-04 s
 * c) 3.77E-04 s
 * d) 4.57E-04 s
 * e) 5.53E-04 s

11) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.95E-09 Tesla
 * b) 4.97E-09 Tesla
 * c) 6.26E-09 Tesla
 * d) 7.88E-09 Tesla
 * e) 9.92E-09 Tesla

T9 C1
1) A circlular capactitor of radius 3.2 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 2.49E-04 s
 * b) 3.02E-04 s
 * c) 3.66E-04 s
 * d) 4.43E-04 s
 * e) 5.37E-04 s

2) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * a) 7.315E-02 A
 * b) 8.047E-02 A
 * c) 8.851E-02 A
 * d) 9.737E-02 A
 * e) 1.071E-01 A

3) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * a) 7.693E+01 V
 * b) 8.463E+01 V
 * c) 9.309E+01 V
 * d) 1.024E+02 V
 * e) 1.126E+02 V

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 22 turns per centimeter and the current applied to the solenoid is 568 mA, the net magnetic field is measured to be 1.29 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 8.205E+02
 * b) $$\chi \text{ (chi) }=$$ 9.026E+02
 * c) $$\chi \text{ (chi) }=$$ 9.928E+02
 * d) $$\chi \text{ (chi) }=$$ 1.092E+03
 * e) $$\chi \text{ (chi) }=$$ 1.201E+03

5) A step-down transformer steps 18 kV down to 170 V. The high-voltage input is provided by a 240 &Omega; power line that carries 5 A of currentWhat is the output current (at the 170 V side ?)


 * a) 5.294E+02 A
 * b) 5.824E+02 A
 * c) 6.406E+02 A
 * d) 7.046E+02 A
 * e) 7.751E+02 A

6) A long solenoid has a radius of 0.857 m and 58 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 0.144 m from the axis at time t=0.0898 s ?


 * a) 1.256E-05 V/m
 * b) 1.382E-05 V/m
 * c) 1.520E-05 V/m
 * d) 1.672E-05 V/m
 * e) 1.839E-05 V/m

7) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 2.82E-09 Tesla
 * b) 3.54E-09 Tesla
 * c) 4.46E-09 Tesla
 * d) 5.62E-09 Tesla
 * e) 7.07E-09 Tesla

8) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * a) 1.131E+00 N/m
 * b) 1.244E+00 N/m
 * c) 1.368E+00 N/m
 * d) 1.505E+00 N/m
 * e) 1.655E+00 N/m

9) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.571 m and $$B_{max}=\,$$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.321 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.226E+05 A
 * b) 3.549E+05 A
 * c) 3.904E+05 A
 * d) 4.294E+05 A
 * e) 4.724E+05 A

10) In an LC circuit, the self-inductance is 0.0735 H and the capacitance is 2.300E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.220E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 4.411E-04 s
 * b) 4.852E-04 s
 * c) 5.338E-04 s
 * d) 5.871E-04 s
 * e) 6.458E-04 s

11) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 5.49 mT and 5.570E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 9.223E+05 m/s
 * b) 1.015E+06 m/s
 * c) 1.116E+06 m/s
 * d) 1.228E+06 m/s
 * e) 1.350E+06 m/s

T9 C2
1) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 5.04 mT and 7.820E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 1.060E+06 m/s
 * b) 1.166E+06 m/s
 * c) 1.282E+06 m/s
 * d) 1.411E+06 m/s
 * e) 1.552E+06 m/s

2) A step-down transformer steps 9 kV down to 210 V. The high-voltage input is provided by a 170 &Omega; power line that carries 5 A of currentWhat is the output current (at the 210 V side ?)


 * a) 1.948E+02 A
 * b) 2.143E+02 A
 * c) 2.357E+02 A
 * d) 2.593E+02 A
 * e) 2.852E+02 A

3) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5 A and $$\alpha=$$29 s&minus;1.What is the induced electric fied at a distance 0.209 m from the axis at time t=0.0604 s ?


 * a) 6.277E-05 V/m
 * b) 6.904E-05 V/m
 * c) 7.595E-05 V/m
 * d) 8.354E-05 V/m
 * e) 9.190E-05 V/m

4) A long rigid wire carries a 3 A current. What is the magnetic force per unit length on the wire if a 0.534 T magnetic field is directed 18&deg; away from the wire?


 * a) 4.950E-01 N/m
 * b) 5.445E-01 N/m
 * c) 5.990E-01 N/m
 * d) 6.589E-01 N/m
 * e) 7.248E-01 N/m

5) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.230E-04 s
 * b) 6.853E-04 s
 * c) 7.538E-04 s
 * d) 8.292E-04 s
 * e) 9.121E-04 s

6) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.248 m and $$B_{max}=\,$$ 0.459 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.152 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 2.228E+05 A
 * b) 2.451E+05 A
 * c) 2.696E+05 A
 * d) 2.966E+05 A
 * e) 3.262E+05 A

7) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * a) 5.017E+01 V
 * b) 5.519E+01 V
 * c) 6.071E+01 V
 * d) 6.678E+01 V
 * e) 7.345E+01 V

8) A circlular capactitor of radius 3.6 m has a gap of 19 mm, and a charge of 98 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 1.90E-08 Tesla
 * b) 2.40E-08 Tesla
 * c) 3.02E-08 Tesla
 * d) 3.80E-08 Tesla
 * e) 4.78E-08 Tesla

9) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * a) 6.624E-02 A
 * b) 7.287E-02 A
 * c) 8.016E-02 A
 * d) 8.817E-02 A
 * e) 9.699E-02 A

10) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.188E+03
 * b) $$\chi \text{ (chi) }=$$ 1.307E+03
 * c) $$\chi \text{ (chi) }=$$ 1.438E+03
 * d) $$\chi \text{ (chi) }=$$ 1.582E+03
 * e) $$\chi \text{ (chi) }=$$ 1.740E+03

11) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is the decay time?


 * a) 2.57E-04 s
 * b) 3.11E-04 s
 * c) 3.77E-04 s
 * d) 4.57E-04 s
 * e) 5.53E-04 s

T9 D0
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * a) 3.575E+00 N/m
 * b) 3.932E+00 N/m
 * c) 4.325E+00 N/m
 * d) 4.758E+00 N/m
 * e) 5.234E+00 N/m

2) A 76 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.367 T. What current is required to maintain this balance?


 * a) 3.432E-01 A
 * b) 3.775E-01 A
 * c) 4.152E-01 A
 * d) 4.568E-01 A
 * e) 5.024E-01 A

3) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.76 cm to z=+1.99 cm


 * a) 2.762E-04 T-m
 * b) 3.038E-04 T-m
 * c) 3.342E-04 T-m
 * d) 3.676E-04 T-m
 * e) 4.043E-04 T-m

4) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 7.035E-05 T
 * b) By= 7.739E-05 T
 * c) By= 8.512E-05 T
 * d) By= 9.364E-05 T
 * e) By= 1.030E-04 T

5) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * a) 6.040E-05 V/m
 * b) 6.644E-05 V/m
 * c) 7.309E-05 V/m
 * d) 8.039E-05 V/m
 * e) 8.843E-05 V/m

6) An induced emf of 1.92V is measured across a coil of 74 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.38A in 0.69s. What is the self-inductance of the coil?


 * a) 1.560E-01 H
 * b) 1.716E-01 H
 * c) 1.888E-01 H
 * d) 2.076E-01 H
 * e) 2.284E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 480 Hz and an amplitude of 0.63 V;. If R =7 &Omega;, L= 3.80E-03H, and C=5.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 9.972E-01 &rad;
 * b) 1.097E+00 &rad;
 * c) 1.207E+00 &rad;
 * d) 1.327E+00 &rad;
 * e) 1.460E+00 &rad;

8) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 8.969E-08 N
 * b) 9.866E-08 N
 * c) 1.085E-07 N
 * d) 1.194E-07 N
 * e) 1.313E-07 N

9) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * a) 5.017E+01 V
 * b) 5.519E+01 V
 * c) 6.071E+01 V
 * d) 6.678E+01 V
 * e) 7.345E+01 V

10) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.30E-09 Tesla
 * b) 4.15E-09 Tesla
 * c) 5.23E-09 Tesla
 * d) 6.58E-09 Tesla
 * e) 8.29E-09 Tesla

11) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 62 &mu;C.  What is the electric field between the plates?


 * a) 9.50E+04 N/C (or V/m)
 * b) 1.15E+05 N/C (or V/m)
 * c) 1.39E+05 N/C (or V/m)
 * d) 1.69E+05 N/C (or V/m)
 * e) 2.05E+05 N/C (or V/m)

T9 D1
1) An induced emf of 1.7V is measured across a coil of 81 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.07A in 0.174s. What is the self-inductance of the coil?


 * a) 3.458E-02 H
 * b) 3.804E-02 H
 * c) 4.184E-02 H
 * d) 4.602E-02 H
 * e) 5.062E-02 H

2) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 &Omega;, L= 7.70E-03H, and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 1.329E+00 &rad;
 * b) 1.462E+00 &rad;
 * c) 1.608E+00 &rad;
 * d) 1.769E+00 &rad;
 * e) 1.946E+00 &rad;

3) A circlular capactitor of radius 4.9 m has a gap of 11 mm, and a charge of 85 &mu;C.  What is the electric field between the plates?


 * a) 1.27E+05 N/C (or V/m)
 * b) 1.54E+05 N/C (or V/m)
 * c) 1.87E+05 N/C (or V/m)
 * d) 2.26E+05 N/C (or V/m)
 * e) 2.74E+05 N/C (or V/m)

4) Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 5.930E-05 T
 * b) By= 6.523E-05 T
 * c) By= 7.175E-05 T
 * d) By= 7.892E-05 T
 * e) By= 8.682E-05 T

5) A long solenoid has a radius of 0.757 m and 90 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$30 s&minus;1.What is the induced electric fied at a distance 2.08 m from the axis at time t=0.0442 s ?


 * a) 6.527E-04 V/m
 * b) 7.180E-04 V/m
 * c) 7.898E-04 V/m
 * d) 8.688E-04 V/m
 * e) 9.556E-04 V/m

6) A 17 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.768 T. What current is required to maintain this balance?


 * a) 4.963E-01 A
 * b) 5.459E-01 A
 * c) 6.005E-01 A
 * d) 6.605E-01 A
 * e) 7.266E-01 A

7) A circlular capactitor of radius 4.6 m has a gap of 18 mm, and a charge of 44 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 6.64E-09 Tesla
 * b) 8.36E-09 Tesla
 * c) 1.05E-08 Tesla
 * d) 1.32E-08 Tesla
 * e) 1.67E-08 Tesla

8) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * a) 3.575E+00 N/m
 * b) 3.932E+00 N/m
 * c) 4.325E+00 N/m
 * d) 4.758E+00 N/m
 * e) 5.234E+00 N/m

9) A parallel plate capacitor with a capicatnce C=8.30E-06 F whose plates have an area A=7.00E+03 m2 and separation d=7.50E-03 m is connected via a swith to a 51 &Omega; resistor and a battery of voltage V0=81 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.20E-03?


 * a) 5.728E+01 V
 * b) 6.301E+01 V
 * c) 6.931E+01 V
 * d) 7.624E+01 V
 * e) 8.387E+01 V

10) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.11 cm to z=+2.76 cm


 * a) 1.068E-04 T-m
 * b) 1.175E-04 T-m
 * c) 1.292E-04 T-m
 * d) 1.421E-04 T-m
 * e) 1.563E-04 T-m

11) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.673E-07 N
 * b) 2.940E-07 N
 * c) 3.234E-07 N
 * d) 3.558E-07 N
 * e) 3.913E-07 N

T9 D2
1) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.32E-09 Tesla
 * b) 1.05E-08 Tesla
 * c) 1.32E-08 Tesla
 * d) 1.66E-08 Tesla
 * e) 2.09E-08 Tesla

2) A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?


 * a) 5.131E+01 V
 * b) 5.644E+01 V
 * c) 6.209E+01 V
 * d) 6.830E+01 V
 * e) 7.513E+01 V

3) An induced emf of 6.29V is measured across a coil of 85 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.15A in 0.913s. What is the self-inductance of the coil?


 * a) 2.428E+00 H
 * b) 2.671E+00 H
 * c) 2.938E+00 H
 * d) 3.232E+00 H
 * e) 3.555E+00 H

4) A long solenoid has a radius of 0.583 m and 38 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$24 s&minus;1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?


 * a) 1.655E-04 V/m
 * b) 1.821E-04 V/m
 * c) 2.003E-04 V/m
 * d) 2.203E-04 V/m
 * e) 2.424E-04 V/m

5) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 &Omega;, L= 9.50E-03H, and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.646E-01 &rad;
 * b) 9.511E-01 &rad;
 * c) 1.046E+00 &rad;
 * d) 1.151E+00 &rad;
 * e) 1.266E+00 &rad;

6) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * a) 3.575E+00 N/m
 * b) 3.932E+00 N/m
 * c) 4.325E+00 N/m
 * d) 4.758E+00 N/m
 * e) 5.234E+00 N/m

7) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.275E-07 N
 * b) 5.803E-07 N
 * c) 6.383E-07 N
 * d) 7.021E-07 N
 * e) 7.723E-07 N

8) A 96 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.325 T. What current is required to maintain this balance?


 * a) 2.596E-01 A
 * b) 2.855E-01 A
 * c) 3.141E-01 A
 * d) 3.455E-01 A
 * e) 3.801E-01 A

9) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * a) 2.44E+05 N/C (or V/m)
 * b) 2.95E+05 N/C (or V/m)
 * c) 3.58E+05 N/C (or V/m)
 * d) 4.34E+05 N/C (or V/m)
 * e) 5.25E+05 N/C (or V/m)

10) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 7.035E-05 T
 * b) By= 7.739E-05 T
 * c) By= 8.512E-05 T
 * d) By= 9.364E-05 T
 * e) By= 1.030E-04 T

11) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.41 cm to z=+2.56 cm


 * a) 7.257E-05 T-m
 * b) 7.983E-05 T-m
 * c) 8.781E-05 T-m
 * d) 9.660E-05 T-m
 * e) 1.063E-04 T-m

T9 E0
1) The silver ribbon shown are a=4.81 cm, b=3.96 cm, and c= 1.3 cm. The current carries a current of 274 A and it lies in a uniform magnetic field of 3.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 7.202E-06 V
 * b) 7.922E-06 V
 * c) 8.714E-06 V
 * d) 9.586E-06 V
 * e) 1.054E-05 V

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0887 T . It emerges after being deflected by 69&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 2.561E-07 s
 * b) 2.817E-07 s
 * c) 3.099E-07 s
 * d) 3.409E-07 s
 * e) 3.750E-07 s

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.82 kA, I2=0.964 kA, and I3=2.21 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.069E-03 T-m
 * b) 1.176E-03 T-m
 * c) 1.294E-03 T-m
 * d) 1.423E-03 T-m
 * e) 1.566E-03 T-m

4) Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.171E-05 T
 * b) Bx= 6.788E-05 T
 * c) Bx= 7.467E-05 T
 * d) Bx= 8.213E-05 T
 * e) Bx= 9.035E-05 T

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * a) 1.605E-04 V/m
 * b) 1.766E-04 V/m
 * c) 1.942E-04 V/m
 * d) 2.136E-04 V/m
 * e) 2.350E-04 V/m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if &epsilon; = 6.08 V, R = 1.88 &Omega;, and L = 4.67 H?


 * a) -5.192E+00 s
 * b) -5.711E+00 s
 * c) -6.282E+00 s
 * d) -6.910E+00 s
 * e) -7.601E+00 s

7) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a  99 mF capacitor?


 * a) 1.644E+00 A
 * b) 1.808E+00 A
 * c) 1.989E+00 A
 * d) 2.188E+00 A
 * e) 2.407E+00 A

8) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * a) 6.624E-02 A
 * b) 7.287E-02 A
 * c) 8.016E-02 A
 * d) 8.817E-02 A
 * e) 9.699E-02 A

9) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.673E-07 N
 * b) 2.940E-07 N
 * c) 3.234E-07 N
 * d) 3.558E-07 N
 * e) 3.913E-07 N

10) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.28E-11 Vs2m-1
 * b) 8.82E-11 Vs2m-1
 * c) 1.07E-10 Vs2m-1
 * d) 1.29E-10 Vs2m-1
 * e) 1.57E-10 Vs2m-1

11) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 3.07E-04 s
 * b) 3.71E-04 s
 * c) 4.50E-04 s
 * d) 5.45E-04 s
 * e) 6.61E-04 s

T9 E1
1) A circlular capactitor of radius 4.4 m has a gap of 17 mm, and a charge of 65 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.56E-11 Vs2m-1
 * b) 6.74E-11 Vs2m-1
 * c) 8.17E-11 Vs2m-1
 * d) 9.90E-11 Vs2m-1
 * e) 1.20E-10 Vs2m-1

2) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.63% of its maximum value if &epsilon; = 8.7 V, R = 8.35 &Omega;, and L = 1.44 H?


 * a) -3.137E-01 s
 * b) -3.451E-01 s
 * c) -3.796E-01 s
 * d) -4.176E-01 s
 * e) -4.593E-01 s

3) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.075 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.002E-08 N
 * b) 5.502E-08 N
 * c) 6.052E-08 N
 * d) 6.657E-08 N
 * e) 7.323E-08 N

4) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 1.16E-04 s
 * b) 1.41E-04 s
 * c) 1.71E-04 s
 * d) 2.07E-04 s
 * e) 2.50E-04 s

5) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0582 T . It emerges after being deflected by 77&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 4.791E-07 s
 * b) 5.271E-07 s
 * c) 5.798E-07 s
 * d) 6.377E-07 s
 * e) 7.015E-07 s

6) Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 3.394E-05 T
 * b) Bx= 3.733E-05 T
 * c) Bx= 4.106E-05 T
 * d) Bx= 4.517E-05 T
 * e) Bx= 4.969E-05 T

7) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?


 * a) 6.182E-04 V/m
 * b) 6.801E-04 V/m
 * c) 7.481E-04 V/m
 * d) 8.229E-04 V/m
 * e) 9.052E-04 V/m

8) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * a) 7.315E-02 A
 * b) 8.047E-02 A
 * c) 8.851E-02 A
 * d) 9.737E-02 A
 * e) 1.071E-01 A

9) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a  59 mF capacitor?


 * a) 5.042E+00 A
 * b) 5.546E+00 A
 * c) 6.100E+00 A
 * d) 6.710E+00 A
 * e) 7.381E+00 A

10) The silver ribbon shown are a=3.68 cm, b=2.66 cm, and c= 0.505 cm. The current carries a current of 113 A and it lies in a uniform magnetic field of 3.12 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 6.104E-06 V
 * b) 6.714E-06 V
 * c) 7.385E-06 V
 * d) 8.124E-06 V
 * e) 8.936E-06 V

11) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.55 kA, I2=1.02 kA, and I3=1.81 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 8.204E-04 T-m
 * b) 9.025E-04 T-m
 * c) 9.927E-04 T-m
 * d) 1.092E-03 T-m
 * e) 1.201E-03 T-m

T9 E2
1) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a  6 mF capacitor?


 * a) 5.253E-02 A
 * b) 5.778E-02 A
 * c) 6.356E-02 A
 * d) 6.991E-02 A
 * e) 7.691E-02 A

2) The silver ribbon shown are a=4.14 cm, b=3.69 cm, and c= 1.13 cm. The current carries a current of 291 A and it lies in a uniform magnetic field of 3.32 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 6.795E-06 V
 * b) 7.475E-06 V
 * c) 8.222E-06 V
 * d) 9.045E-06 V
 * e) 9.949E-06 V

3) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=1.00E+04 m2 and separation d=9.00E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * a) 6.394E-02 A
 * b) 7.033E-02 A
 * c) 7.736E-02 A
 * d) 8.510E-02 A
 * e) 9.361E-02 A

4) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?


 * a) 6.182E-04 V/m
 * b) 6.801E-04 V/m
 * c) 7.481E-04 V/m
 * d) 8.229E-04 V/m
 * e) 9.052E-04 V/m

5) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.51 kA, I2=1.32 kA, and I3=2.73 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.331E-03 T-m
 * b) 1.464E-03 T-m
 * c) 1.611E-03 T-m
 * d) 1.772E-03 T-m
 * e) 1.949E-03 T-m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.59% of its maximum value if &epsilon; = 1.14 V, R = 6.17 &Omega;, and L = 5.45 H?


 * a) -1.614E+00 s
 * b) -1.775E+00 s
 * c) -1.952E+00 s
 * d) -2.148E+00 s
 * e) -2.362E+00 s

7) What is the radiation force on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.630E-08 N
 * b) 1.793E-08 N
 * c) 1.972E-08 N
 * d) 2.169E-08 N
 * e) 2.386E-08 N

8) Three wires sit at the corners of a square of length 0.75 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.1 A, 1.11 A, 2.26 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.507E-05 T
 * b) Bx= 8.257E-05 T
 * c) Bx= 9.083E-05 T
 * d) Bx= 9.991E-05 T
 * e) Bx= 1.099E-04 T

9) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 3.62E-04 s
 * b) 4.38E-04 s
 * c) 5.31E-04 s
 * d) 6.43E-04 s
 * e) 7.79E-04 s

10) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0883 T . It emerges after being deflected by 74&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 2.280E-07 s
 * b) 2.508E-07 s
 * c) 2.759E-07 s
 * d) 3.035E-07 s
 * e) 3.339E-07 s

11) A circlular capactitor of radius 4.1 m has a gap of 8 mm, and a charge of 24 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 2.05E-11 Vs2m-1
 * b) 2.49E-11 Vs2m-1
 * c) 3.02E-11 Vs2m-1
 * d) 3.65E-11 Vs2m-1
 * e) 4.43E-11 Vs2m-1

T9 F0
1) A charged particle in a magnetic field of 4.910E-04 T is moving perpendicular to the magnetic field with a speed of 3.000E+05 m/s. What is the period of orbit if orbital radius is 0.507 m?


 * a) 1.062E-05 s
 * b) 1.168E-05 s
 * c) 1.285E-05 s
 * d) 1.413E-05 s
 * e) 1.555E-05 s

2) A 24 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.706 T. What current is required to maintain this balance?


 * a) 5.258E-01 A
 * b) 5.784E-01 A
 * c) 6.362E-01 A
 * d) 6.998E-01 A
 * e) 7.698E-01 A

3) A wire carries a current of 332 A in a circular arc with radius 2.47 cm swept through 44 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * a) 3.389E+00 Tesla
 * b) 3.727E+00 Tesla
 * c) 4.100E+00 Tesla
 * d) 4.510E+00 Tesla
 * e) 4.961E+00 Tesla

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.45 kA, I2=2.68 kA, and I3=5.5 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 3.544E-03 T-m
 * b) 3.898E-03 T-m
 * c) 4.288E-03 T-m
 * d) 4.717E-03 T-m
 * e) 5.188E-03 T-m

5) The current through the windings of a solenoid with n= 1.850E+03 turns per meter is changing at a rate dI/dt=17 A/s. The solenoid is 98 cm long and has a cross-sectional diameter of 3.38 cm.  A small coil consisting of N=23turns wraped in a circle of diameter 1.72 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 1.587E-04 V
 * b) 1.745E-04 V
 * c) 1.920E-04 V
 * d) 2.112E-04 V
 * e) 2.323E-04 V

6) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if &epsilon; = 7.04 V, R = 7.69 &Omega;, and L = 5.78 H?


 * a) 4.249E-01 V
 * b) 5.099E-01 V
 * c) 6.118E-01 V
 * d) 7.342E-01 V
 * e) 8.810E-01 V

7) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 6.60E-03H, and C=5.30E-06 F, what is the rms power transferred to the resistor?


 * a) 2.007E-03 Watts
 * b) 2.208E-03 Watts
 * c) 2.429E-03 Watts
 * d) 2.672E-03 Watts
 * e) 2.939E-03 Watts

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.003E+02 km
 * b) 1.103E+02 km
 * c) 1.213E+02 km
 * d) 1.335E+02 km
 * e) 1.468E+02 km

9) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m2 and separation d=3.50E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?


 * a) 3.751E+03 V/m
 * b) 4.126E+03 V/m
 * c) 4.539E+03 V/m
 * d) 4.993E+03 V/m
 * e) 5.492E+03 V/m

10) A circlular capactitor of radius 3.3 m has a gap of 12 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 9.94E-05 s
 * b) 1.20E-04 s
 * c) 1.46E-04 s
 * d) 1.77E-04 s
 * e) 2.14E-04 s

11) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 8.75E-12 Vs2m-1
 * b) 1.06E-11 Vs2m-1
 * c) 1.28E-11 Vs2m-1
 * d) 1.56E-11 Vs2m-1
 * e) 1.88E-11 Vs2m-1

T9 F1
1) A circlular capactitor of radius 4.5 m has a gap of 18 mm, and a charge of 92 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.88E-11 Vs2m-1
 * b) 9.54E-11 Vs2m-1
 * c) 1.16E-10 Vs2m-1
 * d) 1.40E-10 Vs2m-1
 * e) 1.70E-10 Vs2m-1

2) A charged particle in a magnetic field of 3.600E-04 T is moving perpendicular to the magnetic field with a speed of 5.960E+05 m/s. What is the period of orbit if orbital radius is 0.397 m?


 * a) 3.805E-06 s
 * b) 4.185E-06 s
 * c) 4.604E-06 s
 * d) 5.064E-06 s
 * e) 5.571E-06 s

3) The output of an ac generator connected to an RLC series combination has a frequency of 6.10E+04 Hz and an amplitude of 8 V. If R =5 &Omega;, L= 9.10E-03H, and C=8.80E-06 F, what is the rms power transferred to the resistor?


 * a) 4.320E-04 Watts
 * b) 4.752E-04 Watts
 * c) 5.227E-04 Watts
 * d) 5.750E-04 Watts
 * e) 6.325E-04 Watts

4) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?


 * a) 1.174E+00 A
 * b) 1.291E+00 A
 * c) 1.420E+00 A
 * d) 1.562E+00 A
 * e) 1.719E+00 A

5) A circlular capactitor of radius 3.6 m has a gap of 14 mm, and a charge of 98 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 1.40E-04 s
 * b) 1.70E-04 s
 * c) 2.06E-04 s
 * d) 2.50E-04 s
 * e) 3.02E-04 s

6) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.250E-03 T-m
 * b) 1.375E-03 T-m
 * c) 1.512E-03 T-m
 * d) 1.663E-03 T-m
 * e) 1.830E-03 T-m

7) A 57 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.020E+02 km
 * b) 1.122E+02 km
 * c) 1.235E+02 km
 * d) 1.358E+02 km
 * e) 1.494E+02 km

8) The current through the windings of a solenoid with n= 2.040E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 76 cm long and has a cross-sectional diameter of 3.23 cm.  A small coil consisting of N=25turns wraped in a circle of diameter 1.67 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 2.204E-04 V
 * b) 2.425E-04 V
 * c) 2.667E-04 V
 * d) 2.934E-04 V
 * e) 3.227E-04 V

9) A parallel plate capacitor with a capicatnce C=5.20E-06 F whose plates have an area A=2.90E+03 m2 and separation d=4.90E-03 m is connected via a swith to a 93 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.20E-03?


 * a) 6.896E+02 V/m
 * b) 7.585E+02 V/m
 * c) 8.344E+02 V/m
 * d) 9.178E+02 V/m
 * e) 1.010E+03 V/m

10) A wire carries a current of 106 A in a circular arc with radius 1.32 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * a) 1.589E+00 Tesla
 * b) 1.748E+00 Tesla
 * c) 1.923E+00 Tesla
 * d) 2.116E+00 Tesla
 * e) 2.327E+00 Tesla

11) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =0.741 s if &epsilon; = 7.36 V, R = 5.33 &Omega;, and L = 1.27 H?


 * a) 7.635E-01 V
 * b) 9.162E-01 V
 * c) 1.099E+00 V
 * d) 1.319E+00 V
 * e) 1.583E+00 V

T9 F2
1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.51 kA, I2=2.33 kA, and I3=5.35 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 3.795E-03 T-m
 * b) 4.175E-03 T-m
 * c) 4.592E-03 T-m
 * d) 5.051E-03 T-m
 * e) 5.556E-03 T-m

2) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * a) 1.753E+02 km
 * b) 1.928E+02 km
 * c) 2.121E+02 km
 * d) 2.333E+02 km
 * e) 2.567E+02 km

3) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 7.00E-03H, and C=6.60E-06 F, what is the rms power transferred to the resistor?


 * a) 1.146E-03 Watts
 * b) 1.260E-03 Watts
 * c) 1.386E-03 Watts
 * d) 1.525E-03 Watts
 * e) 1.677E-03 Watts

4) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm.  A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 1.407E-04 V
 * b) 1.548E-04 V
 * c) 1.703E-04 V
 * d) 1.873E-04 V
 * e) 2.061E-04 V

5) A 25 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.702 T. What current is required to maintain this balance?


 * a) 5.076E-01 A
 * b) 5.584E-01 A
 * c) 6.142E-01 A
 * d) 6.757E-01 A
 * e) 7.432E-01 A

6) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =20.1 s if &epsilon; = 5.77 V, R = 1.38 &Omega;, and L = 5.45 H?


 * a) 3.463E+00 V
 * b) 4.156E+00 V
 * c) 4.987E+00 V
 * d) 5.984E+00 V
 * e) 7.181E+00 V

7) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 3.62E-04 s
 * b) 4.38E-04 s
 * c) 5.31E-04 s
 * d) 6.43E-04 s
 * e) 7.79E-04 s

8) A wire carries a current of 303 A in a circular arc with radius 2.2 cm swept through 72 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * a) 3.881E+00 Tesla
 * b) 4.269E+00 Tesla
 * c) 4.696E+00 Tesla
 * d) 5.165E+00 Tesla
 * e) 5.682E+00 Tesla

9) A charged particle in a magnetic field of 3.600E-04 T is moving perpendicular to the magnetic field with a speed of 5.960E+05 m/s. What is the period of orbit if orbital radius is 0.397 m?


 * a) 3.805E-06 s
 * b) 4.185E-06 s
 * c) 4.604E-06 s
 * d) 5.064E-06 s
 * e) 5.571E-06 s

10) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 8.75E-12 Vs2m-1
 * b) 1.06E-11 Vs2m-1
 * c) 1.28E-11 Vs2m-1
 * d) 1.56E-11 Vs2m-1
 * e) 1.88E-11 Vs2m-1

11) A parallel plate capacitor with a capicatnce C=4.50E-06 F whose plates have an area A=3.30E+03 m2 and separation d=6.40E-03 m is connected via a swith to a 83 &Omega; resistor and a battery of voltage V0=56 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.40E-03?


 * a) 7.767E+03 V/m
 * b) 8.544E+03 V/m
 * c) 9.398E+03 V/m
 * d) 1.034E+04 V/m
 * e) 1.137E+04 V/m

T9 G0
1) A charged particle in a magnetic field of 6.400E-04 T is moving perpendicular to the magnetic field with a speed of 1.360E+05 m/s. What is the period of orbit if orbital radius is 0.751 m?


 * a) 3.154E-05 s
 * b) 3.470E-05 s
 * c) 3.817E-05 s
 * d) 4.198E-05 s
 * e) 4.618E-05 s

2) A circular current loop of radius 1.94 cm carries a current of 1.83 mA. What is the magnitude of the torque if the dipole is oriented at 43 &deg; to a uniform magnetic fied of 0.156 T?


 * a) 1.903E-07 N m
 * b) 2.093E-07 N m
 * c) 2.302E-07 N m
 * d) 2.532E-07 N m
 * e) 2.785E-07 N m

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.250E-03 T-m
 * b) 1.375E-03 T-m
 * c) 1.512E-03 T-m
 * d) 1.663E-03 T-m
 * e) 1.830E-03 T-m

4) Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 5.930E-05 T
 * b) By= 6.523E-05 T
 * c) By= 7.175E-05 T
 * d) By= 7.892E-05 T
 * e) By= 8.682E-05 T

5) A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 7.479E+00 cm3/s
 * b) 8.227E+00 cm3/s
 * c) 9.049E+00 cm3/s
 * d) 9.954E+00 cm3/s
 * e) 1.095E+01 cm3/s

6) In an LC circuit, the self-inductance is 0.0126 H and the capacitance is 3.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.420E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 2.204E-04 s
 * b) 2.425E-04 s
 * c) 2.667E-04 s
 * d) 2.934E-04 s
 * e) 3.227E-04 s

7) An ac generator produces an emf of amplitude 73 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a  70 mF inductor?


 * a) 1.134E+00 A
 * b) 1.247E+00 A
 * c) 1.372E+00 A
 * d) 1.509E+00 A
 * e) 1.660E+00 A

8) A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?


 * a) 5.131E+01 V
 * b) 5.644E+01 V
 * c) 6.209E+01 V
 * d) 6.830E+01 V
 * e) 7.513E+01 V

9) What is the radiation pressure on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.057 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 3.075E-07 N/m2
 * b) 3.382E-07 N/m2
 * c) 3.720E-07 N/m2
 * d) 4.092E-07 N/m2
 * e) 4.502E-07 N/m2

10) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.32E-09 Tesla
 * b) 1.05E-08 Tesla
 * c) 1.32E-08 Tesla
 * d) 1.66E-08 Tesla
 * e) 2.09E-08 Tesla

11) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 45 &mu;C.  What is the electric field between the plates?


 * a) 6.31E+04 N/C (or V/m)
 * b) 7.65E+04 N/C (or V/m)
 * c) 9.26E+04 N/C (or V/m)
 * d) 1.12E+05 N/C (or V/m)
 * e) 1.36E+05 N/C (or V/m)

T9 G1
1) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * a) 2.44E+05 N/C (or V/m)
 * b) 2.95E+05 N/C (or V/m)
 * c) 3.58E+05 N/C (or V/m)
 * d) 4.34E+05 N/C (or V/m)
 * e) 5.25E+05 N/C (or V/m)

2) Three wires sit at the corners of a square of length 0.703 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.49 A, 1.32 A, 1.75 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 8.962E-05 T
 * b) By= 9.858E-05 T
 * c) By= 1.084E-04 T
 * d) By= 1.193E-04 T
 * e) By= 1.312E-04 T

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.250E-03 T-m
 * b) 1.375E-03 T-m
 * c) 1.512E-03 T-m
 * d) 1.663E-03 T-m
 * e) 1.830E-03 T-m

4) A circular current loop of radius 3.0 cm carries a current of 1.58 mA. What is the magnitude of the torque if the dipole is oriented at 63 &deg; to a uniform magnetic fied of 0.408 T?


 * a) 1.476E-06 N m
 * b) 1.624E-06 N m
 * c) 1.786E-06 N m
 * d) 1.965E-06 N m
 * e) 2.162E-06 N m

5) A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 7.280E+01 cm3/s
 * b) 8.008E+01 cm3/s
 * c) 8.808E+01 cm3/s
 * d) 9.689E+01 cm3/s
 * e) 1.066E+02 cm3/s

6) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.253E-05 N/m2
 * b) 1.378E-05 N/m2
 * c) 1.516E-05 N/m2
 * d) 1.667E-05 N/m2
 * e) 1.834E-05 N/m2

7) In an LC circuit, the self-inductance is 0.0273 H and the capacitance is 6.440E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.620E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 5.443E-04 s
 * b) 5.988E-04 s
 * c) 6.586E-04 s
 * d) 7.245E-04 s
 * e) 7.969E-04 s

8) A charged particle in a magnetic field of 4.970E-04 T is moving perpendicular to the magnetic field with a speed of 2.950E+05 m/s. What is the period of orbit if orbital radius is 0.344 m?


 * a) 7.327E-06 s
 * b) 8.060E-06 s
 * c) 8.865E-06 s
 * d) 9.752E-06 s
 * e) 1.073E-05 s

9) A parallel plate capacitor with a capicatnce C=1.80E-06 F whose plates have an area A=670.0 m2 and separation d=3.30E-03 m is connected via a swith to a 40 &Omega; resistor and a battery of voltage V0=97 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.40E-04?


 * a) 7.731E+01 V
 * b) 8.504E+01 V
 * c) 9.354E+01 V
 * d) 1.029E+02 V
 * e) 1.132E+02 V

10) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.95E-09 Tesla
 * b) 4.97E-09 Tesla
 * c) 6.26E-09 Tesla
 * d) 7.88E-09 Tesla
 * e) 9.92E-09 Tesla

11) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a  97 mF inductor?


 * a) 4.972E-01 A
 * b) 5.469E-01 A
 * c) 6.016E-01 A
 * d) 6.618E-01 A
 * e) 7.280E-01 A

T9 G2
1) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * a) 2.80E+04 N/C (or V/m)
 * b) 3.40E+04 N/C (or V/m)
 * c) 4.12E+04 N/C (or V/m)
 * d) 4.99E+04 N/C (or V/m)
 * e) 6.04E+04 N/C (or V/m)

2) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?


 * a) 1.141E-05 s
 * b) 1.255E-05 s
 * c) 1.381E-05 s
 * d) 1.519E-05 s
 * e) 1.671E-05 s

3) Three wires sit at the corners of a square of length 0.76 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.91 A, 1.34 A, 1.05 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 5.611E-05 T
 * b) By= 6.172E-05 T
 * c) By= 6.789E-05 T
 * d) By= 7.468E-05 T
 * e) By= 8.215E-05 T

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.66 kA, I2=1.25 kA, and I3=2.74 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.547E-03 T-m
 * b) 1.702E-03 T-m
 * c) 1.872E-03 T-m
 * d) 2.060E-03 T-m
 * e) 2.266E-03 T-m

5) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a  35 mF inductor?


 * a) 2.422E+00 A
 * b) 2.664E+00 A
 * c) 2.930E+00 A
 * d) 3.224E+00 A
 * e) 3.546E+00 A

6) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 88 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 1.86E-08 Tesla
 * b) 2.34E-08 Tesla
 * c) 2.95E-08 Tesla
 * d) 3.72E-08 Tesla
 * e) 4.68E-08 Tesla

7) What is the radiation pressure on an object that is 8.30E+11 m away from the sun and has cross-sectional area of 0.097 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.928E-07 N/m2
 * b) 3.221E-07 N/m2
 * c) 3.543E-07 N/m2
 * d) 3.898E-07 N/m2
 * e) 4.287E-07 N/m2

8) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.166E-04 s
 * b) 6.783E-04 s
 * c) 7.461E-04 s
 * d) 8.207E-04 s
 * e) 9.028E-04 s

9) A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 3.093E+01 cm3/s
 * b) 3.403E+01 cm3/s
 * c) 3.743E+01 cm3/s
 * d) 4.117E+01 cm3/s
 * e) 4.529E+01 cm3/s

10) A parallel plate capacitor with a capicatnce C=9.60E-06 F whose plates have an area A=5.40E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 29 &Omega; resistor and a battery of voltage V0=50 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.30E-04?


 * a) 3.923E+01 V
 * b) 4.315E+01 V
 * c) 4.746E+01 V
 * d) 5.221E+01 V
 * e) 5.743E+01 V

11) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 &deg; to a uniform magnetic fied of 0.402 T?


 * a) 1.022E-06 N m
 * b) 1.124E-06 N m
 * c) 1.236E-06 N m
 * d) 1.360E-06 N m
 * e) 1.496E-06 N m

T9 H0
1) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.83 T magnetic field is directed 22&deg; away from the wire?


 * a) 1.062E+00 N/m
 * b) 1.168E+00 N/m
 * c) 1.285E+00 N/m
 * d) 1.413E+00 N/m
 * e) 1.555E+00 N/m

2) A circular current loop of radius 1.17 cm carries a current of 3.68 mA. What is the magnitude of the torque if the dipole is oriented at 55 &deg; to a uniform magnetic fied of 0.179 T?


 * a) 1.585E-07 N m
 * b) 1.743E-07 N m
 * c) 1.918E-07 N m
 * d) 2.110E-07 N m
 * e) 2.321E-07 N m

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.04 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.115E-05 T
 * b) 1.226E-05 T
 * c) 1.349E-05 T
 * d) 1.484E-05 T
 * e) 1.632E-05 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.736 m and $$B_{max}=\,$$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.764E+05 A
 * b) 4.140E+05 A
 * c) 4.554E+05 A
 * d) 5.010E+05 A
 * e) 5.510E+05 A

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.75 T and $$\omega=$$9.800E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.22 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 4.198E+04 V
 * b) 4.618E+04 V
 * c) 5.080E+04 V
 * d) 5.588E+04 V
 * e) 6.147E+04 V

6) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.7mm$$, and $$n=2.76$$. What is the volume of the washer?


 * a) 1.038E+00 cm3
 * b) 1.142E+00 cm3
 * c) 1.256E+00 cm3
 * d) 1.381E+00 cm3
 * e) 1.520E+00 cm3

7) An ac generator produces an emf of amplitude 46 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a  63 mF inductor?


 * a) 4.961E-01 A
 * b) 5.457E-01 A
 * c) 6.002E-01 A
 * d) 6.603E-01 A
 * e) 7.263E-01 A

8) A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=3.20E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 27 &Omega; resistor and a battery of voltage V0=80 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.60E-04?


 * a) 9.524E-01 A
 * b) 1.048E+00 A
 * c) 1.152E+00 A
 * d) 1.268E+00 A
 * e) 1.394E+00 A

9) What is the radiation pressure on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.057 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 3.075E-07 N/m2
 * b) 3.382E-07 N/m2
 * c) 3.720E-07 N/m2
 * d) 4.092E-07 N/m2
 * e) 4.502E-07 N/m2

10) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * a) 2.44E+05 N/C (or V/m)
 * b) 2.95E+05 N/C (or V/m)
 * c) 3.58E+05 N/C (or V/m)
 * d) 4.34E+05 N/C (or V/m)
 * e) 5.25E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.3 m has a gap of 11 mm, and a charge of 66 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 6.85E-11 Vs2m-1
 * b) 8.29E-11 Vs2m-1
 * c) 1.00E-10 Vs2m-1
 * d) 1.22E-10 Vs2m-1
 * e) 1.47E-10 Vs2m-1

T9 H1
1) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.355 T magnetic field is directed 53&deg; away from the wire?


 * a) 8.520E-01 N/m
 * b) 9.372E-01 N/m
 * c) 1.031E+00 N/m
 * d) 1.134E+00 N/m
 * e) 1.247E+00 N/m

2) A circlular capactitor of radius 3.7 m has a gap of 10 mm, and a charge of 12 &mu;C.  What is the electric field between the plates?


 * a) 2.15E+04 N/C (or V/m)
 * b) 2.60E+04 N/C (or V/m)
 * c) 3.15E+04 N/C (or V/m)
 * d) 3.82E+04 N/C (or V/m)
 * e) 4.63E+04 N/C (or V/m)

3) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.39mm$$, and $$n=2.55$$. What is the volume of the washer?


 * a) 7.754E-01 cm3
 * b) 8.530E-01 cm3
 * c) 9.383E-01 cm3
 * d) 1.032E+00 cm3
 * e) 1.135E+00 cm3

4) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.315E-07 N/m2
 * b) 2.547E-07 N/m2
 * c) 2.801E-07 N/m2
 * d) 3.082E-07 N/m2
 * e) 3.390E-07 N/m2

5) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 1.791E-05 T
 * b) 1.970E-05 T
 * c) 2.167E-05 T
 * d) 2.384E-05 T
 * e) 2.622E-05 T

6) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * a) 6.624E-02 A
 * b) 7.287E-02 A
 * c) 8.016E-02 A
 * d) 8.817E-02 A
 * e) 9.699E-02 A

7) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.58 T and $$\omega=$$4.310E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 7.043E+04 V
 * b) 7.747E+04 V
 * c) 8.522E+04 V
 * d) 9.374E+04 V
 * e) 1.031E+05 V

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.645 m and $$B_{max}=\,$$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.26 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 2.949E+05 A
 * b) 3.244E+05 A
 * c) 3.568E+05 A
 * d) 3.925E+05 A
 * e) 4.317E+05 A

9) An ac generator produces an emf of amplitude 8 V at a frequency of 80 Hz. What is the maximum amplitude of the current if the generator is connected to a  14 mF inductor?


 * a) 8.541E-01 A
 * b) 9.395E-01 A
 * c) 1.033E+00 A
 * d) 1.137E+00 A
 * e) 1.251E+00 A

10) A circular current loop of radius 1.59 cm carries a current of 1.13 mA. What is the magnitude of the torque if the dipole is oriented at 41 &deg; to a uniform magnetic fied of 0.189 T?


 * a) 1.113E-07 N m
 * b) 1.224E-07 N m
 * c) 1.347E-07 N m
 * d) 1.481E-07 N m
 * e) 1.629E-07 N m

11) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.11E-11 Vs2m-1
 * b) 8.61E-11 Vs2m-1
 * c) 1.04E-10 Vs2m-1
 * d) 1.26E-10 Vs2m-1
 * e) 1.53E-10 Vs2m-1

T9 H2
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * a) 3.575E+00 N/m
 * b) 3.932E+00 N/m
 * c) 4.325E+00 N/m
 * d) 4.758E+00 N/m
 * e) 5.234E+00 N/m

2) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * a) 6.624E-02 A
 * b) 7.287E-02 A
 * c) 8.016E-02 A
 * d) 8.817E-02 A
 * e) 9.699E-02 A

3) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.14mm$$, and $$n=2.86$$. What is the volume of the washer?


 * a) 1.071E+00 cm3
 * b) 1.178E+00 cm3
 * c) 1.296E+00 cm3
 * d) 1.425E+00 cm3
 * e) 1.568E+00 cm3

4) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 78 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 4.55E-11 Vs2m-1
 * b) 5.51E-11 Vs2m-1
 * c) 6.68E-11 Vs2m-1
 * d) 8.09E-11 Vs2m-1
 * e) 9.80E-11 Vs2m-1

5) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.66 mm from the center of a wire of radius 4 mm if the current is 1A?


 * a) 3.325E-05 T
 * b) 3.658E-05 T
 * c) 4.023E-05 T
 * d) 4.426E-05 T
 * e) 4.868E-05 T

6) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.036 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.378E-05 N/m2
 * b) 1.516E-05 N/m2
 * c) 1.667E-05 N/m2
 * d) 1.834E-05 N/m2
 * e) 2.017E-05 N/m2

7) A circlular capactitor of radius 4.3 m has a gap of 7 mm, and a charge of 47 &mu;C.  What is the electric field between the plates?


 * a) 7.54E+04 N/C (or V/m)
 * b) 9.14E+04 N/C (or V/m)
 * c) 1.11E+05 N/C (or V/m)
 * d) 1.34E+05 N/C (or V/m)
 * e) 1.63E+05 N/C (or V/m)

8) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.54 T and $$\omega=$$1.860E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.642 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 2.415E+04 V
 * b) 2.656E+04 V
 * c) 2.922E+04 V
 * d) 3.214E+04 V
 * e) 3.535E+04 V

9) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a  97 mF inductor?


 * a) 4.972E-01 A
 * b) 5.469E-01 A
 * c) 6.016E-01 A
 * d) 6.618E-01 A
 * e) 7.280E-01 A

10) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.52 m and $$B_{max}=\,$$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 7.876E+05 A
 * b) 8.664E+05 A
 * c) 9.530E+05 A
 * d) 1.048E+06 A
 * e) 1.153E+06 A

11) A circular current loop of radius 2.1 cm carries a current of 5.02 mA. What is the magnitude of the torque if the dipole is oriented at 26 &deg; to a uniform magnetic fied of 0.184 T?


 * a) 5.610E-07 N m
 * b) 6.171E-07 N m
 * c) 6.788E-07 N m
 * d) 7.467E-07 N m
 * e) 8.213E-07 N m

T9 I0
1) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.559 T magnetic field is directed 46&deg; away from the wire?


 * a) 2.417E+00 N/m
 * b) 2.659E+00 N/m
 * c) 2.924E+00 N/m
 * d) 3.217E+00 N/m
 * e) 3.539E+00 N/m

2) A charged particle in a magnetic field of 3.820E-04 T is moving perpendicular to the magnetic field with a speed of 3.890E+05 m/s. What is the period of orbit if orbital radius is 0.718 m?


 * a) 8.713E-06 s
 * b) 9.584E-06 s
 * c) 1.054E-05 s
 * d) 1.160E-05 s
 * e) 1.276E-05 s

3) A solenoid has 9.880E+04 turns wound around a cylinder of diameter 1.5 cm and length 15 m. The current through the coils is 0.981 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.56 cm to z=+3.22 cm


 * a) 2.916E-04 T-m
 * b) 3.208E-04 T-m
 * c) 3.528E-04 T-m
 * d) 3.881E-04 T-m
 * e) 4.269E-04 T-m

4) Three wires sit at the corners of a square of length 0.716 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.94 A, 2.04 A, 2.41 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 6.833E-05 T
 * b) By= 7.517E-05 T
 * c) By= 8.268E-05 T
 * d) By= 9.095E-05 T
 * e) By= 1.000E-04 T

5) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$20 s&minus;1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?


 * a) 3.924E-04 V/m
 * b) 4.317E-04 V/m
 * c) 4.748E-04 V/m
 * d) 5.223E-04 V/m
 * e) 5.745E-04 V/m

6) An induced emf of 7.94V is measured across a coil of 94 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.65A in 0.478s. What is the self-inductance of the coil?


 * a) 5.047E-01 H
 * b) 5.552E-01 H
 * c) 6.107E-01 H
 * d) 6.717E-01 H
 * e) 7.389E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 5.50E+04 Hz and an amplitude of 2 V. If R =8 &Omega;, L= 9.60E-03H, and C=8.30E-06 F, what is the rms power transferred to the resistor?


 * a) 4.347E-05 Watts
 * b) 4.782E-05 Watts
 * c) 5.260E-05 Watts
 * d) 5.786E-05 Watts
 * e) 6.364E-05 Watts

8) A parallel plate capacitor with a capicatnce C=8.90E-06 F whose plates have an area A=6.90E+03 m2 and separation d=6.90E-03 m is connected via a swith to a 89 &Omega; resistor and a battery of voltage V0=89 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-03?


 * a) 6.595E+01 V
 * b) 7.255E+01 V
 * c) 7.980E+01 V
 * d) 8.778E+01 V
 * e) 9.656E+01 V

9) What is the radiation pressure on an object that is 9.30E+11 m away from the sun and has cross-sectional area of 0.019 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.332E-07 N/m2
 * b) 2.566E-07 N/m2
 * c) 2.822E-07 N/m2
 * d) 3.104E-07 N/m2
 * e) 3.415E-07 N/m2

10) A circlular capactitor of radius 3.2 m has a gap of 18 mm, and a charge of 82 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.79E-11 Vs2m-1
 * b) 7.02E-11 Vs2m-1
 * c) 8.51E-11 Vs2m-1
 * d) 1.03E-10 Vs2m-1
 * e) 1.25E-10 Vs2m-1

11) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 &mu;C.  What is the electric field between the plates?


 * a) 1.92E+05 N/C (or V/m)
 * b) 2.32E+05 N/C (or V/m)
 * c) 2.81E+05 N/C (or V/m)
 * d) 3.41E+05 N/C (or V/m)
 * e) 4.13E+05 N/C (or V/m)

T9 I1
1) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.28E-11 Vs2m-1
 * b) 8.82E-11 Vs2m-1
 * c) 1.07E-10 Vs2m-1
 * d) 1.29E-10 Vs2m-1
 * e) 1.57E-10 Vs2m-1

2) An induced emf of 6.75V is measured across a coil of 79 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.76A in 0.115s. What is the self-inductance of the coil?


 * a) 9.094E-02 H
 * b) 1.000E-01 H
 * c) 1.100E-01 H
 * d) 1.210E-01 H
 * e) 1.331E-01 H

3) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 7.035E-05 T
 * b) By= 7.739E-05 T
 * c) By= 8.512E-05 T
 * d) By= 9.364E-05 T
 * e) By= 1.030E-04 T

4) The output of an ac generator connected to an RLC series combination has a frequency of 3.60E+04 Hz and an amplitude of 9 V. If R =2 &Omega;, L= 7.60E-03H, and C=7.50E-06 F, what is the rms power transferred to the resistor?


 * a) 1.011E-03 Watts
 * b) 1.112E-03 Watts
 * c) 1.223E-03 Watts
 * d) 1.345E-03 Watts
 * e) 1.480E-03 Watts

5) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * a) 1.131E+00 N/m
 * b) 1.244E+00 N/m
 * c) 1.368E+00 N/m
 * d) 1.505E+00 N/m
 * e) 1.655E+00 N/m

6) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;3.68 cm to z=+1.29 cm


 * a) 1.863E-04 T-m
 * b) 2.050E-04 T-m
 * c) 2.255E-04 T-m
 * d) 2.480E-04 T-m
 * e) 2.728E-04 T-m

7) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.036 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.378E-05 N/m2
 * b) 1.516E-05 N/m2
 * c) 1.667E-05 N/m2
 * d) 1.834E-05 N/m2
 * e) 2.017E-05 N/m2

8) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=2.70E+03 m2 and separation d=6.30E-03 m is connected via a swith to a 4 &Omega; resistor and a battery of voltage V0=7 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-05?


 * a) 6.252E+00 V
 * b) 6.878E+00 V
 * c) 7.565E+00 V
 * d) 8.322E+00 V
 * e) 9.154E+00 V

9) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 75 &mu;C.  What is the electric field between the plates?


 * a) 5.43E+04 N/C (or V/m)
 * b) 6.58E+04 N/C (or V/m)
 * c) 7.97E+04 N/C (or V/m)
 * d) 9.66E+04 N/C (or V/m)
 * e) 1.17E+05 N/C (or V/m)

10) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?


 * a) 1.616E-04 V/m
 * b) 1.778E-04 V/m
 * c) 1.955E-04 V/m
 * d) 2.151E-04 V/m
 * e) 2.366E-04 V/m

11) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?


 * a) 5.792E-06 s
 * b) 6.371E-06 s
 * c) 7.008E-06 s
 * d) 7.709E-06 s
 * e) 8.480E-06 s

T9 I2
1) A charged particle in a magnetic field of 3.720E-04 T is moving perpendicular to the magnetic field with a speed of 4.780E+05 m/s. What is the period of orbit if orbital radius is 0.868 m?


 * a) 7.793E-06 s
 * b) 8.572E-06 s
 * c) 9.429E-06 s
 * d) 1.037E-05 s
 * e) 1.141E-05 s

2) A circlular capactitor of radius 3.2 m has a gap of 19 mm, and a charge of 46 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.78E-11 Vs2m-1
 * b) 7.00E-11 Vs2m-1
 * c) 8.48E-11 Vs2m-1
 * d) 1.03E-10 Vs2m-1
 * e) 1.25E-10 Vs2m-1

3) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 55 &mu;C.  What is the electric field between the plates?


 * a) 6.37E+04 N/C (or V/m)
 * b) 7.71E+04 N/C (or V/m)
 * c) 9.34E+04 N/C (or V/m)
 * d) 1.13E+05 N/C (or V/m)
 * e) 1.37E+05 N/C (or V/m)

4) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.559 T magnetic field is directed 46&deg; away from the wire?


 * a) 2.417E+00 N/m
 * b) 2.659E+00 N/m
 * c) 2.924E+00 N/m
 * d) 3.217E+00 N/m
 * e) 3.539E+00 N/m

5) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 3 V. If R =5 &Omega;, L= 3.90E-03H, and C=9.00E-06 F, what is the rms power transferred to the resistor?


 * a) 2.339E-03 Watts
 * b) 2.573E-03 Watts
 * c) 2.830E-03 Watts
 * d) 3.113E-03 Watts
 * e) 3.424E-03 Watts

6) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.025 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.511E-07 N/m2
 * b) 6.063E-07 N/m2
 * c) 6.669E-07 N/m2
 * d) 7.336E-07 N/m2
 * e) 8.069E-07 N/m2

7) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * a) 6.040E-05 V/m
 * b) 6.644E-05 V/m
 * c) 7.309E-05 V/m
 * d) 8.039E-05 V/m
 * e) 8.843E-05 V/m

8) An induced emf of 7.87V is measured across a coil of 66 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.05A in 0.781s. What is the self-inductance of the coil?


 * a) 7.926E-01 H
 * b) 8.718E-01 H
 * c) 9.590E-01 H
 * d) 1.055E+00 H
 * e) 1.160E+00 H

9) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.52 cm to z=+2.04 cm


 * a) 2.176E-04 T-m
 * b) 2.393E-04 T-m
 * c) 2.633E-04 T-m
 * d) 2.896E-04 T-m
 * e) 3.186E-04 T-m

10) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * a) 7.693E+01 V
 * b) 8.463E+01 V
 * c) 9.309E+01 V
 * d) 1.024E+02 V
 * e) 1.126E+02 V

11) Three wires sit at the corners of a square of length 0.534 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.45 A, 2.44 A, 1.61 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 9.388E-05 T
 * b) By= 1.033E-04 T
 * c) By= 1.136E-04 T
 * d) By= 1.250E-04 T
 * e) By= 1.375E-04 T

T9 J0
1) A circular current loop of radius 1.17 cm carries a current of 3.68 mA. What is the magnitude of the torque if the dipole is oriented at 55 &deg; to a uniform magnetic fied of 0.179 T?


 * a) 1.585E-07 N m
 * b) 1.743E-07 N m
 * c) 1.918E-07 N m
 * d) 2.110E-07 N m
 * e) 2.321E-07 N m

2) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?


 * a) 5.792E-06 s
 * b) 6.371E-06 s
 * c) 7.008E-06 s
 * d) 7.709E-06 s
 * e) 8.480E-06 s

3) Three wires sit at the corners of a square of length 0.819 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 4.688E-05 T
 * b) By= 5.156E-05 T
 * c) By= 5.672E-05 T
 * d) By= 6.239E-05 T
 * e) By= 6.863E-05 T

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.386E-03 T-m
 * b) 4.825E-03 T-m
 * c) 5.307E-03 T-m
 * d) 5.838E-03 T-m
 * e) 6.421E-03 T-m

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * a) 1.605E-04 V/m
 * b) 1.766E-04 V/m
 * c) 1.942E-04 V/m
 * d) 2.136E-04 V/m
 * e) 2.350E-04 V/m

6) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 4.489E-04 s
 * b) 4.938E-04 s
 * c) 5.432E-04 s
 * d) 5.975E-04 s
 * e) 6.572E-04 s

7) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a  59 mF capacitor?


 * a) 5.042E+00 A
 * b) 5.546E+00 A
 * c) 6.100E+00 A
 * d) 6.710E+00 A
 * e) 7.381E+00 A

8) What is the radiation force on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.044 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 7.088E-09 N
 * b) 7.796E-09 N
 * c) 8.576E-09 N
 * d) 9.434E-09 N
 * e) 1.038E-08 N

9) A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 41 &Omega; resistor and a battery of voltage V0=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?


 * a) 6.755E+01 V
 * b) 7.431E+01 V
 * c) 8.174E+01 V
 * d) 8.991E+01 V
 * e) 9.890E+01 V

10) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.28E-11 Vs2m-1
 * b) 8.82E-11 Vs2m-1
 * c) 1.07E-10 Vs2m-1
 * d) 1.29E-10 Vs2m-1
 * e) 1.57E-10 Vs2m-1

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * a) 2.80E+04 N/C (or V/m)
 * b) 3.40E+04 N/C (or V/m)
 * c) 4.12E+04 N/C (or V/m)
 * d) 4.99E+04 N/C (or V/m)
 * e) 6.04E+04 N/C (or V/m)

T9 J1
1) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?


 * a) 2.730E-06 s
 * b) 3.003E-06 s
 * c) 3.303E-06 s
 * d) 3.633E-06 s
 * e) 3.997E-06 s

2) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a  6 mF capacitor?


 * a) 5.253E-02 A
 * b) 5.778E-02 A
 * c) 6.356E-02 A
 * d) 6.991E-02 A
 * e) 7.691E-02 A

3) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 4.028E-05 T
 * b) By= 4.431E-05 T
 * c) By= 4.874E-05 T
 * d) By= 5.361E-05 T
 * e) By= 5.897E-05 T

4) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 21 &mu;C.  What is the electric field between the plates?


 * a) 6.16E+04 N/C (or V/m)
 * b) 7.47E+04 N/C (or V/m)
 * c) 9.05E+04 N/C (or V/m)
 * d) 1.10E+05 N/C (or V/m)
 * e) 1.33E+05 N/C (or V/m)

5) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.230E-04 s
 * b) 6.853E-04 s
 * c) 7.538E-04 s
 * d) 8.292E-04 s
 * e) 9.121E-04 s

6) A circlular capactitor of radius 4.5 m has a gap of 19 mm, and a charge of 13 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 1.35E-11 Vs2m-1
 * b) 1.63E-11 Vs2m-1
 * c) 1.98E-11 Vs2m-1
 * d) 2.40E-11 Vs2m-1
 * e) 2.91E-11 Vs2m-1

7) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=5.60E+03 m2 and separation d=5.10E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=54 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.50E-04?


 * a) 3.015E+01 V
 * b) 3.316E+01 V
 * c) 3.648E+01 V
 * d) 4.013E+01 V
 * e) 4.414E+01 V

8) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.075 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.002E-08 N
 * b) 5.502E-08 N
 * c) 6.052E-08 N
 * d) 6.657E-08 N
 * e) 7.323E-08 N

9) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?


 * a) 1.616E-04 V/m
 * b) 1.778E-04 V/m
 * c) 1.955E-04 V/m
 * d) 2.151E-04 V/m
 * e) 2.366E-04 V/m

10) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.42 kA, I2=0.904 kA, and I3=1.34 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 2.696E-03 T-m
 * b) 2.966E-03 T-m
 * c) 3.263E-03 T-m
 * d) 3.589E-03 T-m
 * e) 3.948E-03 T-m

11) A circular current loop of radius 1.63 cm carries a current of 2.38 mA. What is the magnitude of the torque if the dipole is oriented at 54 &deg; to a uniform magnetic fied of 0.125 T?


 * a) 2.009E-07 N m
 * b) 2.210E-07 N m
 * c) 2.431E-07 N m
 * d) 2.674E-07 N m
 * e) 2.941E-07 N m

T9 J2
1) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.167E-08 N
 * b) 1.284E-08 N
 * c) 1.412E-08 N
 * d) 1.553E-08 N
 * e) 1.708E-08 N

2) Three wires sit at the corners of a square of length 0.793 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 3.480E-05 T
 * b) By= 3.828E-05 T
 * c) By= 4.210E-05 T
 * d) By= 4.631E-05 T
 * e) By= 5.095E-05 T

3) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * a) 5.017E+01 V
 * b) 5.519E+01 V
 * c) 6.071E+01 V
 * d) 6.678E+01 V
 * e) 7.345E+01 V

4) In an LC circuit, the self-inductance is 0.0464 H and the capacitance is 7.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.280E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 8.339E-04 s
 * b) 9.173E-04 s
 * c) 1.009E-03 s
 * d) 1.110E-03 s
 * e) 1.221E-03 s

5) A long solenoid has a radius of 0.583 m and 38 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$24 s&minus;1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?


 * a) 1.655E-04 V/m
 * b) 1.821E-04 V/m
 * c) 2.003E-04 V/m
 * d) 2.203E-04 V/m
 * e) 2.424E-04 V/m

6) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?


 * a) 1.141E-05 s
 * b) 1.255E-05 s
 * c) 1.381E-05 s
 * d) 1.519E-05 s
 * e) 1.671E-05 s

7) A circular current loop of radius 1.11 cm carries a current of 4.0 mA. What is the magnitude of the torque if the dipole is oriented at 68 &deg; to a uniform magnetic fied of 0.173 T?


 * a) 1.866E-07 N m
 * b) 2.052E-07 N m
 * c) 2.258E-07 N m
 * d) 2.484E-07 N m
 * e) 2.732E-07 N m

8) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a  99 mF capacitor?


 * a) 1.644E+00 A
 * b) 1.808E+00 A
 * c) 1.989E+00 A
 * d) 2.188E+00 A
 * e) 2.407E+00 A

9) A circlular capactitor of radius 4.9 m has a gap of 11 mm, and a charge of 85 &mu;C.  What is the electric field between the plates?


 * a) 1.27E+05 N/C (or V/m)
 * b) 1.54E+05 N/C (or V/m)
 * c) 1.87E+05 N/C (or V/m)
 * d) 2.26E+05 N/C (or V/m)
 * e) 2.74E+05 N/C (or V/m)

10) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 2.05E-11 Vs2m-1
 * b) 2.48E-11 Vs2m-1
 * c) 3.01E-11 Vs2m-1
 * d) 3.64E-11 Vs2m-1
 * e) 4.42E-11 Vs2m-1

11) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.46 kA, I2=2.14 kA, and I3=4.44 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.943E-03 T-m
 * b) 5.438E-03 T-m
 * c) 5.982E-03 T-m
 * d) 6.580E-03 T-m
 * e) 7.238E-03 T-m

T9 K0
1) The silver ribbon shown are a=4.23 cm, b=3.7 cm, and c= 0.721 cm. The current carries a current of 144 A and it lies in a uniform magnetic field of 1.21 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.746E-06 V
 * b) 1.921E-06 V
 * c) 2.113E-06 V
 * d) 2.324E-06 V
 * e) 2.557E-06 V

2) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.394 T magnetic field is directed 14&deg; away from the wire?


 * a) 6.302E-01 N/m
 * b) 6.932E-01 N/m
 * c) 7.625E-01 N/m
 * d) 8.388E-01 N/m
 * e) 9.227E-01 N/m

3) Two loops of wire carry the same current of 43 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.516 m while the other has a radius of 1.22 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.565 m from the first (smaller) loopif the disance between the loops is 1.78 m?


 * a) 1.798E-02 T
 * b) 1.978E-02 T
 * c) 2.176E-02 T
 * d) 2.394E-02 T
 * e) 2.633E-02 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 595 mA, the net magnetic field is measured to be 1.46 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 6.716E+02
 * b) $$\chi \text{ (chi) }=$$ 7.387E+02
 * c) $$\chi \text{ (chi) }=$$ 8.126E+02
 * d) $$\chi \text{ (chi) }=$$ 8.939E+02
 * e) $$\chi \text{ (chi) }=$$ 9.833E+02

5) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 1.567E+00 A
 * b) 1.724E+00 A
 * c) 1.897E+00 A
 * d) 2.086E+00 A
 * e) 2.295E+00 A

6) An induced emf of 3.78V is measured across a coil of 99 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.36A in 0.821s. What is the self-inductance of the coil?


 * a) 4.033E-01 H
 * b) 4.436E-01 H
 * c) 4.880E-01 H
 * d) 5.367E-01 H
 * e) 5.904E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 &Omega;, L= 2.80E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.759E-01 &rad;
 * b) 9.635E-01 &rad;
 * c) 1.060E+00 &rad;
 * d) 1.166E+00 &rad;
 * e) 1.282E+00 &rad;

8) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.099 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.464E-07 N/m2
 * b) 1.611E-07 N/m2
 * c) 1.772E-07 N/m2
 * d) 1.949E-07 N/m2
 * e) 2.144E-07 N/m2

9) A 46 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 78 kW?


 * a) 1.563E+02 km
 * b) 1.719E+02 km
 * c) 1.891E+02 km
 * d) 2.080E+02 km
 * e) 2.288E+02 km

10) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 6.62E-05 s
 * b) 8.02E-05 s
 * c) 9.71E-05 s
 * d) 1.18E-04 s
 * e) 1.43E-04 s

11) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 &mu;C.  What is the electric field between the plates?


 * a) 1.29E+05 N/C (or V/m)
 * b) 1.56E+05 N/C (or V/m)
 * c) 1.89E+05 N/C (or V/m)
 * d) 2.29E+05 N/C (or V/m)
 * e) 2.77E+05 N/C (or V/m)

T9 K1
1) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 &Omega;, L= 8.20E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.146E-01 &rad;
 * b) 8.960E-01 &rad;
 * c) 9.856E-01 &rad;
 * d) 1.084E+00 &rad;
 * e) 1.193E+00 &rad;

2) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * a) 4.55E+04 N/C (or V/m)
 * b) 5.52E+04 N/C (or V/m)
 * c) 6.68E+04 N/C (or V/m)
 * d) 8.10E+04 N/C (or V/m)
 * e) 9.81E+04 N/C (or V/m)

3) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * a) 2.094E+02 km
 * b) 2.304E+02 km
 * c) 2.534E+02 km
 * d) 2.788E+02 km
 * e) 3.066E+02 km

4) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.025 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.511E-07 N/m2
 * b) 6.063E-07 N/m2
 * c) 6.669E-07 N/m2
 * d) 7.336E-07 N/m2
 * e) 8.069E-07 N/m2

5) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 7.917E+02
 * b) $$\chi \text{ (chi) }=$$ 8.708E+02
 * c) $$\chi \text{ (chi) }=$$ 9.579E+02
 * d) $$\chi \text{ (chi) }=$$ 1.054E+03
 * e) $$\chi \text{ (chi) }=$$ 1.159E+03

6) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.355 T magnetic field is directed 53&deg; away from the wire?


 * a) 8.520E-01 N/m
 * b) 9.372E-01 N/m
 * c) 1.031E+00 N/m
 * d) 1.134E+00 N/m
 * e) 1.247E+00 N/m

7) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.776 m while the other has a radius of 1.2 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?


 * a) 1.127E-02 T
 * b) 1.240E-02 T
 * c) 1.364E-02 T
 * d) 1.500E-02 T
 * e) 1.650E-02 T

8) An induced emf of 5.08V is measured across a coil of 78 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.07A in 0.681s. What is the self-inductance of the coil?


 * a) 4.660E-01 H
 * b) 5.127E-01 H
 * c) 5.639E-01 H
 * d) 6.203E-01 H
 * e) 6.823E-01 H

9) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.080E-06 V
 * b) 1.188E-06 V
 * c) 1.306E-06 V
 * d) 1.437E-06 V
 * e) 1.581E-06 V

10) A square coil has sides that are L= 0.465 m long and is tightly wound with N=954 turns of wire. The resistance of the coil is R=6.06 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0367 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 1.136E+00 A
 * b) 1.249E+00 A
 * c) 1.374E+00 A
 * d) 1.512E+00 A
 * e) 1.663E+00 A

11) A circlular capactitor of radius 4.8 m has a gap of 16 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.98E-04 s
 * b) 2.40E-04 s
 * c) 2.91E-04 s
 * d) 3.53E-04 s
 * e) 4.27E-04 s

T9 K2
1) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * a) 2.094E+02 km
 * b) 2.304E+02 km
 * c) 2.534E+02 km
 * d) 2.788E+02 km
 * e) 3.066E+02 km

2) An induced emf of 4.7V is measured across a coil of 52 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.08A in 0.961s. What is the self-inductance of the coil?


 * a) 1.102E+00 H
 * b) 1.212E+00 H
 * c) 1.333E+00 H
 * d) 1.466E+00 H
 * e) 1.613E+00 H

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 525 mA, the net magnetic field is measured to be 1.45 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 8.249E+02
 * b) $$\chi \text{ (chi) }=$$ 9.074E+02
 * c) $$\chi \text{ (chi) }=$$ 9.981E+02
 * d) $$\chi \text{ (chi) }=$$ 1.098E+03
 * e) $$\chi \text{ (chi) }=$$ 1.208E+03

4) A circlular capactitor of radius 3.7 m has a gap of 10 mm, and a charge of 41 &mu;C.  What is the electric field between the plates?


 * a) 1.08E+05 N/C (or V/m)
 * b) 1.30E+05 N/C (or V/m)
 * c) 1.58E+05 N/C (or V/m)
 * d) 1.91E+05 N/C (or V/m)
 * e) 2.32E+05 N/C (or V/m)

5) Two loops of wire carry the same current of 66 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.485 m while the other has a radius of 1.27 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.507 m from the first (smaller) loopif the disance between the loops is 1.76 m?


 * a) 2.733E-02 T
 * b) 3.007E-02 T
 * c) 3.307E-02 T
 * d) 3.638E-02 T
 * e) 4.002E-02 T

6) A circlular capactitor of radius 3.7 m has a gap of 15 mm, and a charge of 36 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.04E-04 s
 * b) 1.26E-04 s
 * c) 1.52E-04 s
 * d) 1.85E-04 s
 * e) 2.24E-04 s

7) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 4.414E+00 A
 * b) 4.855E+00 A
 * c) 5.341E+00 A
 * d) 5.875E+00 A
 * e) 6.462E+00 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 200 Hz and an amplitude of 0.14 V;. If R =3 &Omega;, L= 1.70E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 3.691E-01 &rad;
 * b) 4.060E-01 &rad;
 * c) 4.466E-01 &rad;
 * d) 4.913E-01 &rad;
 * e) 5.404E-01 &rad;

9) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * a) 3.575E+00 N/m
 * b) 3.932E+00 N/m
 * c) 4.325E+00 N/m
 * d) 4.758E+00 N/m
 * e) 5.234E+00 N/m

10) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.144E-07 N/m2
 * b) 2.358E-07 N/m2
 * c) 2.594E-07 N/m2
 * d) 2.854E-07 N/m2
 * e) 3.139E-07 N/m2

11) The silver ribbon shown are a=3.89 cm, b=2.94 cm, and c= 0.58 cm. The current carries a current of 242 A and it lies in a uniform magnetic field of 2.47 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 9.911E-06 V
 * b) 1.090E-05 V
 * c) 1.199E-05 V
 * d) 1.319E-05 V
 * e) 1.451E-05 V

T9 L0
1) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.88 T magnetic field is directed 47&deg; away from the wire?


 * a) 4.096E+00 N/m
 * b) 4.505E+00 N/m
 * c) 4.956E+00 N/m
 * d) 5.451E+00 N/m
 * e) 5.996E+00 N/m

2) A 27 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.85 T. What current is required to maintain this balance?


 * a) 3.106E-01 A
 * b) 3.416E-01 A
 * c) 3.758E-01 A
 * d) 4.134E-01 A
 * e) 4.547E-01 A

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.51 kA, I2=1.32 kA, and I3=2.73 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.331E-03 T-m
 * b) 1.464E-03 T-m
 * c) 1.611E-03 T-m
 * d) 1.772E-03 T-m
 * e) 1.949E-03 T-m

4) Three wires sit at the corners of a square of length 0.687 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.134E-05 T
 * b) Bx= 7.847E-05 T
 * c) Bx= 8.632E-05 T
 * d) Bx= 9.495E-05 T
 * e) Bx= 1.044E-04 T

5) A cylinder of height 1.3 cm and radius 6.01 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.61 cm from point O and moves at a speed of 2.11 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 1.372E+01 cm3/s
 * b) 1.509E+01 cm3/s
 * c) 1.660E+01 cm3/s
 * d) 1.826E+01 cm3/s
 * e) 2.009E+01 cm3/s

6) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.230E-04 s
 * b) 6.853E-04 s
 * c) 7.538E-04 s
 * d) 8.292E-04 s
 * e) 9.121E-04 s

7) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 &Omega;, L= 6.80E-03H, and C=9.60E-04 F, what is the impedance?


 * a) 3.575E+01 &Omega;
 * b) 3.933E+01 &Omega;
 * c) 4.326E+01 &Omega;
 * d) 4.758E+01 &Omega;
 * e) 5.234E+01 &Omega;

8) A 55 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 93 kW?


 * a) 1.270E+02 km
 * b) 1.397E+02 km
 * c) 1.537E+02 km
 * d) 1.690E+02 km
 * e) 1.859E+02 km

9) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 7.396E-08 N
 * b) 8.136E-08 N
 * c) 8.950E-08 N
 * d) 9.845E-08 N
 * e) 1.083E-07 N

10) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 8.75E-12 Vs2m-1
 * b) 1.06E-11 Vs2m-1
 * c) 1.28E-11 Vs2m-1
 * d) 1.56E-11 Vs2m-1
 * e) 1.88E-11 Vs2m-1

11) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.95E-09 Tesla
 * b) 4.97E-09 Tesla
 * c) 6.26E-09 Tesla
 * d) 7.88E-09 Tesla
 * e) 9.92E-09 Tesla

T9 L1
1) A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 1.892E+01 cm3/s
 * b) 2.081E+01 cm3/s
 * c) 2.289E+01 cm3/s
 * d) 2.518E+01 cm3/s
 * e) 2.770E+01 cm3/s

2) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.166E-04 s
 * b) 6.783E-04 s
 * c) 7.461E-04 s
 * d) 8.207E-04 s
 * e) 9.028E-04 s

3) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 &Omega;, L= 1.70E-03H, and C=5.40E-04 F, what is the impedance?


 * a) 8.123E+00 &Omega;
 * b) 8.935E+00 &Omega;
 * c) 9.828E+00 &Omega;
 * d) 1.081E+01 &Omega;
 * e) 1.189E+01 &Omega;

4) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.275E-07 N
 * b) 5.803E-07 N
 * c) 6.383E-07 N
 * d) 7.021E-07 N
 * e) 7.723E-07 N

5) A 42 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * a) 1.641E+02 km
 * b) 1.805E+02 km
 * c) 1.986E+02 km
 * d) 2.184E+02 km
 * e) 2.403E+02 km

6) A circlular capactitor of radius 3.2 m has a gap of 19 mm, and a charge of 46 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.78E-11 Vs2m-1
 * b) 7.00E-11 Vs2m-1
 * c) 8.48E-11 Vs2m-1
 * d) 1.03E-10 Vs2m-1
 * e) 1.25E-10 Vs2m-1

7) Three wires sit at the corners of a square of length 0.518 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.31 A, 1.32 A, 1.62 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.013E-05 T
 * b) Bx= 6.614E-05 T
 * c) Bx= 7.275E-05 T
 * d) Bx= 8.003E-05 T
 * e) Bx= 8.803E-05 T

8) A 42 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 7 g, and the magnitude of the magnetic field is 0.48 T. What current is required to maintain this balance?


 * a) 2.812E-01 A
 * b) 3.093E-01 A
 * c) 3.403E-01 A
 * d) 3.743E-01 A
 * e) 4.117E-01 A

9) A circlular capactitor of radius 4.6 m has a gap of 18 mm, and a charge of 44 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 6.64E-09 Tesla
 * b) 8.36E-09 Tesla
 * c) 1.05E-08 Tesla
 * d) 1.32E-08 Tesla
 * e) 1.67E-08 Tesla

10) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.55 kA, I2=1.02 kA, and I3=1.81 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 8.204E-04 T-m
 * b) 9.025E-04 T-m
 * c) 9.927E-04 T-m
 * d) 1.092E-03 T-m
 * e) 1.201E-03 T-m

11) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * a) 3.575E+00 N/m
 * b) 3.932E+00 N/m
 * c) 4.325E+00 N/m
 * d) 4.758E+00 N/m
 * e) 5.234E+00 N/m

T9 L2
1) A 92 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 15 g, and the magnitude of the magnetic field is 0.713 T. What current is required to maintain this balance?


 * a) 2.037E-01 A
 * b) 2.241E-01 A
 * c) 2.465E-01 A
 * d) 2.712E-01 A
 * e) 2.983E-01 A

2) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * a) 2.094E+02 km
 * b) 2.304E+02 km
 * c) 2.534E+02 km
 * d) 2.788E+02 km
 * e) 3.066E+02 km

3) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 34 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 2.40E-11 Vs2m-1
 * b) 2.91E-11 Vs2m-1
 * c) 3.53E-11 Vs2m-1
 * d) 4.27E-11 Vs2m-1
 * e) 5.18E-11 Vs2m-1

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.250E-03 T-m
 * b) 1.375E-03 T-m
 * c) 1.512E-03 T-m
 * d) 1.663E-03 T-m
 * e) 1.830E-03 T-m

5) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.18 V;. If R =6 &Omega;, L= 7.50E-03H, and C=7.50E-04 F, what is the impedance?


 * a) 2.708E+01 &Omega;
 * b) 2.978E+01 &Omega;
 * c) 3.276E+01 &Omega;
 * d) 3.604E+01 &Omega;
 * e) 3.964E+01 &Omega;

6) A cylinder of height 2.12 cm and radius 2.28 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.52 cm from point O and moves at a speed of 8.21 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 2.976E+01 cm3/s
 * b) 3.274E+01 cm3/s
 * c) 3.601E+01 cm3/s
 * d) 3.961E+01 cm3/s
 * e) 4.358E+01 cm3/s

7) Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 8.371E-05 T
 * b) Bx= 9.208E-05 T
 * c) Bx= 1.013E-04 T
 * d) Bx= 1.114E-04 T
 * e) Bx= 1.226E-04 T

8) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.30E-09 Tesla
 * b) 4.15E-09 Tesla
 * c) 5.23E-09 Tesla
 * d) 6.58E-09 Tesla
 * e) 8.29E-09 Tesla

9) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.275E-07 N
 * b) 5.803E-07 N
 * c) 6.383E-07 N
 * d) 7.021E-07 N
 * e) 7.723E-07 N

10) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.761 T magnetic field is directed 44&deg; away from the wire?


 * a) 2.527E+00 N/m
 * b) 2.780E+00 N/m
 * c) 3.058E+00 N/m
 * d) 3.364E+00 N/m
 * e) 3.700E+00 N/m

11) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 6.166E-04 s
 * b) 6.783E-04 s
 * c) 7.461E-04 s
 * d) 8.207E-04 s
 * e) 9.028E-04 s

T9 M0
1) The silver ribbon shown are a=3.52 cm, b=2.88 cm, and c= 0.515 cm. The current carries a current of 137 A and it lies in a uniform magnetic field of 2.02 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 5.685E-06 V
 * b) 6.253E-06 V
 * c) 6.878E-06 V
 * d) 7.566E-06 V
 * e) 8.323E-06 V

2) A circular current loop of radius 1.88 cm carries a current of 3.41 mA. What is the magnitude of the torque if the dipole is oriented at 62 &deg; to a uniform magnetic fied of 0.415 T?


 * a) 1.387E-06 N m
 * b) 1.526E-06 N m
 * c) 1.679E-06 N m
 * d) 1.847E-06 N m
 * e) 2.031E-06 N m

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.58 kA, I2=1.27 kA, and I3=1.99 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 3.770E-03 T-m
 * b) 4.147E-03 T-m
 * c) 4.562E-03 T-m
 * d) 5.018E-03 T-m
 * e) 5.520E-03 T-m

4) Three wires sit at the corners of a square of length 0.832 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.545E-05 T
 * b) Bx= 7.200E-05 T
 * c) Bx= 7.919E-05 T
 * d) Bx= 8.711E-05 T
 * e) Bx= 9.583E-05 T

5) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 2.081E-04 V
 * b) 2.289E-04 V
 * c) 2.518E-04 V
 * d) 2.770E-04 V
 * e) 3.047E-04 V

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if &epsilon; = 2.64 V, R = 6.37 &Omega;, and L = 7.33 H?


 * a) -1.700E+00 s
 * b) -1.870E+00 s
 * c) -2.057E+00 s
 * d) -2.262E+00 s
 * e) -2.489E+00 s

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * a) Q = 1.288E+02
 * b) Q = 1.482E+02
 * c) Q = 1.704E+02
 * d) Q = 1.959E+02
 * e) Q = 2.253E+02

8) What is the radiation pressure on an object that is 2.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 3.131E-06 N/m2
 * b) 3.445E-06 N/m2
 * c) 3.789E-06 N/m2
 * d) 4.168E-06 N/m2
 * e) 4.585E-06 N/m2

9) A 46 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 78 kW?


 * a) 1.563E+02 km
 * b) 1.719E+02 km
 * c) 1.891E+02 km
 * d) 2.080E+02 km
 * e) 2.288E+02 km

10) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 33 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.42E-04 s
 * b) 1.73E-04 s
 * c) 2.09E-04 s
 * d) 2.53E-04 s
 * e) 3.07E-04 s

11) A circlular capactitor of radius 3.9 m has a gap of 8 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 5.30E-09 Tesla
 * b) 6.67E-09 Tesla
 * c) 8.39E-09 Tesla
 * d) 1.06E-08 Tesla
 * e) 1.33E-08 Tesla

T9 M1
1) The silver ribbon shown are a=3.55 cm, b=2.99 cm, and c= 1.03 cm. The current carries a current of 135 A and it lies in a uniform magnetic field of 1.26 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.193E-06 V
 * b) 1.313E-06 V
 * c) 1.444E-06 V
 * d) 1.588E-06 V
 * e) 1.747E-06 V

2) A circlular capactitor of radius 4 m has a gap of 14 mm, and a charge of 78 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 9.77E-09 Tesla
 * b) 1.23E-08 Tesla
 * c) 1.55E-08 Tesla
 * d) 1.95E-08 Tesla
 * e) 2.45E-08 Tesla

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 &Omega;, L= 4.90E-03H, and C=2.10E-06 F, respectively.


 * a) Q = 1.381E+02
 * b) Q = 1.588E+02
 * c) Q = 1.826E+02
 * d) Q = 2.100E+02
 * e) Q = 2.415E+02

4) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.019 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.392E-06 N/m2
 * b) 2.631E-06 N/m2
 * c) 2.894E-06 N/m2
 * d) 3.184E-06 N/m2
 * e) 3.502E-06 N/m2

5) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if &epsilon; = 6.08 V, R = 1.88 &Omega;, and L = 4.67 H?


 * a) -5.192E+00 s
 * b) -5.711E+00 s
 * c) -6.282E+00 s
 * d) -6.910E+00 s
 * e) -7.601E+00 s

6) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm.  A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 1.407E-04 V
 * b) 1.548E-04 V
 * c) 1.703E-04 V
 * d) 1.873E-04 V
 * e) 2.061E-04 V

7) A 56 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 72 kW?


 * a) 1.084E+02 km
 * b) 1.193E+02 km
 * c) 1.312E+02 km
 * d) 1.443E+02 km
 * e) 1.587E+02 km

8) A circlular capactitor of radius 3.3 m has a gap of 12 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 9.94E-05 s
 * b) 1.20E-04 s
 * c) 1.46E-04 s
 * d) 1.77E-04 s
 * e) 2.14E-04 s

9) A circular current loop of radius 2.21 cm carries a current of 1.43 mA. What is the magnitude of the torque if the dipole is oriented at 67 &deg; to a uniform magnetic fied of 0.276 T?


 * a) 4.188E-07 N m
 * b) 4.607E-07 N m
 * c) 5.068E-07 N m
 * d) 5.574E-07 N m
 * e) 6.132E-07 N m

10) Three wires sit at the corners of a square of length 0.51 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 9.053E-05 T
 * b) Bx= 9.959E-05 T
 * c) Bx= 1.095E-04 T
 * d) Bx= 1.205E-04 T
 * e) Bx= 1.325E-04 T

11) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 2.812E-03 T-m
 * b) 3.093E-03 T-m
 * c) 3.402E-03 T-m
 * d) 3.742E-03 T-m
 * e) 4.117E-03 T-m

T9 M2
1) What is the radiation pressure on an object that is 1.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 9.568E-06 N/m2
 * b) 1.053E-05 N/m2
 * c) 1.158E-05 N/m2
 * d) 1.274E-05 N/m2
 * e) 1.401E-05 N/m2

2) A 48 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 80 kW?


 * a) 1.678E+02 km
 * b) 1.846E+02 km
 * c) 2.031E+02 km
 * d) 2.234E+02 km
 * e) 2.457E+02 km

3) Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 3.394E-05 T
 * b) Bx= 3.733E-05 T
 * c) Bx= 4.106E-05 T
 * d) Bx= 4.517E-05 T
 * e) Bx= 4.969E-05 T

4) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 88 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 1.86E-08 Tesla
 * b) 2.34E-08 Tesla
 * c) 2.95E-08 Tesla
 * d) 3.72E-08 Tesla
 * e) 4.68E-08 Tesla

5) A circular current loop of radius 2.99 cm carries a current of 4.54 mA. What is the magnitude of the torque if the dipole is oriented at 34 &deg; to a uniform magnetic fied of 0.107 T?


 * a) 7.629E-07 N m
 * b) 8.392E-07 N m
 * c) 9.232E-07 N m
 * d) 1.015E-06 N m
 * e) 1.117E-06 N m

6) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 3.62E-04 s
 * b) 4.38E-04 s
 * c) 5.31E-04 s
 * d) 6.43E-04 s
 * e) 7.79E-04 s

7) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 1.066E-04 V
 * b) 1.173E-04 V
 * c) 1.290E-04 V
 * d) 1.419E-04 V
 * e) 1.561E-04 V

8) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.81 kA, I2=1.2 kA, and I3=1.84 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 3.583E-03 T-m
 * b) 3.941E-03 T-m
 * c) 4.335E-03 T-m
 * d) 4.769E-03 T-m
 * e) 5.246E-03 T-m

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 &Omega;, L= 4.90E-03H, and C=2.10E-06 F, respectively.


 * a) Q = 1.381E+02
 * b) Q = 1.588E+02
 * c) Q = 1.826E+02
 * d) Q = 2.100E+02
 * e) Q = 2.415E+02

10) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.69% of its maximum value if &epsilon; = 4.79 V, R = 4.18 &Omega;, and L = 2.7 H?


 * a) -8.773E-01 s
 * b) -9.651E-01 s
 * c) -1.062E+00 s
 * d) -1.168E+00 s
 * e) -1.284E+00 s

11) The silver ribbon shown are a=4.14 cm, b=3.69 cm, and c= 1.13 cm. The current carries a current of 291 A and it lies in a uniform magnetic field of 3.32 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 6.795E-06 V
 * b) 7.475E-06 V
 * c) 8.222E-06 V
 * d) 9.045E-06 V
 * e) 9.949E-06 V

T9 N0
1) A charged particle in a magnetic field of 4.660E-04 T is moving perpendicular to the magnetic field with a speed of 7.720E+05 m/s. What is the period of orbit if orbital radius is 0.747 m?


 * a) 6.080E-06 s
 * b) 6.688E-06 s
 * c) 7.356E-06 s
 * d) 8.092E-06 s
 * e) 8.901E-06 s

2) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 4.13 mT and 2.810E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 6.804E+05 m/s
 * b) 7.484E+05 m/s
 * c) 8.233E+05 m/s
 * d) 9.056E+05 m/s
 * e) 9.962E+05 m/s

3) Two loops of wire carry the same current of 14 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.835 m while the other has a radius of 1.29 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.607 m from the first (smaller) loopif the disance between the loops is 1.61 m?


 * a) 6.099E-03 T
 * b) 6.709E-03 T
 * c) 7.380E-03 T
 * d) 8.118E-03 T
 * e) 8.930E-03 T

4) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.11 cm to z=+2.76 cm


 * a) 1.068E-04 T-m
 * b) 1.175E-04 T-m
 * c) 1.292E-04 T-m
 * d) 1.421E-04 T-m
 * e) 1.563E-04 T-m

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * a) 1.605E-04 V/m
 * b) 1.766E-04 V/m
 * c) 1.942E-04 V/m
 * d) 2.136E-04 V/m
 * e) 2.350E-04 V/m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.65% of its maximum value if &epsilon; = 3.62 V, R = 4.07 &Omega;, and L = 7.19 H?


 * a) -2.476E+00 s
 * b) -2.724E+00 s
 * c) -2.996E+00 s
 * d) -3.296E+00 s
 * e) -3.625E+00 s

7) An ac generator produces an emf of amplitude 40 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a  52 mF inductor?


 * a) 7.783E-01 A
 * b) 8.561E-01 A
 * c) 9.417E-01 A
 * d) 1.036E+00 A
 * e) 1.140E+00 A

8) A parallel plate capacitor with a capicatnce C=4.50E-06 F whose plates have an area A=3.30E+03 m2 and separation d=6.40E-03 m is connected via a swith to a 83 &Omega; resistor and a battery of voltage V0=56 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.40E-03?


 * a) 7.767E+03 V/m
 * b) 8.544E+03 V/m
 * c) 9.398E+03 V/m
 * d) 1.034E+04 V/m
 * e) 1.137E+04 V/m

9) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.275E-07 N
 * b) 5.803E-07 N
 * c) 6.383E-07 N
 * d) 7.021E-07 N
 * e) 7.723E-07 N

10) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 6.62E-05 s
 * b) 8.02E-05 s
 * c) 9.71E-05 s
 * d) 1.18E-04 s
 * e) 1.43E-04 s

11) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 2.82E-09 Tesla
 * b) 3.54E-09 Tesla
 * c) 4.46E-09 Tesla
 * d) 5.62E-09 Tesla
 * e) 7.07E-09 Tesla

T9 N1
1) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.673E-07 N
 * b) 2.940E-07 N
 * c) 3.234E-07 N
 * d) 3.558E-07 N
 * e) 3.913E-07 N

2) An ac generator produces an emf of amplitude 24 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a  96 mF inductor?


 * a) 3.014E-01 A
 * b) 3.316E-01 A
 * c) 3.647E-01 A
 * d) 4.012E-01 A
 * e) 4.413E-01 A

3) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?


 * a) 1.141E-05 s
 * b) 1.255E-05 s
 * c) 1.381E-05 s
 * d) 1.519E-05 s
 * e) 1.671E-05 s

4) A solenoid has 5.160E+04 turns wound around a cylinder of diameter 1.55 cm and length 18 m. The current through the coils is 0.57 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.88 cm to z=+1.52 cm


 * a) 6.788E-05 T-m
 * b) 7.467E-05 T-m
 * c) 8.213E-05 T-m
 * d) 9.035E-05 T-m
 * e) 9.938E-05 T-m

5) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 2.62 mT and 2.120E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 8.092E+05 m/s
 * b) 8.901E+05 m/s
 * c) 9.791E+05 m/s
 * d) 1.077E+06 m/s
 * e) 1.185E+06 m/s

6) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.95E-09 Tesla
 * b) 4.97E-09 Tesla
 * c) 6.26E-09 Tesla
 * d) 7.88E-09 Tesla
 * e) 9.92E-09 Tesla

7) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 43 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 1.95E-04 s
 * b) 2.36E-04 s
 * c) 2.86E-04 s
 * d) 3.46E-04 s
 * e) 4.20E-04 s

8) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if &epsilon; = 6.08 V, R = 1.88 &Omega;, and L = 4.67 H?


 * a) -5.192E+00 s
 * b) -5.711E+00 s
 * c) -6.282E+00 s
 * d) -6.910E+00 s
 * e) -7.601E+00 s

9) A long solenoid has a radius of 0.434 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.28 m from the axis at time t=0.0392 s ?


 * a) 1.479E-04 V/m
 * b) 1.627E-04 V/m
 * c) 1.789E-04 V/m
 * d) 1.968E-04 V/m
 * e) 2.165E-04 V/m

10) A parallel plate capacitor with a capicatnce C=1.30E-06 F whose plates have an area A=1.10E+03 m2 and separation d=7.60E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.30E-04?


 * a) 4.842E+02 V/m
 * b) 5.326E+02 V/m
 * c) 5.858E+02 V/m
 * d) 6.444E+02 V/m
 * e) 7.089E+02 V/m

11) Two loops of wire carry the same current of 99 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.798 m while the other has a radius of 1.29 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.394 m from the first (smaller) loopif the disance between the loops is 1.29 m?


 * a) 8.291E-02 T
 * b) 9.120E-02 T
 * c) 1.003E-01 T
 * d) 1.104E-01 T
 * e) 1.214E-01 T

T9 N2
1) A charged particle in a magnetic field of 3.330E-04 T is moving perpendicular to the magnetic field with a speed of 4.800E+05 m/s. What is the period of orbit if orbital radius is 0.402 m?


 * a) 4.784E-06 s
 * b) 5.262E-06 s
 * c) 5.788E-06 s
 * d) 6.367E-06 s
 * e) 7.004E-06 s

2) A circlular capactitor of radius 4 m has a gap of 13 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.62E-09 Tesla
 * b) 1.09E-08 Tesla
 * c) 1.37E-08 Tesla
 * d) 1.72E-08 Tesla
 * e) 2.17E-08 Tesla

3) Two loops of wire carry the same current of 67 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.847 m while the other has a radius of 1.15 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.408 m from the first (smaller) loopif the disance between the loops is 1.15 m?


 * a) 4.799E-02 T
 * b) 5.278E-02 T
 * c) 5.806E-02 T
 * d) 6.387E-02 T
 * e) 7.026E-02 T

4) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * a) 6.040E-05 V/m
 * b) 6.644E-05 V/m
 * c) 7.309E-05 V/m
 * d) 8.039E-05 V/m
 * e) 8.843E-05 V/m

5) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.16% of its maximum value if &epsilon; = 4.79 V, R = 4.37 &Omega;, and L = 5.29 H?


 * a) -2.110E+00 s
 * b) -2.321E+00 s
 * c) -2.553E+00 s
 * d) -2.809E+00 s
 * e) -3.090E+00 s

6) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 9.23 mT and 6.120E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 4.982E+05 m/s
 * b) 5.480E+05 m/s
 * c) 6.028E+05 m/s
 * d) 6.631E+05 m/s
 * e) 7.294E+05 m/s

7) A solenoid has 4.380E+04 turns wound around a cylinder of diameter 1.77 cm and length 16 m. The current through the coils is 0.916 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;4.39 cm to z=+4.26 cm


 * a) 2.478E-04 T-m
 * b) 2.726E-04 T-m
 * c) 2.998E-04 T-m
 * d) 3.298E-04 T-m
 * e) 3.628E-04 T-m

8) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.673E-07 N
 * b) 2.940E-07 N
 * c) 3.234E-07 N
 * d) 3.558E-07 N
 * e) 3.913E-07 N

9) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.65E-04 s
 * b) 2.00E-04 s
 * c) 2.43E-04 s
 * d) 2.94E-04 s
 * e) 3.56E-04 s

10) A parallel plate capacitor with a capicatnce C=1.30E-06 F whose plates have an area A=1.10E+03 m2 and separation d=7.60E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.30E-04?


 * a) 4.842E+02 V/m
 * b) 5.326E+02 V/m
 * c) 5.858E+02 V/m
 * d) 6.444E+02 V/m
 * e) 7.089E+02 V/m

11) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a  35 mF inductor?


 * a) 2.422E+00 A
 * b) 2.664E+00 A
 * c) 2.930E+00 A
 * d) 3.224E+00 A
 * e) 3.546E+00 A

T9 O0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0631 T . It emerges after being deflected by 44&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 1.897E-07 s
 * b) 2.087E-07 s
 * c) 2.296E-07 s
 * d) 2.525E-07 s
 * e) 2.778E-07 s

2) A charged particle in a magnetic field of 3.820E-04 T is moving perpendicular to the magnetic field with a speed of 3.890E+05 m/s. What is the period of orbit if orbital radius is 0.718 m?


 * a) 8.713E-06 s
 * b) 9.584E-06 s
 * c) 1.054E-05 s
 * d) 1.160E-05 s
 * e) 1.276E-05 s

3) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.76 cm to z=+1.99 cm


 * a) 2.762E-04 T-m
 * b) 3.038E-04 T-m
 * c) 3.342E-04 T-m
 * d) 3.676E-04 T-m
 * e) 4.043E-04 T-m

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.89 kA, I2=1.19 kA, and I3=3.5 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 6.535E-03 T-m
 * b) 7.188E-03 T-m
 * c) 7.907E-03 T-m
 * d) 8.697E-03 T-m
 * e) 9.567E-03 T-m

5) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 6.581E-01 A
 * b) 7.239E-01 A
 * c) 7.963E-01 A
 * d) 8.759E-01 A
 * e) 9.635E-01 A

6) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 4.093E-04 s
 * b) 4.502E-04 s
 * c) 4.952E-04 s
 * d) 5.447E-04 s
 * e) 5.992E-04 s

7) A step-down transformer steps 12 kV down to 170 V. The high-voltage input is provided by a 140 &Omega; power line that carries 9 A of currentWhat is the output current (at the 170 V side ?)


 * a) 4.773E+02 A
 * b) 5.250E+02 A
 * c) 5.775E+02 A
 * d) 6.353E+02 A
 * e) 6.988E+02 A

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.517E+02 km
 * b) 1.669E+02 km
 * c) 1.835E+02 km
 * d) 2.019E+02 km
 * e) 2.221E+02 km

9) A parallel plate capacitor with a capicatnce C=4.90E-06 F whose plates have an area A=3.00E+03 m2 and separation d=5.40E-03 m is connected via a swith to a 10 &Omega; resistor and a battery of voltage V0=12 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.00E-04?


 * a) 1.841E-02 A
 * b) 2.026E-02 A
 * c) 2.228E-02 A
 * d) 2.451E-02 A
 * e) 2.696E-02 A

10) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 6.62E-10 Tesla
 * b) 8.33E-10 Tesla
 * c) 1.05E-09 Tesla
 * d) 1.32E-09 Tesla
 * e) 1.66E-09 Tesla

11) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.11E-11 Vs2m-1
 * b) 8.61E-11 Vs2m-1
 * c) 1.04E-10 Vs2m-1
 * d) 1.26E-10 Vs2m-1
 * e) 1.53E-10 Vs2m-1

T9 O1
1) A step-down transformer steps 19 kV down to 260 V. The high-voltage input is provided by a 290 &Omega; power line that carries 6 A of currentWhat is the output current (at the 260 V side ?)


 * a) 3.294E+02 A
 * b) 3.624E+02 A
 * c) 3.986E+02 A
 * d) 4.385E+02 A
 * e) 4.823E+02 A

2) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.003E+02 km
 * b) 1.103E+02 km
 * c) 1.213E+02 km
 * d) 1.335E+02 km
 * e) 1.468E+02 km

3) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 6.62E-10 Tesla
 * b) 8.33E-10 Tesla
 * c) 1.05E-09 Tesla
 * d) 1.32E-09 Tesla
 * e) 1.66E-09 Tesla

4) In an LC circuit, the self-inductance is 0.0776 H and the capacitance is 6.940E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.400E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 1.048E-03 s
 * b) 1.153E-03 s
 * c) 1.268E-03 s
 * d) 1.395E-03 s
 * e) 1.534E-03 s

5) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 1.791E-01 A
 * b) 1.970E-01 A
 * c) 2.167E-01 A
 * d) 2.384E-01 A
 * e) 2.622E-01 A

6) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.89 kA, I2=1.19 kA, and I3=3.5 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 6.535E-03 T-m
 * b) 7.188E-03 T-m
 * c) 7.907E-03 T-m
 * d) 8.697E-03 T-m
 * e) 9.567E-03 T-m

7) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=3.00E+03 m2 and separation d=7.10E-03 m is connected via a swith to a 78 &Omega; resistor and a battery of voltage V0=25 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.30E-03?


 * a) 2.998E-03 A
 * b) 3.298E-03 A
 * c) 3.628E-03 A
 * d) 3.991E-03 A
 * e) 4.390E-03 A

8) A solenoid has 7.170E+04 turns wound around a cylinder of diameter 1.56 cm and length 9 m. The current through the coils is 0.391 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.73 cm to z=+2.56 cm


 * a) 1.414E-04 T-m
 * b) 1.556E-04 T-m
 * c) 1.711E-04 T-m
 * d) 1.882E-04 T-m
 * e) 2.071E-04 T-m

9) A circlular capactitor of radius 4.8 m has a gap of 17 mm, and a charge of 73 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 9.17E-11 Vs2m-1
 * b) 1.11E-10 Vs2m-1
 * c) 1.35E-10 Vs2m-1
 * d) 1.63E-10 Vs2m-1
 * e) 1.98E-10 Vs2m-1

10) A charged particle in a magnetic field of 2.740E-04 T is moving perpendicular to the magnetic field with a speed of 1.390E+05 m/s. What is the period of orbit if orbital radius is 0.776 m?


 * a) 2.899E-05 s
 * b) 3.189E-05 s
 * c) 3.508E-05 s
 * d) 3.859E-05 s
 * e) 4.244E-05 s

11) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0327 T . It emerges after being deflected by 89&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 9.857E-07 s
 * b) 1.084E-06 s
 * c) 1.193E-06 s
 * d) 1.312E-06 s
 * e) 1.443E-06 s

T9 O2
1) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 2.609E+00 A
 * b) 2.870E+00 A
 * c) 3.157E+00 A
 * d) 3.473E+00 A
 * e) 3.820E+00 A

2) A circlular capactitor of radius 4.8 m has a gap of 9 mm, and a charge of 53 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.26E-09 Tesla
 * b) 4.11E-09 Tesla
 * c) 5.17E-09 Tesla
 * d) 6.51E-09 Tesla
 * e) 8.19E-09 Tesla

3) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?


 * a) 3.856E-04 s
 * b) 4.242E-04 s
 * c) 4.666E-04 s
 * d) 5.133E-04 s
 * e) 5.646E-04 s

4) A 56 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 72 kW?


 * a) 1.084E+02 km
 * b) 1.193E+02 km
 * c) 1.312E+02 km
 * d) 1.443E+02 km
 * e) 1.587E+02 km

5) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.78 kA, I2=2.61 kA, and I3=3.76 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.939E-03 T-m
 * b) 5.432E-03 T-m
 * c) 5.976E-03 T-m
 * d) 6.573E-03 T-m
 * e) 7.231E-03 T-m

6) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0631 T . It emerges after being deflected by 44&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 1.897E-07 s
 * b) 2.087E-07 s
 * c) 2.296E-07 s
 * d) 2.525E-07 s
 * e) 2.778E-07 s

7) A parallel plate capacitor with a capicatnce C=6.80E-06 F whose plates have an area A=6.60E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 62 &Omega; resistor and a battery of voltage V0=36 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * a) 8.288E-02 A
 * b) 9.117E-02 A
 * c) 1.003E-01 A
 * d) 1.103E-01 A
 * e) 1.213E-01 A

8) A solenoid has 9.560E+04 turns wound around a cylinder of diameter 1.18 cm and length 12 m. The current through the coils is 0.664 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;4.49 cm to z=+3.61 cm


 * a) 4.895E-04 T-m
 * b) 5.384E-04 T-m
 * c) 5.923E-04 T-m
 * d) 6.515E-04 T-m
 * e) 7.167E-04 T-m

9) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 &Omega; power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)


 * a) 3.938E+02 A
 * b) 4.331E+02 A
 * c) 4.764E+02 A
 * d) 5.241E+02 A
 * e) 5.765E+02 A

10) A circlular capactitor of radius 4.4 m has a gap of 16 mm, and a charge of 41 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 3.51E-11 Vs2m-1
 * b) 4.25E-11 Vs2m-1
 * c) 5.15E-11 Vs2m-1
 * d) 6.24E-11 Vs2m-1
 * e) 7.56E-11 Vs2m-1

11) A charged particle in a magnetic field of 4.970E-04 T is moving perpendicular to the magnetic field with a speed of 2.950E+05 m/s. What is the period of orbit if orbital radius is 0.344 m?


 * a) 7.327E-06 s
 * b) 8.060E-06 s
 * c) 8.865E-06 s
 * d) 9.752E-06 s
 * e) 1.073E-05 s

T9 P0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0883 T . It emerges after being deflected by 74&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 2.280E-07 s
 * b) 2.508E-07 s
 * c) 2.759E-07 s
 * d) 3.035E-07 s
 * e) 3.339E-07 s

2) A charged particle in a magnetic field of 2.740E-04 T is moving perpendicular to the magnetic field with a speed of 1.390E+05 m/s. What is the period of orbit if orbital radius is 0.776 m?


 * a) 2.899E-05 s
 * b) 3.189E-05 s
 * c) 3.508E-05 s
 * d) 3.859E-05 s
 * e) 4.244E-05 s

3) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?


 * a) 2.449E-10 N/m
 * b) 2.694E-10 N/m
 * c) 2.963E-10 N/m
 * d) 3.260E-10 N/m
 * e) 3.586E-10 N/m

4) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 4.028E-05 T
 * b) By= 4.431E-05 T
 * c) By= 4.874E-05 T
 * d) By= 5.361E-05 T
 * e) By= 5.897E-05 T

5) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 6.581E-01 A
 * b) 7.239E-01 A
 * c) 7.963E-01 A
 * d) 8.759E-01 A
 * e) 9.635E-01 A

6) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.28mm$$, and $$n=2.4$$. What is the volume of the washer?


 * a) 1.097E+00 cm3
 * b) 1.207E+00 cm3
 * c) 1.328E+00 cm3
 * d) 1.460E+00 cm3
 * e) 1.606E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 &Omega;, L= 4.20E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 1.081E+00 &rad;
 * b) 1.189E+00 &rad;
 * c) 1.308E+00 &rad;
 * d) 1.439E+00 &rad;
 * e) 1.583E+00 &rad;

8) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=4.20E+03 m2 and separation d=8.00E-03 m is connected via a swith to a 6 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.60E-05?


 * a) 7.253E+03 V/m
 * b) 7.978E+03 V/m
 * c) 8.776E+03 V/m
 * d) 9.653E+03 V/m
 * e) 1.062E+04 V/m

9) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * a) 7.693E+01 V
 * b) 8.463E+01 V
 * c) 9.309E+01 V
 * d) 1.024E+02 V
 * e) 1.126E+02 V

10) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.30E-09 Tesla
 * b) 4.15E-09 Tesla
 * c) 5.23E-09 Tesla
 * d) 6.58E-09 Tesla
 * e) 8.29E-09 Tesla

11) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 43 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 1.95E-04 s
 * b) 2.36E-04 s
 * c) 2.86E-04 s
 * d) 3.46E-04 s
 * e) 4.20E-04 s

T9 P1
1) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?


 * a) 1.283E-10 N/m
 * b) 1.411E-10 N/m
 * c) 1.552E-10 N/m
 * d) 1.708E-10 N/m
 * e) 1.878E-10 N/m

2) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 4.028E-05 T
 * b) By= 4.431E-05 T
 * c) By= 4.874E-05 T
 * d) By= 5.361E-05 T
 * e) By= 5.897E-05 T

3) A circlular capactitor of radius 4.1 m has a gap of 11 mm, and a charge of 51 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 3.40E-04 s
 * b) 4.12E-04 s
 * c) 4.99E-04 s
 * d) 6.05E-04 s
 * e) 7.33E-04 s

4) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 &Omega;, L= 8.20E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.146E-01 &rad;
 * b) 8.960E-01 &rad;
 * c) 9.856E-01 &rad;
 * d) 1.084E+00 &rad;
 * e) 1.193E+00 &rad;

5) A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m2 and separation d=6.40E-03 m is connected via a swith to a 54 &Omega; resistor and a battery of voltage V0=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?


 * a) 6.111E+01 V
 * b) 6.722E+01 V
 * c) 7.395E+01 V
 * d) 8.134E+01 V
 * e) 8.947E+01 V

6) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 3.661E+00 A
 * b) 4.028E+00 A
 * c) 4.430E+00 A
 * d) 4.873E+00 A
 * e) 5.361E+00 A

7) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.47mm$$, and $$n=2.8$$. What is the volume of the washer?


 * a) 8.932E-01 cm3
 * b) 9.825E-01 cm3
 * c) 1.081E+00 cm3
 * d) 1.189E+00 cm3
 * e) 1.308E+00 cm3

8) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0393 T . It emerges after being deflected by 49&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 4.105E-07 s
 * b) 4.515E-07 s
 * c) 4.967E-07 s
 * d) 5.464E-07 s
 * e) 6.010E-07 s

9) A circlular capactitor of radius 4 m has a gap of 13 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.62E-09 Tesla
 * b) 1.09E-08 Tesla
 * c) 1.37E-08 Tesla
 * d) 1.72E-08 Tesla
 * e) 2.17E-08 Tesla

10) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m2 and separation d=3.50E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?


 * a) 3.751E+03 V/m
 * b) 4.126E+03 V/m
 * c) 4.539E+03 V/m
 * d) 4.993E+03 V/m
 * e) 5.492E+03 V/m

11) A charged particle in a magnetic field of 1.480E-04 T is moving perpendicular to the magnetic field with a speed of 4.520E+05 m/s. What is the period of orbit if orbital radius is 0.4 m?


 * a) 5.560E-06 s
 * b) 6.116E-06 s
 * c) 6.728E-06 s
 * d) 7.401E-06 s
 * e) 8.141E-06 s

T9 P2
1) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * a) 1.118E+00 cm3
 * b) 1.229E+00 cm3
 * c) 1.352E+00 cm3
 * d) 1.487E+00 cm3
 * e) 1.636E+00 cm3

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0454 T . It emerges after being deflected by 74&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 4.878E-07 s
 * b) 5.366E-07 s
 * c) 5.903E-07 s
 * d) 6.493E-07 s
 * e) 7.143E-07 s

3) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 6.62E-05 s
 * b) 8.02E-05 s
 * c) 9.71E-05 s
 * d) 1.18E-04 s
 * e) 1.43E-04 s

4) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 &Omega;, L= 8.20E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.146E-01 &rad;
 * b) 8.960E-01 &rad;
 * c) 9.856E-01 &rad;
 * d) 1.084E+00 &rad;
 * e) 1.193E+00 &rad;

5) A charged particle in a magnetic field of 3.350E-04 T is moving perpendicular to the magnetic field with a speed of 4.350E+05 m/s. What is the period of orbit if orbital radius is 0.841 m?


 * a) 1.004E-05 s
 * b) 1.104E-05 s
 * c) 1.215E-05 s
 * d) 1.336E-05 s
 * e) 1.470E-05 s

6) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 6.581E-01 A
 * b) 7.239E-01 A
 * c) 7.963E-01 A
 * d) 8.759E-01 A
 * e) 9.635E-01 A

7) A parallel plate capacitor with a capicatnce C=2.00E-06 F whose plates have an area A=1.90E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=45 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.30E-04?


 * a) 3.223E+03 V/m
 * b) 3.546E+03 V/m
 * c) 3.900E+03 V/m
 * d) 4.290E+03 V/m
 * e) 4.719E+03 V/m

8) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.95E-09 Tesla
 * b) 4.97E-09 Tesla
 * c) 6.26E-09 Tesla
 * d) 7.88E-09 Tesla
 * e) 9.92E-09 Tesla

9) Three wires sit at the corners of a square of length 0.703 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.49 A, 1.32 A, 1.75 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 8.962E-05 T
 * b) By= 9.858E-05 T
 * c) By= 1.084E-04 T
 * d) By= 1.193E-04 T
 * e) By= 1.312E-04 T

10) A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 41 &Omega; resistor and a battery of voltage V0=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?


 * a) 6.755E+01 V
 * b) 7.431E+01 V
 * c) 8.174E+01 V
 * d) 8.991E+01 V
 * e) 9.890E+01 V

11) Two parallel wires each carry a 7.59 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.98 cm, 0.969 cm), while the other is located at (5.13 cm, 5.53 cm). What is the force per unit length between the wires?


 * a) 1.840E-10 N/m
 * b) 2.024E-10 N/m
 * c) 2.227E-10 N/m
 * d) 2.449E-10 N/m
 * e) 2.694E-10 N/m

T9 Q0
1) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.379 T magnetic field is directed 53&deg; away from the wire?


 * a) 1.001E+00 N/m
 * b) 1.101E+00 N/m
 * c) 1.211E+00 N/m
 * d) 1.332E+00 N/m
 * e) 1.465E+00 N/m

2) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?


 * a) 5.792E-06 s
 * b) 6.371E-06 s
 * c) 7.008E-06 s
 * d) 7.709E-06 s
 * e) 8.480E-06 s

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 2.812E-03 T-m
 * b) 3.093E-03 T-m
 * c) 3.402E-03 T-m
 * d) 3.742E-03 T-m
 * e) 4.117E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.432 m and $$B_{max}=\,$$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.277E+05 A
 * b) 3.604E+05 A
 * c) 3.965E+05 A
 * d) 4.361E+05 A
 * e) 4.797E+05 A

5) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 1.056E+00 A
 * b) 1.161E+00 A
 * c) 1.278E+00 A
 * d) 1.405E+00 A
 * e) 1.546E+00 A

6) A washer has an inner diameter of 2.3 cm and an outer diamter of 4.44 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.31mm$$, and $$n=2.66$$. What is the volume of the washer?


 * a) 1.089E+00 cm3
 * b) 1.198E+00 cm3
 * c) 1.318E+00 cm3
 * d) 1.449E+00 cm3
 * e) 1.594E+00 cm3

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=5 V. The resistance, inductance, and capacitance are R =0.27 &Omega;, L= 4.30E-03H, and C=2.20E-06 F, respectively.


 * a) Q = 1.238E+02
 * b) Q = 1.424E+02
 * c) Q = 1.637E+02
 * d) Q = 1.883E+02
 * e) Q = 2.165E+02

8) What is the radiation pressure on an object that is 8.30E+11 m away from the sun and has cross-sectional area of 0.097 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.928E-07 N/m2
 * b) 3.221E-07 N/m2
 * c) 3.543E-07 N/m2
 * d) 3.898E-07 N/m2
 * e) 4.287E-07 N/m2

9) A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 98 &Omega; resistor and a battery of voltage V0=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?


 * a) 5.050E+03 V/m
 * b) 5.555E+03 V/m
 * c) 6.111E+03 V/m
 * d) 6.722E+03 V/m
 * e) 7.394E+03 V/m

10) A circlular capactitor of radius 4 m has a gap of 13 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.62E-09 Tesla
 * b) 1.09E-08 Tesla
 * c) 1.37E-08 Tesla
 * d) 1.72E-08 Tesla
 * e) 2.17E-08 Tesla

11) A circlular capactitor of radius 3.4 m has a gap of 15 mm, and a charge of 63 &mu;C.  What is the electric field between the plates?


 * a) 1.62E+05 N/C (or V/m)
 * b) 1.96E+05 N/C (or V/m)
 * c) 2.37E+05 N/C (or V/m)
 * d) 2.88E+05 N/C (or V/m)
 * e) 3.48E+05 N/C (or V/m)

T9 Q1
1) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * a) 1.131E+00 N/m
 * b) 1.244E+00 N/m
 * c) 1.368E+00 N/m
 * d) 1.505E+00 N/m
 * e) 1.655E+00 N/m

2) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * a) 2.04E+04 N/C (or V/m)
 * b) 2.47E+04 N/C (or V/m)
 * c) 3.00E+04 N/C (or V/m)
 * d) 3.63E+04 N/C (or V/m)
 * e) 4.40E+04 N/C (or V/m)

3) A parallel plate capacitor with a capicatnce C=5.60E-06 F whose plates have an area A=2.00E+03 m2 and separation d=3.10E-03 m is connected via a swith to a 68 &Omega; resistor and a battery of voltage V0=73 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=8.50E-04?


 * a) 1.579E+04 V/m
 * b) 1.737E+04 V/m
 * c) 1.911E+04 V/m
 * d) 2.102E+04 V/m
 * e) 2.312E+04 V/m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.259 m and $$B_{max}=\,$$ 0.575 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.191 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.492E+05 A
 * b) 3.841E+05 A
 * c) 4.225E+05 A
 * d) 4.648E+05 A
 * e) 5.113E+05 A

5) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 &Omega;, L= 5.00E-03H, and C=3.20E-06 F, respectively.


 * a) Q = 1.300E+02
 * b) Q = 1.494E+02
 * c) Q = 1.719E+02
 * d) Q = 1.976E+02
 * e) Q = 2.273E+02

6) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 2.82E-09 Tesla
 * b) 3.54E-09 Tesla
 * c) 4.46E-09 Tesla
 * d) 5.62E-09 Tesla
 * e) 7.07E-09 Tesla

7) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.144E-07 N/m2
 * b) 2.358E-07 N/m2
 * c) 2.594E-07 N/m2
 * d) 2.854E-07 N/m2
 * e) 3.139E-07 N/m2

8) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 2.609E+00 A
 * b) 2.870E+00 A
 * c) 3.157E+00 A
 * d) 3.473E+00 A
 * e) 3.820E+00 A

9) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.57 kA, I2=0.708 kA, and I3=1.48 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.200E-03 T-m
 * b) 4.620E-03 T-m
 * c) 5.082E-03 T-m
 * d) 5.590E-03 T-m
 * e) 6.149E-03 T-m

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.39mm$$, and $$n=2.55$$. What is the volume of the washer?


 * a) 7.754E-01 cm3
 * b) 8.530E-01 cm3
 * c) 9.383E-01 cm3
 * d) 1.032E+00 cm3
 * e) 1.135E+00 cm3

11) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?


 * a) 2.730E-06 s
 * b) 3.003E-06 s
 * c) 3.303E-06 s
 * d) 3.633E-06 s
 * e) 3.997E-06 s

T9 Q2
1) A charged particle in a magnetic field of 1.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.330E+05 m/s. What is the period of orbit if orbital radius is 0.893 m?


 * a) 2.189E-05 s
 * b) 2.408E-05 s
 * c) 2.649E-05 s
 * d) 2.914E-05 s
 * e) 3.205E-05 s

2) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.315E-07 N/m2
 * b) 2.547E-07 N/m2
 * c) 2.801E-07 N/m2
 * d) 3.082E-07 N/m2
 * e) 3.390E-07 N/m2

3) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * a) 2.609E+00 A
 * b) 2.870E+00 A
 * c) 3.157E+00 A
 * d) 3.473E+00 A
 * e) 3.820E+00 A

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.386E-03 T-m
 * b) 4.825E-03 T-m
 * c) 5.307E-03 T-m
 * d) 5.838E-03 T-m
 * e) 6.421E-03 T-m

5) A long rigid wire carries a 3 A current. What is the magnetic force per unit length on the wire if a 0.534 T magnetic field is directed 18&deg; away from the wire?


 * a) 4.950E-01 N/m
 * b) 5.445E-01 N/m
 * c) 5.990E-01 N/m
 * d) 6.589E-01 N/m
 * e) 7.248E-01 N/m

6) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.568 m and $$B_{max}=\,$$ 0.214 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.387 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.382E+05 A
 * b) 3.720E+05 A
 * c) 4.092E+05 A
 * d) 4.502E+05 A
 * e) 4.952E+05 A

7) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 75 &mu;C.  What is the electric field between the plates?


 * a) 5.43E+04 N/C (or V/m)
 * b) 6.58E+04 N/C (or V/m)
 * c) 7.97E+04 N/C (or V/m)
 * d) 9.66E+04 N/C (or V/m)
 * e) 1.17E+05 N/C (or V/m)

8) A parallel plate capacitor with a capicatnce C=1.30E-06 F whose plates have an area A=1.10E+03 m2 and separation d=7.60E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.30E-04?


 * a) 4.842E+02 V/m
 * b) 5.326E+02 V/m
 * c) 5.858E+02 V/m
 * d) 6.444E+02 V/m
 * e) 7.089E+02 V/m

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=2 V. The resistance, inductance, and capacitance are R =0.25 &Omega;, L= 5.40E-03H, and C=3.20E-06 F, respectively.


 * a) Q = 9.395E+01
 * b) Q = 1.080E+02
 * c) Q = 1.242E+02
 * d) Q = 1.429E+02
 * e) Q = 1.643E+02

10) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.32E-09 Tesla
 * b) 1.05E-08 Tesla
 * c) 1.32E-08 Tesla
 * d) 1.66E-08 Tesla
 * e) 2.09E-08 Tesla

11) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.18 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.42mm$$, and $$n=2.62$$. What is the volume of the washer?


 * a) 1.351E+00 cm3
 * b) 1.486E+00 cm3
 * c) 1.635E+00 cm3
 * d) 1.798E+00 cm3
 * e) 1.978E+00 cm3

T9 R0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.011 T . It emerges after being deflected by 70&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 2.095E-06 s
 * b) 2.305E-06 s
 * c) 2.535E-06 s
 * d) 2.789E-06 s
 * e) 3.067E-06 s

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.232 m and a magneticfield of 1.1 T. What is their maximum kinetic energy?


 * a) 2.853E+00 MeV
 * b) 3.139E+00 MeV
 * c) 3.453E+00 MeV
 * d) 3.798E+00 MeV
 * e) 4.178E+00 MeV

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.208E-05 T
 * b) 1.329E-05 T
 * c) 1.462E-05 T
 * d) 1.608E-05 T
 * e) 1.769E-05 T

4) Three wires sit at the corners of a square of length 0.78 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.13 A, 1.35 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.282E-05 T
 * b) Bx= 6.910E-05 T
 * c) Bx= 7.601E-05 T
 * d) Bx= 8.361E-05 T
 * e) Bx= 9.198E-05 T

5) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.


 * a) 1.090E+04 V
 * b) 1.199E+04 V
 * c) 1.319E+04 V
 * d) 1.451E+04 V
 * e) 1.596E+04 V

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.67% of its maximum value if &epsilon; = 5.07 V, R = 7.8 &Omega;, and L = 4.39 H?


 * a) -1.047E+00 s
 * b) -1.152E+00 s
 * c) -1.267E+00 s
 * d) -1.393E+00 s
 * e) -1.533E+00 s

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 &Omega;, L= 4.60E-03H, and C=8.10E-04 F, respectively. What is the amplitude of the current?


 * a) 1.417E-01 A
 * b) 1.559E-01 A
 * c) 1.715E-01 A
 * d) 1.886E-01 A
 * e) 2.075E-01 A

8) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * a) 7.315E-02 A
 * b) 8.047E-02 A
 * c) 8.851E-02 A
 * d) 9.737E-02 A
 * e) 1.071E-01 A

9) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.096 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 4.373E-08 N
 * b) 4.810E-08 N
 * c) 5.291E-08 N
 * d) 5.820E-08 N
 * e) 6.402E-08 N

10) A circlular capactitor of radius 4.9 m has a gap of 11 mm, and a charge of 85 &mu;C.  What is the electric field between the plates?


 * a) 1.27E+05 N/C (or V/m)
 * b) 1.54E+05 N/C (or V/m)
 * c) 1.87E+05 N/C (or V/m)
 * d) 2.26E+05 N/C (or V/m)
 * e) 2.74E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.4 m has a gap of 17 mm, and a charge of 65 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.56E-11 Vs2m-1
 * b) 6.74E-11 Vs2m-1
 * c) 8.17E-11 Vs2m-1
 * d) 9.90E-11 Vs2m-1
 * e) 1.20E-10 Vs2m-1

T9 R1
1) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 8.969E-08 N
 * b) 9.866E-08 N
 * c) 1.085E-07 N
 * d) 1.194E-07 N
 * e) 1.313E-07 N

2) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 &Omega;, L= 4.60E-03H, and C=8.10E-04 F, respectively. What is the amplitude of the current?


 * a) 1.417E-01 A
 * b) 1.559E-01 A
 * c) 1.715E-01 A
 * d) 1.886E-01 A
 * e) 2.075E-01 A

3) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 21 &mu;C.  What is the electric field between the plates?


 * a) 6.16E+04 N/C (or V/m)
 * b) 7.47E+04 N/C (or V/m)
 * c) 9.05E+04 N/C (or V/m)
 * d) 1.10E+05 N/C (or V/m)
 * e) 1.33E+05 N/C (or V/m)

4) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.448 m and a magneticfield of 0.812 T. What is their maximum kinetic energy?


 * a) 5.798E+00 MeV
 * b) 6.377E+00 MeV
 * c) 7.015E+00 MeV
 * d) 7.717E+00 MeV
 * e) 8.488E+00 MeV

5) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if &epsilon; = 5.95 V, R = 7.26 &Omega;, and L = 1.29 H?


 * a) -3.114E-01 s
 * b) -3.425E-01 s
 * c) -3.767E-01 s
 * d) -4.144E-01 s
 * e) -4.559E-01 s

6) A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m2 and separation d=3.60E-03 m is connected via a swith to a 87 &Omega; resistor and a battery of voltage V0=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?


 * a) 8.320E-02 A
 * b) 9.152E-02 A
 * c) 1.007E-01 A
 * d) 1.107E-01 A
 * e) 1.218E-01 A

7) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 1.791E-05 T
 * b) 1.970E-05 T
 * c) 2.167E-05 T
 * d) 2.384E-05 T
 * e) 2.622E-05 T

8) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0279 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 7.270E-07 s
 * b) 7.997E-07 s
 * c) 8.797E-07 s
 * d) 9.676E-07 s
 * e) 1.064E-06 s

9) Calculate the motional emf induced along a 27.5 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.520E-05 Tesla magnetic field.


 * a) 8.074E+03 V
 * b) 8.882E+03 V
 * c) 9.770E+03 V
 * d) 1.075E+04 V
 * e) 1.182E+04 V

10) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.87E-11 Vs2m-1
 * b) 7.11E-11 Vs2m-1
 * c) 8.61E-11 Vs2m-1
 * d) 1.04E-10 Vs2m-1
 * e) 1.26E-10 Vs2m-1

11) Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.171E-05 T
 * b) Bx= 6.788E-05 T
 * c) Bx= 7.467E-05 T
 * d) Bx= 8.213E-05 T
 * e) Bx= 9.035E-05 T

T9 R2
1) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if &epsilon; = 5.95 V, R = 7.26 &Omega;, and L = 1.29 H?


 * a) -3.114E-01 s
 * b) -3.425E-01 s
 * c) -3.767E-01 s
 * d) -4.144E-01 s
 * e) -4.559E-01 s

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0775 T . It emerges after being deflected by 73&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 2.819E-07 s
 * b) 3.101E-07 s
 * c) 3.411E-07 s
 * d) 3.752E-07 s
 * e) 4.128E-07 s

3) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=1.00E+04 m2 and separation d=9.00E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * a) 6.394E-02 A
 * b) 7.033E-02 A
 * c) 7.736E-02 A
 * d) 8.510E-02 A
 * e) 9.361E-02 A

4) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.88 V. The resistance, inductance, and capacitance are R =7 &Omega;, L= 8.00E-03H, and C=5.50E-04 F, respectively. What is the amplitude of the current?


 * a) 1.143E-01 A
 * b) 1.257E-01 A
 * c) 1.383E-01 A
 * d) 1.521E-01 A
 * e) 1.673E-01 A

5) A circlular capactitor of radius 4.3 m has a gap of 7 mm, and a charge of 47 &mu;C.  What is the electric field between the plates?


 * a) 7.54E+04 N/C (or V/m)
 * b) 9.14E+04 N/C (or V/m)
 * c) 1.11E+05 N/C (or V/m)
 * d) 1.34E+05 N/C (or V/m)
 * e) 1.63E+05 N/C (or V/m)

6) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.157 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?


 * a) 8.608E-01 MeV
 * b) 9.468E-01 MeV
 * c) 1.042E+00 MeV
 * d) 1.146E+00 MeV
 * e) 1.260E+00 MeV

7) What is the radiation force on an object that is 7.40E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.063E-08 N
 * b) 2.270E-08 N
 * c) 2.497E-08 N
 * d) 2.746E-08 N
 * e) 3.021E-08 N

8) Three wires sit at the corners of a square of length 0.518 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.31 A, 1.32 A, 1.62 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.013E-05 T
 * b) Bx= 6.614E-05 T
 * c) Bx= 7.275E-05 T
 * d) Bx= 8.003E-05 T
 * e) Bx= 8.803E-05 T

9) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 3.33 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 2.202E-05 T
 * b) 2.422E-05 T
 * c) 2.664E-05 T
 * d) 2.930E-05 T
 * e) 3.223E-05 T

10) Calculate the motional emf induced along a 21.3 km conductor moving at an orbital speed of 7.75 km/s perpendicular to Earth's 5.320E-05 Tesla magnetic field.


 * a) 6.598E+03 V
 * b) 7.258E+03 V
 * c) 7.984E+03 V
 * d) 8.782E+03 V
 * e) 9.660E+03 V

11) A circlular capactitor of radius 4.3 m has a gap of 11 mm, and a charge of 66 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 6.85E-11 Vs2m-1
 * b) 8.29E-11 Vs2m-1
 * c) 1.00E-10 Vs2m-1
 * d) 1.22E-10 Vs2m-1
 * e) 1.47E-10 Vs2m-1

T9 S0
1) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.080E-06 V
 * b) 1.188E-06 V
 * c) 1.306E-06 V
 * d) 1.437E-06 V
 * e) 1.581E-06 V

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0172 T . It emerges after being deflected by 85&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 1.627E-06 s
 * b) 1.790E-06 s
 * c) 1.969E-06 s
 * d) 2.166E-06 s
 * e) 2.382E-06 s

3) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 4.028E-05 T
 * b) By= 4.431E-05 T
 * c) By= 4.874E-05 T
 * d) By= 5.361E-05 T
 * e) By= 5.897E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 9.310E+02
 * b) $$\chi \text{ (chi) }=$$ 1.024E+03
 * c) $$\chi \text{ (chi) }=$$ 1.126E+03
 * d) $$\chi \text{ (chi) }=$$ 1.239E+03
 * e) $$\chi \text{ (chi) }=$$ 1.363E+03

5) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm.  A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 1.215E-04 V
 * b) 1.337E-04 V
 * c) 1.470E-04 V
 * d) 1.617E-04 V
 * e) 1.779E-04 V

6) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?


 * a) 2.914E-01 H
 * b) 3.205E-01 H
 * c) 3.526E-01 H
 * d) 3.878E-01 H
 * e) 4.266E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 &Omega;, L= 7.70E-03H, and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 1.329E+00 &rad;
 * b) 1.462E+00 &rad;
 * c) 1.608E+00 &rad;
 * d) 1.769E+00 &rad;
 * e) 1.946E+00 &rad;

8) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * a) 1.418E+02 km
 * b) 1.560E+02 km
 * c) 1.716E+02 km
 * d) 1.887E+02 km
 * e) 2.076E+02 km

9) A parallel plate capacitor with a capicatnce C=6.60E-06 F whose plates have an area A=4.90E+03 m2 and separation d=6.60E-03 m is connected via a swith to a 20 &Omega; resistor and a battery of voltage V0=59 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.70E-04?


 * a) 8.138E-01 A
 * b) 8.952E-01 A
 * c) 9.847E-01 A
 * d) 1.083E+00 A
 * e) 1.191E+00 A

10) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 62 &mu;C.  What is the electric field between the plates?


 * a) 9.50E+04 N/C (or V/m)
 * b) 1.15E+05 N/C (or V/m)
 * c) 1.39E+05 N/C (or V/m)
 * d) 1.69E+05 N/C (or V/m)
 * e) 2.05E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.1 m has a gap of 11 mm, and a charge of 51 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 3.40E-04 s
 * b) 4.12E-04 s
 * c) 4.99E-04 s
 * d) 6.05E-04 s
 * e) 7.33E-04 s

T9 S1
1) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?


 * a) 2.549E-01 H
 * b) 2.804E-01 H
 * c) 3.084E-01 H
 * d) 3.392E-01 H
 * e) 3.732E-01 H

2) The current through the windings of a solenoid with n= 2.460E+03 turns per meter is changing at a rate dI/dt=7 A/s. The solenoid is 87 cm long and has a cross-sectional diameter of 3.32 cm.  A small coil consisting of N=38turns wraped in a circle of diameter 1.29 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 7.340E-05 V
 * b) 8.075E-05 V
 * c) 8.882E-05 V
 * d) 9.770E-05 V
 * e) 1.075E-04 V

3) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 &Omega;, L= 9.50E-03H, and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.646E-01 &rad;
 * b) 9.511E-01 &rad;
 * c) 1.046E+00 &rad;
 * d) 1.151E+00 &rad;
 * e) 1.266E+00 &rad;

4) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=3.00E+03 m2 and separation d=7.10E-03 m is connected via a swith to a 78 &Omega; resistor and a battery of voltage V0=25 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.30E-03?


 * a) 2.998E-03 A
 * b) 3.298E-03 A
 * c) 3.628E-03 A
 * d) 3.991E-03 A
 * e) 4.390E-03 A

5) A 59 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 76 kW?


 * a) 1.008E+02 km
 * b) 1.109E+02 km
 * c) 1.219E+02 km
 * d) 1.341E+02 km
 * e) 1.475E+02 km

6) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * e) $$\chi \text{ (chi) }=$$ 1.907E+03

7) The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.648E-06 V
 * b) 1.813E-06 V
 * c) 1.994E-06 V
 * d) 2.194E-06 V
 * e) 2.413E-06 V

8) A circlular capactitor of radius 3.6 m has a gap of 8 mm, and a charge of 53 &mu;C.  What is the electric field between the plates?


 * a) 6.82E+04 N/C (or V/m)
 * b) 8.27E+04 N/C (or V/m)
 * c) 1.00E+05 N/C (or V/m)
 * d) 1.21E+05 N/C (or V/m)
 * e) 1.47E+05 N/C (or V/m)

9) Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 7.576E-05 T
 * b) By= 8.333E-05 T
 * c) By= 9.167E-05 T
 * d) By= 1.008E-04 T
 * e) By= 1.109E-04 T

10) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.65E-04 s
 * b) 2.00E-04 s
 * c) 2.43E-04 s
 * d) 2.94E-04 s
 * e) 3.56E-04 s

11) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0243 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 1.222E-06 s
 * b) 1.344E-06 s
 * c) 1.479E-06 s
 * d) 1.627E-06 s
 * e) 1.789E-06 s

T9 S2
1) A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m2 and separation d=3.60E-03 m is connected via a swith to a 87 &Omega; resistor and a battery of voltage V0=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?


 * a) 8.320E-02 A
 * b) 9.152E-02 A
 * c) 1.007E-01 A
 * d) 1.107E-01 A
 * e) 1.218E-01 A

2) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 &Omega;, L= 2.80E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.759E-01 &rad;
 * b) 9.635E-01 &rad;
 * c) 1.060E+00 &rad;
 * d) 1.166E+00 &rad;
 * e) 1.282E+00 &rad;

3) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 84 kW?


 * a) 9.780E+01 km
 * b) 1.076E+02 km
 * c) 1.183E+02 km
 * d) 1.302E+02 km
 * e) 1.432E+02 km

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.092E+03
 * b) $$\chi \text{ (chi) }=$$ 1.201E+03
 * c) $$\chi \text{ (chi) }=$$ 1.321E+03
 * d) $$\chi \text{ (chi) }=$$ 1.454E+03
 * e) $$\chi \text{ (chi) }=$$ 1.599E+03

5) The silver ribbon shown are a=4.12 cm, b=3.32 cm, and c= 1.46 cm. The current carries a current of 120 A and it lies in a uniform magnetic field of 1.39 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.209E-06 V
 * b) 1.329E-06 V
 * c) 1.462E-06 V
 * d) 1.609E-06 V
 * e) 1.770E-06 V

6) An induced emf of 1.86V is measured across a coil of 59 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.58A in 0.89s. What is the self-inductance of the coil?


 * a) 4.821E-01 H
 * b) 5.303E-01 H
 * c) 5.833E-01 H
 * d) 6.416E-01 H
 * e) 7.058E-01 H

7) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0837 T . It emerges after being deflected by 41&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 1.212E-07 s
 * b) 1.333E-07 s
 * c) 1.466E-07 s
 * d) 1.613E-07 s
 * e) 1.774E-07 s

8) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 62 &mu;C.  What is the electric field between the plates?


 * a) 9.50E+04 N/C (or V/m)
 * b) 1.15E+05 N/C (or V/m)
 * c) 1.39E+05 N/C (or V/m)
 * d) 1.69E+05 N/C (or V/m)
 * e) 2.05E+05 N/C (or V/m)

9) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * a) 1.066E-04 V
 * b) 1.173E-04 V
 * c) 1.290E-04 V
 * d) 1.419E-04 V
 * e) 1.561E-04 V

10) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 6.62E-05 s
 * b) 8.02E-05 s
 * c) 9.71E-05 s
 * d) 1.18E-04 s
 * e) 1.43E-04 s

11) Three wires sit at the corners of a square of length 0.495 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 1.205E-04 T
 * b) By= 1.325E-04 T
 * c) By= 1.458E-04 T
 * d) By= 1.604E-04 T
 * e) By= 1.764E-04 T

T9 T0
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.504 T magnetic field is directed 70&deg; away from the wire?


 * a) 2.348E+00 N/m
 * b) 2.583E+00 N/m
 * c) 2.842E+00 N/m
 * d) 3.126E+00 N/m
 * e) 3.438E+00 N/m

2) The silver ribbon shown are a=4.81 cm, b=3.96 cm, and c= 1.3 cm. The current carries a current of 274 A and it lies in a uniform magnetic field of 3.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 7.202E-06 V
 * b) 7.922E-06 V
 * c) 8.714E-06 V
 * d) 9.586E-06 V
 * e) 1.054E-05 V

3) Three wires sit at the corners of a square of length 0.686 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.28 A, 1.27 A, 1.61 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 5.409E-05 T
 * b) Bx= 5.950E-05 T
 * c) Bx= 6.545E-05 T
 * d) Bx= 7.200E-05 T
 * e) Bx= 7.920E-05 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.547 m and $$B_{max}=\,$$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.158 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 1.751E+05 A
 * b) 1.927E+05 A
 * c) 2.119E+05 A
 * d) 2.331E+05 A
 * e) 2.564E+05 A

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * a) 1.605E-04 V/m
 * b) 1.766E-04 V/m
 * c) 1.942E-04 V/m
 * d) 2.136E-04 V/m
 * e) 2.350E-04 V/m

6) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.47mm$$, and $$n=2.8$$. What is the volume of the washer?


 * a) 8.932E-01 cm3
 * b) 9.825E-01 cm3
 * c) 1.081E+00 cm3
 * d) 1.189E+00 cm3
 * e) 1.308E+00 cm3

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 &Omega;, L= 5.20E-03H, and C=2.90E-06 F, respectively.


 * a) Q = 2.287E+02
 * b) Q = 2.630E+02
 * c) Q = 3.025E+02
 * d) Q = 3.478E+02
 * e) Q = 4.000E+02

8) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.392E-06 N/m2
 * b) 2.631E-06 N/m2
 * c) 2.894E-06 N/m2
 * d) 3.184E-06 N/m2
 * e) 3.502E-06 N/m2

9) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * a) 1.753E+02 km
 * b) 1.928E+02 km
 * c) 2.121E+02 km
 * d) 2.333E+02 km
 * e) 2.567E+02 km

10) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * a) 4.55E+04 N/C (or V/m)
 * b) 5.52E+04 N/C (or V/m)
 * c) 6.68E+04 N/C (or V/m)
 * d) 8.10E+04 N/C (or V/m)
 * e) 9.81E+04 N/C (or V/m)

11) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 61 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.67E-11 Vs2m-1
 * b) 9.29E-11 Vs2m-1
 * c) 1.13E-10 Vs2m-1
 * d) 1.36E-10 Vs2m-1
 * e) 1.65E-10 Vs2m-1

T9 T1
1) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 89 &mu;C.  What is the electric field between the plates?


 * a) 1.93E+05 N/C (or V/m)
 * b) 2.34E+05 N/C (or V/m)
 * c) 2.83E+05 N/C (or V/m)
 * d) 3.43E+05 N/C (or V/m)
 * e) 4.16E+05 N/C (or V/m)

2) The silver ribbon shown are a=3.6 cm, b=2.68 cm, and c= 1.13 cm. The current carries a current of 97 A and it lies in a uniform magnetic field of 1.89 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.560E-06 V
 * b) 1.716E-06 V
 * c) 1.888E-06 V
 * d) 2.077E-06 V
 * e) 2.284E-06 V

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * a) Q = 1.300E+02
 * b) Q = 1.495E+02
 * c) Q = 1.719E+02
 * d) Q = 1.976E+02
 * e) Q = 2.273E+02

4) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23&deg; away from the wire?


 * a) 5.205E-01 N/m
 * b) 5.725E-01 N/m
 * c) 6.297E-01 N/m
 * d) 6.927E-01 N/m
 * e) 7.620E-01 N/m

5) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.392E-06 N/m2
 * b) 2.631E-06 N/m2
 * c) 2.894E-06 N/m2
 * d) 3.184E-06 N/m2
 * e) 3.502E-06 N/m2

6) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.18 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.42mm$$, and $$n=2.62$$. What is the volume of the washer?


 * a) 1.351E+00 cm3
 * b) 1.486E+00 cm3
 * c) 1.635E+00 cm3
 * d) 1.798E+00 cm3
 * e) 1.978E+00 cm3

7) Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 8.371E-05 T
 * b) Bx= 9.208E-05 T
 * c) Bx= 1.013E-04 T
 * d) Bx= 1.114E-04 T
 * e) Bx= 1.226E-04 T

8) A 55 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 93 kW?


 * a) 1.270E+02 km
 * b) 1.397E+02 km
 * c) 1.537E+02 km
 * d) 1.690E+02 km
 * e) 1.859E+02 km

9) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 7.28E-11 Vs2m-1
 * b) 8.82E-11 Vs2m-1
 * c) 1.07E-10 Vs2m-1
 * d) 1.29E-10 Vs2m-1
 * e) 1.57E-10 Vs2m-1

10) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?


 * a) 6.182E-04 V/m
 * b) 6.801E-04 V/m
 * c) 7.481E-04 V/m
 * d) 8.229E-04 V/m
 * e) 9.052E-04 V/m

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.407 m and $$B_{max}=\,$$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.196 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.583E+05 A
 * b) 3.941E+05 A
 * c) 4.335E+05 A
 * d) 4.769E+05 A
 * e) 5.246E+05 A

T9 T2
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23&deg; away from the wire?


 * a) 5.205E-01 N/m
 * b) 5.725E-01 N/m
 * c) 6.297E-01 N/m
 * d) 6.927E-01 N/m
 * e) 7.620E-01 N/m

2) A circlular capactitor of radius 4.3 m has a gap of 11 mm, and a charge of 66 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 6.85E-11 Vs2m-1
 * b) 8.29E-11 Vs2m-1
 * c) 1.00E-10 Vs2m-1
 * d) 1.22E-10 Vs2m-1
 * e) 1.47E-10 Vs2m-1

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 &Omega;, L= 4.20E-03H, and C=3.70E-06 F, respectively.


 * a) Q = 7.135E+01
 * b) Q = 8.205E+01
 * c) Q = 9.435E+01
 * d) Q = 1.085E+02
 * e) Q = 1.248E+02

4) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.517E+02 km
 * b) 1.669E+02 km
 * c) 1.835E+02 km
 * d) 2.019E+02 km
 * e) 2.221E+02 km

5) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$23 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?


 * a) 1.426E-03 V/m
 * b) 1.568E-03 V/m
 * c) 1.725E-03 V/m
 * d) 1.897E-03 V/m
 * e) 2.087E-03 V/m

6) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.547 m and $$B_{max}=\,$$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.158 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 1.751E+05 A
 * b) 1.927E+05 A
 * c) 2.119E+05 A
 * d) 2.331E+05 A
 * e) 2.564E+05 A

7) A washer has an inner diameter of 2.12 cm and an outer diamter of 4.47 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.7mm$$, and $$n=2.72$$. What is the volume of the washer?


 * a) 1.228E+00 cm3
 * b) 1.351E+00 cm3
 * c) 1.486E+00 cm3
 * d) 1.634E+00 cm3
 * e) 1.798E+00 cm3

8) The silver ribbon shown are a=3.47 cm, b=2.98 cm, and c= 0.681 cm. The current carries a current of 289 A and it lies in a uniform magnetic field of 3.37 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.375E-05 V
 * b) 1.513E-05 V
 * c) 1.664E-05 V
 * d) 1.831E-05 V
 * e) 2.014E-05 V

9) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 &mu;C.  What is the electric field between the plates?


 * a) 1.92E+05 N/C (or V/m)
 * b) 2.32E+05 N/C (or V/m)
 * c) 2.81E+05 N/C (or V/m)
 * d) 3.41E+05 N/C (or V/m)
 * e) 4.13E+05 N/C (or V/m)

10) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 6.669E-07 N/m2
 * b) 7.336E-07 N/m2
 * c) 8.069E-07 N/m2
 * d) 8.876E-07 N/m2
 * e) 9.764E-07 N/m2

11) Three wires sit at the corners of a square of length 0.687 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.134E-05 T
 * b) Bx= 7.847E-05 T
 * c) Bx= 8.632E-05 T
 * d) Bx= 9.495E-05 T
 * e) Bx= 1.044E-04 T

T9 U0
1) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.394 T magnetic field is directed 14&deg; away from the wire?


 * a) 6.302E-01 N/m
 * b) 6.932E-01 N/m
 * c) 7.625E-01 N/m
 * d) 8.388E-01 N/m
 * e) 9.227E-01 N/m

2) A circular current loop of radius 1.29 cm carries a current of 1.75 mA. What is the magnitude of the torque if the dipole is oriented at 24 &deg; to a uniform magnetic fied of 0.156 T?


 * a) 5.805E-08 N m
 * b) 6.386E-08 N m
 * c) 7.024E-08 N m
 * d) 7.727E-08 N m
 * e) 8.499E-08 N m

3) A wire carries a current of 293 A in a circular arc with radius 1.75 cm swept through 71 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * a) 4.652E+00 Tesla
 * b) 5.117E+00 Tesla
 * c) 5.629E+00 Tesla
 * d) 6.192E+00 Tesla
 * e) 6.811E+00 Tesla

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.58 kA, I2=1.11 kA, and I3=2.47 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.092E-03 T-m
 * b) 4.501E-03 T-m
 * c) 4.951E-03 T-m
 * d) 5.446E-03 T-m
 * e) 5.991E-03 T-m

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.11 T and $$\omega=$$1.150E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.171 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 2.887E+03 V
 * b) 3.176E+03 V
 * c) 3.493E+03 V
 * d) 3.843E+03 V
 * e) 4.227E+03 V

6) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.67mm$$, and $$n=2.56$$. What is the volume of the washer?


 * a) 1.570E+00 cm3
 * b) 1.727E+00 cm3
 * c) 1.900E+00 cm3
 * d) 2.090E+00 cm3
 * e) 2.299E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 5.50E+04 Hz and an amplitude of 2 V. If R =8 &Omega;, L= 9.60E-03H, and C=8.30E-06 F, what is the rms power transferred to the resistor?


 * a) 4.347E-05 Watts
 * b) 4.782E-05 Watts
 * c) 5.260E-05 Watts
 * d) 5.786E-05 Watts
 * e) 6.364E-05 Watts

8) A 47 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 90 kW?


 * a) 1.799E+02 km
 * b) 1.979E+02 km
 * c) 2.177E+02 km
 * d) 2.394E+02 km
 * e) 2.634E+02 km

9) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.022 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 4.555E-07 N/m2
 * b) 5.010E-07 N/m2
 * c) 5.511E-07 N/m2
 * d) 6.063E-07 N/m2
 * e) 6.669E-07 N/m2

10) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 84 &mu;C.  What is the electric field between the plates?


 * a) 1.37E+05 N/C (or V/m)
 * b) 1.66E+05 N/C (or V/m)
 * c) 2.01E+05 N/C (or V/m)
 * d) 2.43E+05 N/C (or V/m)
 * e) 2.95E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.30E-09 Tesla
 * b) 4.15E-09 Tesla
 * c) 5.23E-09 Tesla
 * d) 6.58E-09 Tesla
 * e) 8.29E-09 Tesla

T9 U1
1) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * a) 4.55E+04 N/C (or V/m)
 * b) 5.52E+04 N/C (or V/m)
 * c) 6.68E+04 N/C (or V/m)
 * d) 8.10E+04 N/C (or V/m)
 * e) 9.81E+04 N/C (or V/m)

2) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.46 kA, I2=2.14 kA, and I3=4.44 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.943E-03 T-m
 * b) 5.438E-03 T-m
 * c) 5.982E-03 T-m
 * d) 6.580E-03 T-m
 * e) 7.238E-03 T-m

3) A wire carries a current of 269 A in a circular arc with radius 2.35 cm swept through 36 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * a) 1.613E+00 Tesla
 * b) 1.774E+00 Tesla
 * c) 1.951E+00 Tesla
 * d) 2.146E+00 Tesla
 * e) 2.361E+00 Tesla

4) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * a) 2.094E+02 km
 * b) 2.304E+02 km
 * c) 2.534E+02 km
 * d) 2.788E+02 km
 * e) 3.066E+02 km

5) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.28mm$$, and $$n=2.4$$. What is the volume of the washer?


 * a) 1.097E+00 cm3
 * b) 1.207E+00 cm3
 * c) 1.328E+00 cm3
 * d) 1.460E+00 cm3
 * e) 1.606E+00 cm3

6) The output of an ac generator connected to an RLC series combination has a frequency of 5.00E+04 Hz and an amplitude of 5 V. If R =6 &Omega;, L= 2.50E-03H, and C=5.20E-06 F, what is the rms power transferred to the resistor?


 * a) 5.097E-03 Watts
 * b) 5.607E-03 Watts
 * c) 6.167E-03 Watts
 * d) 6.784E-03 Watts
 * e) 7.463E-03 Watts

7) A circular current loop of radius 1.17 cm carries a current of 3.68 mA. What is the magnitude of the torque if the dipole is oriented at 55 &deg; to a uniform magnetic fied of 0.179 T?


 * a) 1.585E-07 N m
 * b) 1.743E-07 N m
 * c) 1.918E-07 N m
 * d) 2.110E-07 N m
 * e) 2.321E-07 N m

8) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.88 T magnetic field is directed 47&deg; away from the wire?


 * a) 4.096E+00 N/m
 * b) 4.505E+00 N/m
 * c) 4.956E+00 N/m
 * d) 5.451E+00 N/m
 * e) 5.996E+00 N/m

9) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$2.25 T and $$\omega=$$8.280E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 2.657E+04 V
 * b) 2.923E+04 V
 * c) 3.215E+04 V
 * d) 3.537E+04 V
 * e) 3.890E+04 V

10) A circlular capactitor of radius 4.3 m has a gap of 15 mm, and a charge of 21 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 1.62E-09 Tesla
 * b) 2.04E-09 Tesla
 * c) 2.57E-09 Tesla
 * d) 3.23E-09 Tesla
 * e) 4.07E-09 Tesla

11) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.315E-07 N/m2
 * b) 2.547E-07 N/m2
 * c) 2.801E-07 N/m2
 * d) 3.082E-07 N/m2
 * e) 3.390E-07 N/m2

T9 U2
1) The output of an ac generator connected to an RLC series combination has a frequency of 3.50E+04 Hz and an amplitude of 8 V. If R =7 &Omega;, L= 9.40E-03H, and C=8.50E-06 F, what is the rms power transferred to the resistor?


 * a) 2.111E-03 Watts
 * b) 2.323E-03 Watts
 * c) 2.555E-03 Watts
 * d) 2.810E-03 Watts
 * e) 3.091E-03 Watts

2) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 6.62E-10 Tesla
 * b) 8.33E-10 Tesla
 * c) 1.05E-09 Tesla
 * d) 1.32E-09 Tesla
 * e) 1.66E-09 Tesla

3) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * a) 1.418E+02 km
 * b) 1.560E+02 km
 * c) 1.716E+02 km
 * d) 1.887E+02 km
 * e) 2.076E+02 km

4) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.75 T and $$\omega=$$9.800E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.22 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 4.198E+04 V
 * b) 4.618E+04 V
 * c) 5.080E+04 V
 * d) 5.588E+04 V
 * e) 6.147E+04 V

5) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 2.315E-07 N/m2
 * b) 2.547E-07 N/m2
 * c) 2.801E-07 N/m2
 * d) 3.082E-07 N/m2
 * e) 3.390E-07 N/m2

6) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.31 kA, I2=1.16 kA, and I3=2.13 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 2.815E-03 T-m
 * b) 3.097E-03 T-m
 * c) 3.406E-03 T-m
 * d) 3.747E-03 T-m
 * e) 4.122E-03 T-m

7) A washer has an inner diameter of 2.16 cm and an outer diamter of 4.82 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.22mm$$, and $$n=2.8$$. What is the volume of the washer?


 * a) 1.342E+00 cm3
 * b) 1.477E+00 cm3
 * c) 1.624E+00 cm3
 * d) 1.787E+00 cm3
 * e) 1.965E+00 cm3

8) A wire carries a current of 297 A in a circular arc with radius 2.31 cm swept through 75 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * a) 3.774E+00 Tesla
 * b) 4.151E+00 Tesla
 * c) 4.566E+00 Tesla
 * d) 5.023E+00 Tesla
 * e) 5.525E+00 Tesla

9) A circlular capactitor of radius 3.6 m has a gap of 8 mm, and a charge of 53 &mu;C.  What is the electric field between the plates?


 * a) 6.82E+04 N/C (or V/m)
 * b) 8.27E+04 N/C (or V/m)
 * c) 1.00E+05 N/C (or V/m)
 * d) 1.21E+05 N/C (or V/m)
 * e) 1.47E+05 N/C (or V/m)

10) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * a) 1.131E+00 N/m
 * b) 1.244E+00 N/m
 * c) 1.368E+00 N/m
 * d) 1.505E+00 N/m
 * e) 1.655E+00 N/m

11) A circular current loop of radius 1.67 cm carries a current of 3.81 mA. What is the magnitude of the torque if the dipole is oriented at 40 &deg; to a uniform magnetic fied of 0.884 T?


 * a) 1.568E-06 N m
 * b) 1.724E-06 N m
 * c) 1.897E-06 N m
 * d) 2.087E-06 N m
 * e) 2.295E-06 N m

T9 V0
1) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.83 T magnetic field is directed 22&deg; away from the wire?


 * a) 1.062E+00 N/m
 * b) 1.168E+00 N/m
 * c) 1.285E+00 N/m
 * d) 1.413E+00 N/m
 * e) 1.555E+00 N/m

2) The silver ribbon shown are a=3.84 cm, b=3.45 cm, and c= 1.38 cm. The current carries a current of 92 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 7.153E-07 V
 * b) 7.869E-07 V
 * c) 8.655E-07 V
 * d) 9.521E-07 V
 * e) 1.047E-06 V

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.46 kA, I2=2.14 kA, and I3=4.44 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.943E-03 T-m
 * b) 5.438E-03 T-m
 * c) 5.982E-03 T-m
 * d) 6.580E-03 T-m
 * e) 7.238E-03 T-m

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?


 * a) 1.784E-05 T
 * b) 1.963E-05 T
 * c) 2.159E-05 T
 * d) 2.375E-05 T
 * e) 2.613E-05 T

5) A long solenoid has a radius of 0.749 m and 62 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$25 s&minus;1.What is the induced electric fied at a distance 0.139 m from the axis at time t=0.071 s ?


 * a) 2.065E-04 V/m
 * b) 2.271E-04 V/m
 * c) 2.499E-04 V/m
 * d) 2.748E-04 V/m
 * e) 3.023E-04 V/m

6) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * a) 1.118E+00 cm3
 * b) 1.229E+00 cm3
 * c) 1.352E+00 cm3
 * d) 1.487E+00 cm3
 * e) 1.636E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 &Omega;, L= 2.80E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 8.759E-01 &rad;
 * b) 9.635E-01 &rad;
 * c) 1.060E+00 &rad;
 * d) 1.166E+00 &rad;
 * e) 1.282E+00 &rad;

8) A 42 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * a) 1.641E+02 km
 * b) 1.805E+02 km
 * c) 1.986E+02 km
 * d) 2.184E+02 km
 * e) 2.403E+02 km

9) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=2.70E+03 m2 and separation d=6.30E-03 m is connected via a swith to a 4 &Omega; resistor and a battery of voltage V0=7 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-05?


 * a) 6.252E+00 V
 * b) 6.878E+00 V
 * c) 7.565E+00 V
 * d) 8.322E+00 V
 * e) 9.154E+00 V

10) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 1.16E-04 s
 * b) 1.41E-04 s
 * c) 1.71E-04 s
 * d) 2.07E-04 s
 * e) 2.50E-04 s

11) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 8.75E-12 Vs2m-1
 * b) 1.06E-11 Vs2m-1
 * c) 1.28E-11 Vs2m-1
 * d) 1.56E-11 Vs2m-1
 * e) 1.88E-11 Vs2m-1

T9 V1
1) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$25 s&minus;1.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?


 * a) 5.150E-04 V/m
 * b) 5.665E-04 V/m
 * c) 6.232E-04 V/m
 * d) 6.855E-04 V/m
 * e) 7.540E-04 V/m

2) A circlular capactitor of radius 4.2 m has a gap of 18 mm, and a charge of 97 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 1.91E-04 s
 * b) 2.31E-04 s
 * c) 2.80E-04 s
 * d) 3.39E-04 s
 * e) 4.11E-04 s

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.31 kA, I2=1.16 kA, and I3=2.13 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 2.815E-03 T-m
 * b) 3.097E-03 T-m
 * c) 3.406E-03 T-m
 * d) 3.747E-03 T-m
 * e) 4.122E-03 T-m

4) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.893 T magnetic field is directed 66&deg; away from the wire?


 * a) 2.697E+00 N/m
 * b) 2.967E+00 N/m
 * c) 3.263E+00 N/m
 * d) 3.590E+00 N/m
 * e) 3.948E+00 N/m

5) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.003E+02 km
 * b) 1.103E+02 km
 * c) 1.213E+02 km
 * d) 1.335E+02 km
 * e) 1.468E+02 km

6) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.208E-05 T
 * b) 1.329E-05 T
 * c) 1.462E-05 T
 * d) 1.608E-05 T
 * e) 1.769E-05 T

7) The output of an ac generator connected to an RLC series combination has a frequency of 890 Hz and an amplitude of 0.58 V;. If R =9 &Omega;, L= 2.90E-03H, and C=8.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 7.952E-01 &rad;
 * b) 8.747E-01 &rad;
 * c) 9.622E-01 &rad;
 * d) 1.058E+00 &rad;
 * e) 1.164E+00 &rad;

8) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.7mm$$, and $$n=2.76$$. What is the volume of the washer?


 * a) 1.038E+00 cm3
 * b) 1.142E+00 cm3
 * c) 1.256E+00 cm3
 * d) 1.381E+00 cm3
 * e) 1.520E+00 cm3

9) A parallel plate capacitor with a capicatnce C=8.90E-06 F whose plates have an area A=6.90E+03 m2 and separation d=6.90E-03 m is connected via a swith to a 89 &Omega; resistor and a battery of voltage V0=89 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-03?


 * a) 6.595E+01 V
 * b) 7.255E+01 V
 * c) 7.980E+01 V
 * d) 8.778E+01 V
 * e) 9.656E+01 V

10) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 2.05E-11 Vs2m-1
 * b) 2.48E-11 Vs2m-1
 * c) 3.01E-11 Vs2m-1
 * d) 3.64E-11 Vs2m-1
 * e) 4.42E-11 Vs2m-1

11) The silver ribbon shown are a=3.74 cm, b=2.68 cm, and c= 0.415 cm. The current carries a current of 228 A and it lies in a uniform magnetic field of 1.49 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 8.660E-06 V
 * b) 9.526E-06 V
 * c) 1.048E-05 V
 * d) 1.153E-05 V
 * e) 1.268E-05 V

T9 V2
1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.5 kA, I2=1.28 kA, and I3=3.4 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 4.362E-03 T-m
 * b) 4.798E-03 T-m
 * c) 5.278E-03 T-m
 * d) 5.806E-03 T-m
 * e) 6.386E-03 T-m

2) A circlular capactitor of radius 3.2 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 2.49E-04 s
 * b) 3.02E-04 s
 * c) 3.66E-04 s
 * d) 4.43E-04 s
 * e) 5.37E-04 s

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.944E-05 T
 * b) 2.138E-05 T
 * c) 2.352E-05 T
 * d) 2.587E-05 T
 * e) 2.846E-05 T

4) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * a) 1.753E+02 km
 * b) 1.928E+02 km
 * c) 2.121E+02 km
 * d) 2.333E+02 km
 * e) 2.567E+02 km

5) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.080E-06 V
 * b) 1.188E-06 V
 * c) 1.306E-06 V
 * d) 1.437E-06 V
 * e) 1.581E-06 V

6) A parallel plate capacitor with a capicatnce C=8.30E-06 F whose plates have an area A=7.00E+03 m2 and separation d=7.50E-03 m is connected via a swith to a 51 &Omega; resistor and a battery of voltage V0=81 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.20E-03?


 * a) 5.728E+01 V
 * b) 6.301E+01 V
 * c) 6.931E+01 V
 * d) 7.624E+01 V
 * e) 8.387E+01 V

7) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.28mm$$, and $$n=2.4$$. What is the volume of the washer?


 * a) 1.097E+00 cm3
 * b) 1.207E+00 cm3
 * c) 1.328E+00 cm3
 * d) 1.460E+00 cm3
 * e) 1.606E+00 cm3

8) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.379 T magnetic field is directed 53&deg; away from the wire?


 * a) 1.001E+00 N/m
 * b) 1.101E+00 N/m
 * c) 1.211E+00 N/m
 * d) 1.332E+00 N/m
 * e) 1.465E+00 N/m

9) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 2.05E-11 Vs2m-1
 * b) 2.48E-11 Vs2m-1
 * c) 3.01E-11 Vs2m-1
 * d) 3.64E-11 Vs2m-1
 * e) 4.42E-11 Vs2m-1

10) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$26 s&minus;1.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?


 * a) 2.154E-05 V/m
 * b) 2.369E-05 V/m
 * c) 2.606E-05 V/m
 * d) 2.867E-05 V/m
 * e) 3.154E-05 V/m

11) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 &Omega;, L= 8.40E-03H, and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * a) 1.032E+00 &rad;
 * b) 1.136E+00 &rad;
 * c) 1.249E+00 &rad;
 * d) 1.374E+00 &rad;
 * e) 1.512E+00 &rad;

T9 W0
1) The silver ribbon shown are a=3.74 cm, b=2.68 cm, and c= 0.415 cm. The current carries a current of 228 A and it lies in a uniform magnetic field of 1.49 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 8.660E-06 V
 * b) 9.526E-06 V
 * c) 1.048E-05 V
 * d) 1.153E-05 V
 * e) 1.268E-05 V

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.388 m and a magneticfield of 1.19 T. What is their maximum kinetic energy?


 * a) 8.491E+00 MeV
 * b) 9.340E+00 MeV
 * c) 1.027E+01 MeV
 * d) 1.130E+01 MeV
 * e) 1.243E+01 MeV

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.86 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 3.416E-05 T
 * b) 3.758E-05 T
 * c) 4.133E-05 T
 * d) 4.547E-05 T
 * e) 5.001E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 22 turns per centimeter and the current applied to the solenoid is 568 mA, the net magnetic field is measured to be 1.29 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 8.205E+02
 * b) $$\chi \text{ (chi) }=$$ 9.026E+02
 * c) $$\chi \text{ (chi) }=$$ 9.928E+02
 * d) $$\chi \text{ (chi) }=$$ 1.092E+03
 * e) $$\chi \text{ (chi) }=$$ 1.201E+03

5) A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 3.093E+01 cm3/s
 * b) 3.403E+01 cm3/s
 * c) 3.743E+01 cm3/s
 * d) 4.117E+01 cm3/s
 * e) 4.529E+01 cm3/s

6) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.38mm$$, and $$n=2.62$$. What is the volume of the washer?


 * a) 7.196E-01 cm3
 * b) 7.916E-01 cm3
 * c) 8.707E-01 cm3
 * d) 9.578E-01 cm3
 * e) 1.054E+00 cm3

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.82 V. The resistance, inductance, and capacitance are R =8 &Omega;, L= 6.40E-03H, and C=5.70E-04 F, respectively. What is the amplitude of the current?


 * a) 7.701E-02 A
 * b) 8.471E-02 A
 * c) 9.318E-02 A
 * d) 1.025E-01 A
 * e) 1.128E-01 A

8) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=4.20E+03 m2 and separation d=8.00E-03 m is connected via a swith to a 6 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.60E-05?


 * a) 7.253E+03 V/m
 * b) 7.978E+03 V/m
 * c) 8.776E+03 V/m
 * d) 9.653E+03 V/m
 * e) 1.062E+04 V/m

9) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * a) 2.094E+02 km
 * b) 2.304E+02 km
 * c) 2.534E+02 km
 * d) 2.788E+02 km
 * e) 3.066E+02 km

10) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.87E-11 Vs2m-1
 * b) 7.11E-11 Vs2m-1
 * c) 8.61E-11 Vs2m-1
 * d) 1.04E-10 Vs2m-1
 * e) 1.26E-10 Vs2m-1

11) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 21 &mu;C.  What is the electric field between the plates?


 * a) 6.16E+04 N/C (or V/m)
 * b) 7.47E+04 N/C (or V/m)
 * c) 9.05E+04 N/C (or V/m)
 * d) 1.10E+05 N/C (or V/m)
 * e) 1.33E+05 N/C (or V/m)

T9 W1
1) The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.648E-06 V
 * b) 1.813E-06 V
 * c) 1.994E-06 V
 * d) 2.194E-06 V
 * e) 2.413E-06 V

2) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * a) 2.44E+05 N/C (or V/m)
 * b) 2.95E+05 N/C (or V/m)
 * c) 3.58E+05 N/C (or V/m)
 * d) 4.34E+05 N/C (or V/m)
 * e) 5.25E+05 N/C (or V/m)

3) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * a) 1.118E+00 cm3
 * b) 1.229E+00 cm3
 * c) 1.352E+00 cm3
 * d) 1.487E+00 cm3
 * e) 1.636E+00 cm3

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 242 mA, the net magnetic field is measured to be 1.38 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.718E+03
 * b) $$\chi \text{ (chi) }=$$ 1.890E+03
 * c) $$\chi \text{ (chi) }=$$ 2.079E+03
 * d) $$\chi \text{ (chi) }=$$ 2.287E+03
 * e) $$\chi \text{ (chi) }=$$ 2.515E+03

5) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.44 m and a magneticfield of 1.31 T. What is their maximum kinetic energy?


 * a) 1.323E+01 MeV
 * b) 1.456E+01 MeV
 * c) 1.601E+01 MeV
 * d) 1.761E+01 MeV
 * e) 1.937E+01 MeV

6) A 56 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 72 kW?


 * a) 1.084E+02 km
 * b) 1.193E+02 km
 * c) 1.312E+02 km
 * d) 1.443E+02 km
 * e) 1.587E+02 km

7) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m2 and separation d=3.50E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?


 * a) 3.751E+03 V/m
 * b) 4.126E+03 V/m
 * c) 4.539E+03 V/m
 * d) 4.993E+03 V/m
 * e) 5.492E+03 V/m

8) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.87E-11 Vs2m-1
 * b) 7.11E-11 Vs2m-1
 * c) 8.61E-11 Vs2m-1
 * d) 1.04E-10 Vs2m-1
 * e) 1.26E-10 Vs2m-1

9) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.86 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.488E-05 T
 * b) 1.637E-05 T
 * c) 1.800E-05 T
 * d) 1.981E-05 T
 * e) 2.179E-05 T

10) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =9 &Omega;, L= 8.50E-03H, and C=7.20E-04 F, respectively. What is the amplitude of the current?


 * a) 8.384E-02 A
 * b) 9.222E-02 A
 * c) 1.014E-01 A
 * d) 1.116E-01 A
 * e) 1.227E-01 A

11) A cylinder of height 2.58 cm and radius 9.47 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.62 cm from point O and moves at a speed of 4.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 1.128E+02 cm3/s
 * b) 1.241E+02 cm3/s
 * c) 1.365E+02 cm3/s
 * d) 1.502E+02 cm3/s
 * e) 1.652E+02 cm3/s

T9 W2
1) A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 98 &Omega; resistor and a battery of voltage V0=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?


 * a) 5.050E+03 V/m
 * b) 5.555E+03 V/m
 * c) 6.111E+03 V/m
 * d) 6.722E+03 V/m
 * e) 7.394E+03 V/m

2) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * a) 1.753E+02 km
 * b) 1.928E+02 km
 * c) 2.121E+02 km
 * d) 2.333E+02 km
 * e) 2.567E+02 km

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.185E+03
 * b) $$\chi \text{ (chi) }=$$ 1.303E+03
 * c) $$\chi \text{ (chi) }=$$ 1.433E+03
 * d) $$\chi \text{ (chi) }=$$ 1.577E+03
 * e) $$\chi \text{ (chi) }=$$ 1.734E+03

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.944E-05 T
 * b) 2.138E-05 T
 * c) 2.352E-05 T
 * d) 2.587E-05 T
 * e) 2.846E-05 T

5) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.12 V. The resistance, inductance, and capacitance are R =3 &Omega;, L= 8.80E-03H, and C=6.40E-04 F, respectively. What is the amplitude of the current?


 * a) 2.732E-02 A
 * b) 3.005E-02 A
 * c) 3.306E-02 A
 * d) 3.636E-02 A
 * e) 4.000E-02 A

6) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.14mm$$, and $$n=2.86$$. What is the volume of the washer?


 * a) 1.071E+00 cm3
 * b) 1.178E+00 cm3
 * c) 1.296E+00 cm3
 * d) 1.425E+00 cm3
 * e) 1.568E+00 cm3

7) A cylinder of height 2.58 cm and radius 9.47 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.62 cm from point O and moves at a speed of 4.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * a) 1.128E+02 cm3/s
 * b) 1.241E+02 cm3/s
 * c) 1.365E+02 cm3/s
 * d) 1.502E+02 cm3/s
 * e) 1.652E+02 cm3/s

8) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 &mu;C.  What is the electric field between the plates?


 * a) 1.29E+05 N/C (or V/m)
 * b) 1.56E+05 N/C (or V/m)
 * c) 1.89E+05 N/C (or V/m)
 * d) 2.29E+05 N/C (or V/m)
 * e) 2.77E+05 N/C (or V/m)

9) The silver ribbon shown are a=4.12 cm, b=3.32 cm, and c= 1.46 cm. The current carries a current of 120 A and it lies in a uniform magnetic field of 1.39 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.209E-06 V
 * b) 1.329E-06 V
 * c) 1.462E-06 V
 * d) 1.609E-06 V
 * e) 1.770E-06 V

10) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.232 m and a magneticfield of 1.1 T. What is their maximum kinetic energy?


 * a) 2.853E+00 MeV
 * b) 3.139E+00 MeV
 * c) 3.453E+00 MeV
 * d) 3.798E+00 MeV
 * e) 4.178E+00 MeV

11) A circlular capactitor of radius 4.4 m has a gap of 17 mm, and a charge of 65 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * a) 5.56E-11 Vs2m-1
 * b) 6.74E-11 Vs2m-1
 * c) 8.17E-11 Vs2m-1
 * d) 9.90E-11 Vs2m-1
 * e) 1.20E-10 Vs2m-1

T9 X0
1) A circular current loop of radius 2.84 cm carries a current of 3.01 mA. What is the magnitude of the torque if the dipole is oriented at 63 &deg; to a uniform magnetic fied of 0.174 T?


 * a) 1.075E-06 N m
 * b) 1.182E-06 N m
 * c) 1.301E-06 N m
 * d) 1.431E-06 N m
 * e) 1.574E-06 N m

2) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 8.55 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.96 i + 1.68 j  + 6.92 k) x 104 m/s?


 * a) 4.179E-14 N
 * b) 4.596E-14 N
 * c) 5.056E-14 N
 * d) 5.562E-14 N
 * e) 6.118E-14 N

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.259 m and $$B_{max}=\,$$ 0.575 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.191 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.492E+05 A
 * b) 3.841E+05 A
 * c) 4.225E+05 A
 * d) 4.648E+05 A
 * e) 5.113E+05 A

4) Two parallel wires each carry a 2.12 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.67 cm, 1.25 cm), while the other is located at (4.69 cm, 4.27 cm). What is the force per unit length between the wires?


 * a) 2.119E-11 N/m
 * b) 2.331E-11 N/m
 * c) 2.564E-11 N/m
 * d) 2.820E-11 N/m
 * e) 3.102E-11 N/m

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$1.89 T and $$\omega=$$1.710E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.476 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 7.262E+03 V
 * b) 7.988E+03 V
 * c) 8.787E+03 V
 * d) 9.666E+03 V
 * e) 1.063E+04 V

6) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.32mm$$, and $$n=2.63$$. What is the volume of the washer?


 * a) 7.499E-01 cm3
 * b) 8.249E-01 cm3
 * c) 9.074E-01 cm3
 * d) 9.982E-01 cm3
 * e) 1.098E+00 cm3

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 &Omega;, L= 4.20E-03H, and C=3.70E-06 F, respectively.


 * a) Q = 7.135E+01
 * b) Q = 8.205E+01
 * c) Q = 9.435E+01
 * d) Q = 1.085E+02
 * e) Q = 1.248E+02

8) A parallel plate capacitor with a capicatnce C=6.90E-06 F whose plates have an area A=5.80E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 78 &Omega; resistor and a battery of voltage V0=70 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.50E-03?


 * a) 5.890E-03 A
 * b) 6.479E-03 A
 * c) 7.126E-03 A
 * d) 7.839E-03 A
 * e) 8.623E-03 A

9) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 8.969E-08 N
 * b) 9.866E-08 N
 * c) 1.085E-07 N
 * d) 1.194E-07 N
 * e) 1.313E-07 N

10) A circlular capactitor of radius 4.3 m has a gap of 15 mm, and a charge of 21 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 1.62E-09 Tesla
 * b) 2.04E-09 Tesla
 * c) 2.57E-09 Tesla
 * d) 3.23E-09 Tesla
 * e) 4.07E-09 Tesla

11) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 &mu;C.  What is the electric field between the plates?


 * a) 1.29E+05 N/C (or V/m)
 * b) 1.56E+05 N/C (or V/m)
 * c) 1.89E+05 N/C (or V/m)
 * d) 2.29E+05 N/C (or V/m)
 * e) 2.77E+05 N/C (or V/m)

T9 X1
1) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 89 &mu;C.  What is the electric field between the plates?


 * a) 1.93E+05 N/C (or V/m)
 * b) 2.34E+05 N/C (or V/m)
 * c) 2.83E+05 N/C (or V/m)
 * d) 3.43E+05 N/C (or V/m)
 * e) 4.16E+05 N/C (or V/m)

2) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (5.64 i + 1.93 j  + 8.71 k) x 104 m/s?


 * a) 1.757E-14 N
 * b) 1.933E-14 N
 * c) 2.126E-14 N
 * d) 2.339E-14 N
 * e) 2.573E-14 N

3) Two parallel wires each carry a 3.38 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.46 cm, 1.76 cm), while the other is located at (5.13 cm, 5.5 cm). What is the force per unit length between the wires?


 * a) 3.810E-11 N/m
 * b) 4.191E-11 N/m
 * c) 4.610E-11 N/m
 * d) 5.071E-11 N/m
 * e) 5.578E-11 N/m

4) What is the radiation force on an object that is 1.70E+11 m away from the sun and has cross-sectional area of 0.033 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.904E-07 N
 * b) 2.094E-07 N
 * c) 2.303E-07 N
 * d) 2.534E-07 N
 * e) 2.787E-07 N

5) A parallel plate capacitor with a capicatnce C=6.90E-06 F whose plates have an area A=5.80E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 26 &Omega; resistor and a battery of voltage V0=9 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=4.70E-04?


 * a) 1.894E-02 A
 * b) 2.083E-02 A
 * c) 2.291E-02 A
 * d) 2.520E-02 A
 * e) 2.773E-02 A

6) A circular current loop of radius 1.59 cm carries a current of 1.13 mA. What is the magnitude of the torque if the dipole is oriented at 41 &deg; to a uniform magnetic fied of 0.189 T?


 * a) 1.113E-07 N m
 * b) 1.224E-07 N m
 * c) 1.347E-07 N m
 * d) 1.481E-07 N m
 * e) 1.629E-07 N m

7) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.31 T and $$\omega=$$8.360E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.547 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 7.145E+04 V
 * b) 7.860E+04 V
 * c) 8.646E+04 V
 * d) 9.510E+04 V
 * e) 1.046E+05 V

8) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * a) 1.118E+00 cm3
 * b) 1.229E+00 cm3
 * c) 1.352E+00 cm3
 * d) 1.487E+00 cm3
 * e) 1.636E+00 cm3

9) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 2.82E-09 Tesla
 * b) 3.54E-09 Tesla
 * c) 4.46E-09 Tesla
 * d) 5.62E-09 Tesla
 * e) 7.07E-09 Tesla

10) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * a) Q = 1.288E+02
 * b) Q = 1.482E+02
 * c) Q = 1.704E+02
 * d) Q = 1.959E+02
 * e) Q = 2.253E+02

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.619 m and $$B_{max}=\,$$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.351 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 2.534E+05 A
 * b) 2.787E+05 A
 * c) 3.066E+05 A
 * d) 3.373E+05 A
 * e) 3.710E+05 A

T9 X2
1) A circular current loop of radius 1.88 cm carries a current of 3.41 mA. What is the magnitude of the torque if the dipole is oriented at 62 &deg; to a uniform magnetic fied of 0.415 T?


 * a) 1.387E-06 N m
 * b) 1.526E-06 N m
 * c) 1.679E-06 N m
 * d) 1.847E-06 N m
 * e) 2.031E-06 N m

2) A parallel plate capacitor with a capicatnce C=5.50E-06 F whose plates have an area A=3.00E+03 m2 and separation d=4.90E-03 m is connected via a swith to a 55 &Omega; resistor and a battery of voltage V0=37 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=9.00E-04?


 * a) 2.580E-02 A
 * b) 2.838E-02 A
 * c) 3.121E-02 A
 * d) 3.433E-02 A
 * e) 3.777E-02 A

3) A circlular capactitor of radius 3.7 m has a gap of 10 mm, and a charge of 12 &mu;C.  What is the electric field between the plates?


 * a) 2.15E+04 N/C (or V/m)
 * b) 2.60E+04 N/C (or V/m)
 * c) 3.15E+04 N/C (or V/m)
 * d) 3.82E+04 N/C (or V/m)
 * e) 4.63E+04 N/C (or V/m)

4) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * a) Q = 1.300E+02
 * b) Q = 1.495E+02
 * c) Q = 1.719E+02
 * d) Q = 1.976E+02
 * e) Q = 2.273E+02

5) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?


 * a) 3.882E-10 N/m
 * b) 4.270E-10 N/m
 * c) 4.697E-10 N/m
 * d) 5.167E-10 N/m
 * e) 5.683E-10 N/m

6) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 9.923E-09 N
 * b) 1.092E-08 N
 * c) 1.201E-08 N
 * d) 1.321E-08 N
 * e) 1.453E-08 N

7) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.67mm$$, and $$n=2.56$$. What is the volume of the washer?


 * a) 1.570E+00 cm3
 * b) 1.727E+00 cm3
 * c) 1.900E+00 cm3
 * d) 2.090E+00 cm3
 * e) 2.299E+00 cm3

8) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$2.34 T and $$\omega=$$2.670E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * a) 1.905E+04 V
 * b) 2.096E+04 V
 * c) 2.305E+04 V
 * d) 2.536E+04 V
 * e) 2.790E+04 V

9) A circlular capactitor of radius 4.4 m has a gap of 15 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 7.92E-09 Tesla
 * b) 9.97E-09 Tesla
 * c) 1.26E-08 Tesla
 * d) 1.58E-08 Tesla
 * e) 1.99E-08 Tesla

10) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 9.76 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (6.97 i + 8.52 j  + 9.46 k) x 104 m/s?


 * a) 2.199E-13 N
 * b) 2.419E-13 N
 * c) 2.661E-13 N
 * d) 2.927E-13 N
 * e) 3.220E-13 N

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.871 m and $$B_{max}=\,$$ 0.427 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.688 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 1.404E+06 A
 * b) 1.544E+06 A
 * c) 1.699E+06 A
 * d) 1.869E+06 A
 * e) 2.056E+06 A

T9 Y0
1) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 6.96 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (7.01 i + 5.35 j  + 2.07 k) x 104 m/s?


 * a) 1.192E-13 N
 * b) 1.311E-13 N
 * c) 1.442E-13 N
 * d) 1.586E-13 N
 * e) 1.745E-13 N

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.118 m and a magneticfield of 1.48 T. What is their maximum kinetic energy?


 * a) 1.004E+00 MeV
 * b) 1.104E+00 MeV
 * c) 1.215E+00 MeV
 * d) 1.336E+00 MeV
 * e) 1.470E+00 MeV

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 9.310E+02
 * b) $$\chi \text{ (chi) }=$$ 1.024E+03
 * c) $$\chi \text{ (chi) }=$$ 1.126E+03
 * d) $$\chi \text{ (chi) }=$$ 1.239E+03
 * e) $$\chi \text{ (chi) }=$$ 1.363E+03

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.52 m and $$B_{max}=\,$$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 7.876E+05 A
 * b) 8.664E+05 A
 * c) 9.530E+05 A
 * d) 1.048E+06 A
 * e) 1.153E+06 A

5) Calculate the motional emf induced along a 14.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.910E-05 Tesla magnetic field.


 * a) 3.688E+03 V
 * b) 4.057E+03 V
 * c) 4.463E+03 V
 * d) 4.909E+03 V
 * e) 5.400E+03 V

6) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.14mm$$, and $$n=2.86$$. What is the volume of the washer?


 * a) 1.071E+00 cm3
 * b) 1.178E+00 cm3
 * c) 1.296E+00 cm3
 * d) 1.425E+00 cm3
 * e) 1.568E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 6.60E-03H, and C=5.30E-06 F, what is the rms power transferred to the resistor?


 * a) 2.007E-03 Watts
 * b) 2.208E-03 Watts
 * c) 2.429E-03 Watts
 * d) 2.672E-03 Watts
 * e) 2.939E-03 Watts

8) A parallel plate capacitor with a capicatnce C=5.60E-06 F whose plates have an area A=2.00E+03 m2 and separation d=3.10E-03 m is connected via a swith to a 68 &Omega; resistor and a battery of voltage V0=73 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=8.50E-04?


 * a) 1.579E+04 V/m
 * b) 1.737E+04 V/m
 * c) 1.911E+04 V/m
 * d) 2.102E+04 V/m
 * e) 2.312E+04 V/m

9) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 5.275E-07 N
 * b) 5.803E-07 N
 * c) 6.383E-07 N
 * d) 7.021E-07 N
 * e) 7.723E-07 N

10) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 1.16E-04 s
 * b) 1.41E-04 s
 * c) 1.71E-04 s
 * d) 2.07E-04 s
 * e) 2.50E-04 s

11) A circlular capactitor of radius 4.9 m has a gap of 14 mm, and a charge of 56 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 3.18E-09 Tesla
 * b) 4.00E-09 Tesla
 * c) 5.04E-09 Tesla
 * d) 6.34E-09 Tesla
 * e) 7.99E-09 Tesla

T9 Y1
1) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.23 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (3.84 i + 8.79 j  + 9.05 k) x 104 m/s?


 * a) 7.509E-14 N
 * b) 8.259E-14 N
 * c) 9.085E-14 N
 * d) 9.994E-14 N
 * e) 1.099E-13 N

2) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=980.0 m2 and separation d=6.20E-03 m is connected via a swith to a 8 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.40E-05?


 * a) 5.154E+03 V/m
 * b) 5.669E+03 V/m
 * c) 6.236E+03 V/m
 * d) 6.860E+03 V/m
 * e) 7.545E+03 V/m

3) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.


 * a) 1.279E+04 V
 * b) 1.407E+04 V
 * c) 1.547E+04 V
 * d) 1.702E+04 V
 * e) 1.872E+04 V

4) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 7.00E-03H, and C=6.60E-06 F, what is the rms power transferred to the resistor?


 * a) 1.146E-03 Watts
 * b) 1.260E-03 Watts
 * c) 1.386E-03 Watts
 * d) 1.525E-03 Watts
 * e) 1.677E-03 Watts

5) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 8.32E-09 Tesla
 * b) 1.05E-08 Tesla
 * c) 1.32E-08 Tesla
 * d) 1.66E-08 Tesla
 * e) 2.09E-08 Tesla

6) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 3.07E-04 s
 * b) 3.71E-04 s
 * c) 4.50E-04 s
 * d) 5.45E-04 s
 * e) 6.61E-04 s

7) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 1.167E-08 N
 * b) 1.284E-08 N
 * c) 1.412E-08 N
 * d) 1.553E-08 N
 * e) 1.708E-08 N

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.571 m and $$B_{max}=\,$$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.321 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.226E+05 A
 * b) 3.549E+05 A
 * c) 3.904E+05 A
 * d) 4.294E+05 A
 * e) 4.724E+05 A

9) A washer has an inner diameter of 2.21 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.29mm$$, and $$n=2.62$$. What is the volume of the washer?


 * a) 1.325E+00 cm3
 * b) 1.457E+00 cm3
 * c) 1.603E+00 cm3
 * d) 1.763E+00 cm3
 * e) 1.939E+00 cm3

10) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.355 m and a magneticfield of 1.28 T. What is their maximum kinetic energy?


 * a) 7.476E+00 MeV
 * b) 8.224E+00 MeV
 * c) 9.046E+00 MeV
 * d) 9.951E+00 MeV
 * e) 1.095E+01 MeV

11) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 359 mA, the net magnetic field is measured to be 1.32 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.124E+03
 * b) $$\chi \text{ (chi) }=$$ 1.237E+03
 * c) $$\chi \text{ (chi) }=$$ 1.360E+03
 * d) $$\chi \text{ (chi) }=$$ 1.497E+03
 * e) $$\chi \text{ (chi) }=$$ 1.646E+03

T9 Y2
1) What is the radiation force on an object that is 3.60E+11 m away from the sun and has cross-sectional area of 0.069 m2? The average power output of the Sun is 3.80E+26 W.


 * a) 7.336E-08 N
 * b) 8.069E-08 N
 * c) 8.876E-08 N
 * d) 9.764E-08 N
 * e) 1.074E-07 N

2) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.7mm$$, and $$n=2.76$$. What is the volume of the washer?


 * a) 1.038E+00 cm3
 * b) 1.142E+00 cm3
 * c) 1.256E+00 cm3
 * d) 1.381E+00 cm3
 * e) 1.520E+00 cm3

3) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.41 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (6.21 i + 5.39 j  + 3.81 k) x 104 m/s?


 * a) 4.419E-14 N
 * b) 4.861E-14 N
 * c) 5.347E-14 N
 * d) 5.882E-14 N
 * e) 6.470E-14 N

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.432 m and $$B_{max}=\,$$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 3.277E+05 A
 * b) 3.604E+05 A
 * c) 3.965E+05 A
 * d) 4.361E+05 A
 * e) 4.797E+05 A

5) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 7 V. If R =3 &Omega;, L= 4.10E-03H, and C=8.70E-06 F, what is the rms power transferred to the resistor?


 * a) 8.369E-03 Watts
 * b) 9.206E-03 Watts
 * c) 1.013E-02 Watts
 * d) 1.114E-02 Watts
 * e) 1.225E-02 Watts

6) A circlular capactitor of radius 4.6 m has a gap of 18 mm, and a charge of 44 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * a) 6.64E-09 Tesla
 * b) 8.36E-09 Tesla
 * c) 1.05E-08 Tesla
 * d) 1.32E-08 Tesla
 * e) 1.67E-08 Tesla

7) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.


 * a) 8.111E+03 V
 * b) 8.922E+03 V
 * c) 9.814E+03 V
 * d) 1.080E+04 V
 * e) 1.187E+04 V

8) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.378 m and a magneticfield of 0.835 T. What is their maximum kinetic energy?


 * a) 4.365E+00 MeV
 * b) 4.801E+00 MeV
 * c) 5.281E+00 MeV
 * d) 5.809E+00 MeV
 * e) 6.390E+00 MeV

9) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.188E+03
 * b) $$\chi \text{ (chi) }=$$ 1.307E+03
 * c) $$\chi \text{ (chi) }=$$ 1.438E+03
 * d) $$\chi \text{ (chi) }=$$ 1.582E+03
 * e) $$\chi \text{ (chi) }=$$ 1.740E+03

10) A parallel plate capacitor with a capicatnce C=1.60E-06 F whose plates have an area A=890.0 m2 and separation d=4.90E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=44 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.90E-04?


 * a) 6.651E+03 V/m
 * b) 7.316E+03 V/m
 * c) 8.048E+03 V/m
 * d) 8.853E+03 V/m
 * e) 9.738E+03 V/m

11) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * a) 1.16E-04 s
 * b) 1.41E-04 s
 * c) 1.71E-04 s
 * d) 2.07E-04 s
 * e) 2.50E-04 s

T9 Z0
1) A 24 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.706 T. What current is required to maintain this balance?


 * a) 5.258E-01 A
 * b) 5.784E-01 A
 * c) 6.362E-01 A
 * d) 6.998E-01 A
 * e) 7.698E-01 A

2) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.080E-06 V
 * b) 1.188E-06 V
 * c) 1.306E-06 V
 * d) 1.437E-06 V
 * e) 1.581E-06 V

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.935E-05 T
 * b) 2.128E-05 T
 * c) 2.341E-05 T
 * d) 2.575E-05 T
 * e) 2.832E-05 T

4) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?


 * a) 2.977E-11 N/m
 * b) 3.274E-11 N/m
 * c) 3.602E-11 N/m
 * d) 3.962E-11 N/m
 * e) 4.358E-11 N/m

5) Calculate the motional emf induced along a 34.3 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.780E-05 Tesla magnetic field.


 * a) 8.802E+03 V
 * b) 9.682E+03 V
 * c) 1.065E+04 V
 * d) 1.172E+04 V
 * e) 1.289E+04 V

6) An induced emf of 4.13V is measured across a coil of 70 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.63A in 0.133s. What is the self-inductance of the coil?


 * a) 1.726E-01 H
 * b) 1.899E-01 H
 * c) 2.089E-01 H
 * d) 2.297E-01 H
 * e) 2.527E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 6.60E-03H, and C=5.30E-06 F, what is the rms power transferred to the resistor?


 * a) 2.007E-03 Watts
 * b) 2.208E-03 Watts
 * c) 2.429E-03 Watts
 * d) 2.672E-03 Watts
 * e) 2.939E-03 Watts

8) A 55 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 93 kW?


 * a) 1.270E+02 km
 * b) 1.397E+02 km
 * c) 1.537E+02 km
 * d) 1.690E+02 km
 * e) 1.859E+02 km

9) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 23 &Omega; resistor and a battery of voltage V0=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?


 * a) 2.877E+00 V
 * b) 3.165E+00 V
 * c) 3.481E+00 V
 * d) 3.829E+00 V
 * e) 4.212E+00 V

10) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 45 &mu;C.  What is the electric field between the plates?


 * a) 6.31E+04 N/C (or V/m)
 * b) 7.65E+04 N/C (or V/m)
 * c) 9.26E+04 N/C (or V/m)
 * d) 1.12E+05 N/C (or V/m)
 * e) 1.36E+05 N/C (or V/m)

11) A circlular capactitor of radius 4 m has a gap of 14 mm, and a charge of 24 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * a) 1.84E-04 s
 * b) 2.23E-04 s
 * c) 2.70E-04 s
 * d) 3.27E-04 s
 * e) 3.96E-04 s

T9 Z1
1) The output of an ac generator connected to an RLC series combination has a frequency of 2.70E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 9.10E-03H, and C=9.60E-06 F, what is the rms power transferred to the resistor?


 * a) 2.188E-03 Watts
 * b) 2.407E-03 Watts
 * c) 2.647E-03 Watts
 * d) 2.912E-03 Watts
 * e) 3.203E-03 Watts

2) A 34 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.348 T. What current is required to maintain this balance?


 * a) 6.626E-01 A
 * b) 7.289E-01 A
 * c) 8.018E-01 A
 * d) 8.819E-01 A
 * e) 9.701E-01 A

3) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * a) 1.65E-04 s
 * b) 2.00E-04 s
 * c) 2.43E-04 s
 * d) 2.94E-04 s
 * e) 3.56E-04 s

4) An induced emf of 3.78V is measured across a coil of 99 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.36A in 0.821s. What is the self-inductance of the coil?


 * a) 4.033E-01 H
 * b) 4.436E-01 H
 * c) 4.880E-01 H
 * d) 5.367E-01 H
 * e) 5.904E-01 H

5) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.64 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.920E-05 T
 * b) 2.112E-05 T
 * c) 2.323E-05 T
 * d) 2.556E-05 T
 * e) 2.811E-05 T

6) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.


 * a) 3.736E+03 V
 * b) 4.109E+03 V
 * c) 4.520E+03 V
 * d) 4.972E+03 V
 * e) 5.470E+03 V

7) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * a) 1.517E+02 km
 * b) 1.669E+02 km
 * c) 1.835E+02 km
 * d) 2.019E+02 km
 * e) 2.221E+02 km

8) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * a) 4.55E+04 N/C (or V/m)
 * b) 5.52E+04 N/C (or V/m)
 * c) 6.68E+04 N/C (or V/m)
 * d) 8.10E+04 N/C (or V/m)
 * e) 9.81E+04 N/C (or V/m)

9) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?


 * a) 1.283E-10 N/m
 * b) 1.411E-10 N/m
 * c) 1.552E-10 N/m
 * d) 1.708E-10 N/m
 * e) 1.878E-10 N/m

10) The silver ribbon shown are a=3.84 cm, b=3.45 cm, and c= 1.38 cm. The current carries a current of 92 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 7.153E-07 V
 * b) 7.869E-07 V
 * c) 8.655E-07 V
 * d) 9.521E-07 V
 * e) 1.047E-06 V

11) A parallel plate capacitor with a capicatnce C=6.50E-06 F whose plates have an area A=4.50E+03 m2 and separation d=6.10E-03 m is connected via a swith to a 4 &Omega; resistor and a battery of voltage V0=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.70E-05?


 * a) 1.456E+00 V
 * b) 1.602E+00 V
 * c) 1.762E+00 V
 * d) 1.938E+00 V
 * e) 2.132E+00 V

T9 Z2
1) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * a) 5.017E+01 V
 * b) 5.519E+01 V
 * c) 6.071E+01 V
 * d) 6.678E+01 V
 * e) 7.345E+01 V

2) The output of an ac generator connected to an RLC series combination has a frequency of 3.50E+04 Hz and an amplitude of 8 V. If R =7 &Omega;, L= 9.40E-03H, and C=8.50E-06 F, what is the rms power transferred to the resistor?


 * a) 2.111E-03 Watts
 * b) 2.323E-03 Watts
 * c) 2.555E-03 Watts
 * d) 2.810E-03 Watts
 * e) 3.091E-03 Watts

3) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 45 &mu;C.  What is the electric field between the plates?


 * a) 6.31E+04 N/C (or V/m)
 * b) 7.65E+04 N/C (or V/m)
 * c) 9.26E+04 N/C (or V/m)
 * d) 1.12E+05 N/C (or V/m)
 * e) 1.36E+05 N/C (or V/m)

4) A 46 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 78 kW?


 * a) 1.563E+02 km
 * b) 1.719E+02 km
 * c) 1.891E+02 km
 * d) 2.080E+02 km
 * e) 2.288E+02 km

5) A circlular capactitor of radius 3.1 m has a gap of 11 mm, and a charge of 76 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * a) 1.94E-04 s
 * b) 2.36E-04 s
 * c) 2.85E-04 s
 * d) 3.46E-04 s
 * e) 4.19E-04 s

6) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.


 * a) 1.279E+04 V
 * b) 1.407E+04 V
 * c) 1.547E+04 V
 * d) 1.702E+04 V
 * e) 1.872E+04 V

7) Two parallel wires each carry a 7.48 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.13 cm, 0.955 cm), while the other is located at (5.37 cm, 5.48 cm). What is the force per unit length between the wires?


 * a) 2.015E-10 N/m
 * b) 2.216E-10 N/m
 * c) 2.438E-10 N/m
 * d) 2.682E-10 N/m
 * e) 2.950E-10 N/m

8) The silver ribbon shown are a=3.6 cm, b=2.68 cm, and c= 1.13 cm. The current carries a current of 97 A and it lies in a uniform magnetic field of 1.89 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.560E-06 V
 * b) 1.716E-06 V
 * c) 1.888E-06 V
 * d) 2.077E-06 V
 * e) 2.284E-06 V

9) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?


 * a) 1.022E+00 H
 * b) 1.124E+00 H
 * c) 1.237E+00 H
 * d) 1.360E+00 H
 * e) 1.496E+00 H

10) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?


 * a) 1.935E-05 T
 * b) 2.128E-05 T
 * c) 2.341E-05 T
 * d) 2.575E-05 T
 * e) 2.832E-05 T

11) A 44 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 7 g, and the magnitude of the magnetic field is 0.784 T. What current is required to maintain this balance?


 * a) 1.644E-01 A
 * b) 1.808E-01 A
 * c) 1.989E-01 A
 * d) 2.188E-01 A
 * e) 2.406E-01 A


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Key: A0
1) A circular current loop of radius 2.1 cm carries a current of 5.02 mA. What is the magnitude of the torque if the dipole is oriented at 26 &deg; to a uniform magnetic fied of 0.184 T?


 * +a) 5.610E-07 N m
 * -b) 6.171E-07 N m
 * -c) 6.788E-07 N m
 * -d) 7.467E-07 N m
 * -e) 8.213E-07 N m

2) The silver ribbon shown are a=3.68 cm, b=2.66 cm, and c= 0.505 cm. The current carries a current of 113 A and it lies in a uniform magnetic field of 3.12 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 6.104E-06 V
 * -b) 6.714E-06 V
 * +c) 7.385E-06 V
 * -d) 8.124E-06 V
 * -e) 8.936E-06 V

3) Two loops of wire carry the same current of 66 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.485 m while the other has a radius of 1.27 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.507 m from the first (smaller) loopif the disance between the loops is 1.76 m?


 * -a) 2.733E-02 T
 * -b) 3.007E-02 T
 * -c) 3.307E-02 T
 * -d) 3.638E-02 T
 * +e) 4.002E-02 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.907E+03

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.29 T and $$\omega=$$4.720E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.658 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * +a) 6.420E+04 V
 * -b) 7.062E+04 V
 * -c) 7.768E+04 V
 * -d) 8.545E+04 V
 * -e) 9.400E+04 V

6) A long solenoid has a length 0.777 meters, radius 3.45 cm, and 557 turns. It surrounds  coil of radius 6.01 meters and 10turns.  If the current in the solenoid is changing at a rate of 184 A/s, what is the emf induced in the surounding coil?


 * -a) 1.463E-02 V
 * -b) 1.609E-02 V
 * -c) 1.770E-02 V
 * +d) 1.947E-02 V
 * -e) 2.142E-02 V

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.82 V. The resistance, inductance, and capacitance are R =3 &Omega;, L= 6.20E-03H, and C=6.70E-04 F, respectively. What is the amplitude of the current?


 * -a) 2.259E-01 A
 * -b) 2.485E-01 A
 * +c) 2.733E-01 A
 * -d) 3.007E-01 A
 * -e) 3.307E-01 A

8) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 23 &Omega; resistor and a battery of voltage V0=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?


 * +a) 2.877E+00 V
 * -b) 3.165E+00 V
 * -c) 3.481E+00 V
 * -d) 3.829E+00 V
 * -e) 4.212E+00 V

9) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.253E-05 N/m2
 * -b) 1.378E-05 N/m2
 * -c) 1.516E-05 N/m2
 * +d) 1.667E-05 N/m2
 * -e) 1.834E-05 N/m2

10) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.87E-11 Vs2m-1
 * -b) 7.11E-11 Vs2m-1
 * -c) 8.61E-11 Vs2m-1
 * +d) 1.04E-10 Vs2m-1
 * -e) 1.26E-10 Vs2m-1

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * -a) 2.80E+04 N/C (or V/m)
 * -b) 3.40E+04 N/C (or V/m)
 * +c) 4.12E+04 N/C (or V/m)
 * -d) 4.99E+04 N/C (or V/m)
 * -e) 6.04E+04 N/C (or V/m)

Key: A1
1) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.253E-05 N/m2
 * -b) 1.378E-05 N/m2
 * -c) 1.516E-05 N/m2
 * +d) 1.667E-05 N/m2
 * -e) 1.834E-05 N/m2

2) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 &deg; to a uniform magnetic fied of 0.402 T?


 * +a) 1.022E-06 N m
 * -b) 1.124E-06 N m
 * -c) 1.236E-06 N m
 * -d) 1.360E-06 N m
 * -e) 1.496E-06 N m

3) Two loops of wire carry the same current of 24 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.53 m while the other has a radius of 1.38 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.485 m from the first (smaller) loopif the disance between the loops is 1.78 m?


 * -a) 1.294E-02 T
 * -b) 1.424E-02 T
 * +c) 1.566E-02 T
 * -d) 1.723E-02 T
 * -e) 1.895E-02 T

4) The silver ribbon shown are a=3.6 cm, b=2.68 cm, and c= 1.13 cm. The current carries a current of 97 A and it lies in a uniform magnetic field of 1.89 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.560E-06 V
 * +b) 1.716E-06 V
 * -c) 1.888E-06 V
 * -d) 2.077E-06 V
 * -e) 2.284E-06 V

5) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.188E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.307E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.438E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.582E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.740E+03

6) A circlular capactitor of radius 4.4 m has a gap of 8 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 4.96E-11 Vs2m-1
 * -b) 6.01E-11 Vs2m-1
 * -c) 7.28E-11 Vs2m-1
 * -d) 8.82E-11 Vs2m-1
 * +e) 1.07E-10 Vs2m-1

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =9 &Omega;, L= 8.50E-03H, and C=7.20E-04 F, respectively. What is the amplitude of the current?


 * -a) 8.384E-02 A
 * +b) 9.222E-02 A
 * -c) 1.014E-01 A
 * -d) 1.116E-01 A
 * -e) 1.227E-01 A

8) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 84 &mu;C.  What is the electric field between the plates?


 * -a) 1.37E+05 N/C (or V/m)
 * -b) 1.66E+05 N/C (or V/m)
 * -c) 2.01E+05 N/C (or V/m)
 * -d) 2.43E+05 N/C (or V/m)
 * +e) 2.95E+05 N/C (or V/m)

9) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.7 T and $$\omega=$$8.100E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.827 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 1.416E+05 V
 * +b) 1.557E+05 V
 * -c) 1.713E+05 V
 * -d) 1.884E+05 V
 * -e) 2.073E+05 V

10) A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds  coil of radius 6.86 meters and 14turns.  If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?


 * -a) 1.894E-02 V
 * -b) 2.083E-02 V
 * -c) 2.291E-02 V
 * +d) 2.520E-02 V
 * -e) 2.772E-02 V

11) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * +a) 7.693E+01 V
 * -b) 8.463E+01 V
 * -c) 9.309E+01 V
 * -d) 1.024E+02 V
 * -e) 1.126E+02 V

Key: A2
1) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 6.669E-07 N/m2
 * -b) 7.336E-07 N/m2
 * -c) 8.069E-07 N/m2
 * -d) 8.876E-07 N/m2
 * -e) 9.764E-07 N/m2

2) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.907E+03

3) A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?


 * -a) 5.131E+01 V
 * -b) 5.644E+01 V
 * -c) 6.209E+01 V
 * -d) 6.830E+01 V
 * +e) 7.513E+01 V

4) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 &deg; to a uniform magnetic fied of 0.402 T?


 * +a) 1.022E-06 N m
 * -b) 1.124E-06 N m
 * -c) 1.236E-06 N m
 * -d) 1.360E-06 N m
 * -e) 1.496E-06 N m

5) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.3 V. The resistance, inductance, and capacitance are R =2 &Omega;, L= 8.10E-03H, and C=9.40E-04 F, respectively. What is the amplitude of the current?


 * -a) 1.364E-01 A
 * +b) 1.500E-01 A
 * -c) 1.650E-01 A
 * -d) 1.815E-01 A
 * -e) 1.997E-01 A

6) Two loops of wire carry the same current of 39 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.49 m while the other has a radius of 1.11 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.552 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * -a) 1.564E-02 T
 * -b) 1.720E-02 T
 * -c) 1.892E-02 T
 * -d) 2.081E-02 T
 * +e) 2.289E-02 T

7) The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.648E-06 V
 * -b) 1.813E-06 V
 * -c) 1.994E-06 V
 * +d) 2.194E-06 V
 * -e) 2.413E-06 V

8) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 2.05E-11 Vs2m-1
 * -b) 2.48E-11 Vs2m-1
 * -c) 3.01E-11 Vs2m-1
 * +d) 3.64E-11 Vs2m-1
 * -e) 4.42E-11 Vs2m-1

9) A long solenoid has a length 0.923 meters, radius 4.08 cm, and 579 turns. It surrounds  coil of radius 6.86 meters and 14turns.  If the current in the solenoid is changing at a rate of 139 A/s, what is the emf induced in the surounding coil?


 * -a) 1.894E-02 V
 * -b) 2.083E-02 V
 * -c) 2.291E-02 V
 * +d) 2.520E-02 V
 * -e) 2.772E-02 V

10) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.7 T and $$\omega=$$8.100E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.827 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 1.416E+05 V
 * +b) 1.557E+05 V
 * -c) 1.713E+05 V
 * -d) 1.884E+05 V
 * -e) 2.073E+05 V

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * -a) 2.80E+04 N/C (or V/m)
 * -b) 3.40E+04 N/C (or V/m)
 * +c) 4.12E+04 N/C (or V/m)
 * -d) 4.99E+04 N/C (or V/m)
 * -e) 6.04E+04 N/C (or V/m)

Key: B0
1) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.449 m and a magneticfield of 0.81 T. What is their maximum kinetic energy?


 * -a) 5.795E+00 MeV
 * +b) 6.374E+00 MeV
 * -c) 7.012E+00 MeV
 * -d) 7.713E+00 MeV
 * -e) 8.484E+00 MeV

2) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?


 * -a) 1.174E+00 A
 * -b) 1.291E+00 A
 * -c) 1.420E+00 A
 * -d) 1.562E+00 A
 * +e) 1.719E+00 A

3) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.776 m while the other has a radius of 1.2 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?


 * -a) 1.127E-02 T
 * -b) 1.240E-02 T
 * -c) 1.364E-02 T
 * +d) 1.500E-02 T
 * -e) 1.650E-02 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.86 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.488E-05 T
 * -b) 1.637E-05 T
 * -c) 1.800E-05 T
 * -d) 1.981E-05 T
 * -e) 2.179E-05 T

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * -a) 1.605E-04 V/m
 * +b) 1.766E-04 V/m
 * -c) 1.942E-04 V/m
 * -d) 2.136E-04 V/m
 * -e) 2.350E-04 V/m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.23% of its maximum value if &epsilon; = 3.13 V, R = 3.59 &Omega;, and L = 3.38 H?


 * -a) -1.345E+00 s
 * -b) -1.480E+00 s
 * -c) -1.628E+00 s
 * +d) -1.790E+00 s
 * -e) -1.969E+00 s

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.64 V. The resistance, inductance, and capacitance are R =2 &Omega;, L= 4.00E-03H, and C=8.30E-04 F, respectively. What is the amplitude of the current?


 * +a) 3.200E-01 A
 * -b) 3.520E-01 A
 * -c) 3.872E-01 A
 * -d) 4.259E-01 A
 * -e) 4.685E-01 A

8) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.673E-07 N
 * -b) 2.940E-07 N
 * -c) 3.234E-07 N
 * -d) 3.558E-07 N
 * -e) 3.913E-07 N

9) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * -a) 7.315E-02 A
 * +b) 8.047E-02 A
 * -c) 8.851E-02 A
 * -d) 9.737E-02 A
 * -e) 1.071E-01 A

10) A circlular capactitor of radius 4.4 m has a gap of 12 mm, and a charge of 72 &mu;C.  What is the electric field between the plates?


 * -a) 6.21E+04 N/C (or V/m)
 * -b) 7.52E+04 N/C (or V/m)
 * -c) 9.11E+04 N/C (or V/m)
 * -d) 1.10E+05 N/C (or V/m)
 * +e) 1.34E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is the decay time?


 * +a) 2.57E-04 s
 * -b) 3.11E-04 s
 * -c) 3.77E-04 s
 * -d) 4.57E-04 s
 * -e) 5.53E-04 s

Key: B1
1) A parallel plate capacitor with a capicatnce C=6.80E-06 F whose plates have an area A=6.60E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 62 &Omega; resistor and a battery of voltage V0=36 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * -a) 8.288E-02 A
 * -b) 9.117E-02 A
 * -c) 1.003E-01 A
 * -d) 1.103E-01 A
 * +e) 1.213E-01 A

2) What is the radiation force on an object that is 1.70E+11 m away from the sun and has cross-sectional area of 0.033 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.904E-07 N
 * -b) 2.094E-07 N
 * +c) 2.303E-07 N
 * -d) 2.534E-07 N
 * -e) 2.787E-07 N

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?


 * -a) 1.098E-05 T
 * +b) 1.208E-05 T
 * -c) 1.329E-05 T
 * -d) 1.462E-05 T
 * -e) 1.608E-05 T

4) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.54% of its maximum value if &epsilon; = 2.46 V, R = 2.8 &Omega;, and L = 5.67 H?


 * -a) -2.540E+00 s
 * -b) -2.794E+00 s
 * -c) -3.073E+00 s
 * -d) -3.381E+00 s
 * +e) -3.719E+00 s

5) Two loops of wire carry the same current of 97 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.595 m while the other has a radius of 1.1 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.63 m from the first (smaller) loopif the disance between the loops is 1.72 m?


 * +a) 5.302E-02 T
 * -b) 5.832E-02 T
 * -c) 6.415E-02 T
 * -d) 7.056E-02 T
 * -e) 7.762E-02 T

6) A circlular capactitor of radius 3.4 m has a gap of 15 mm, and a charge of 63 &mu;C.  What is the electric field between the plates?


 * -a) 1.62E+05 N/C (or V/m)
 * +b) 1.96E+05 N/C (or V/m)
 * -c) 2.37E+05 N/C (or V/m)
 * -d) 2.88E+05 N/C (or V/m)
 * -e) 3.48E+05 N/C (or V/m)

7) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.355 m and a magneticfield of 1.28 T. What is their maximum kinetic energy?


 * -a) 7.476E+00 MeV
 * -b) 8.224E+00 MeV
 * -c) 9.046E+00 MeV
 * +d) 9.951E+00 MeV
 * -e) 1.095E+01 MeV

8) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * +a) 3.62E-04 s
 * -b) 4.38E-04 s
 * -c) 5.31E-04 s
 * -d) 6.43E-04 s
 * -e) 7.79E-04 s

9) A 33 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.869 T. What current is required to maintain this balance?


 * -a) 2.259E-01 A
 * -b) 2.485E-01 A
 * +c) 2.734E-01 A
 * -d) 3.007E-01 A
 * -e) 3.308E-01 A

10) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.31 V. The resistance, inductance, and capacitance are R =5 &Omega;, L= 9.00E-03H, and C=5.10E-04 F, respectively. What is the amplitude of the current?


 * -a) 4.235E-02 A
 * -b) 4.658E-02 A
 * -c) 5.124E-02 A
 * -d) 5.636E-02 A
 * +e) 6.200E-02 A

11) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * +a) 6.040E-05 V/m
 * -b) 6.644E-05 V/m
 * -c) 7.309E-05 V/m
 * -d) 8.039E-05 V/m
 * -e) 8.843E-05 V/m

Key: B2
1) A 24 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.706 T. What current is required to maintain this balance?


 * -a) 5.258E-01 A
 * +b) 5.784E-01 A
 * -c) 6.362E-01 A
 * -d) 6.998E-01 A
 * -e) 7.698E-01 A

2) Two loops of wire carry the same current of 21 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.753 m while the other has a radius of 1.47 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.406 m from the first (smaller) loopif the disance between the loops is 1.38 m?


 * -a) 1.559E-02 T
 * +b) 1.715E-02 T
 * -c) 1.886E-02 T
 * -d) 2.075E-02 T
 * -e) 2.283E-02 T

3) A long solenoid has a radius of 0.624 m and 84 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$20 s&minus;1.What is the induced electric fied at a distance 1.78 m from the axis at time t=0.0579 s ?


 * -a) 3.597E-04 V/m
 * -b) 3.956E-04 V/m
 * +c) 4.352E-04 V/m
 * -d) 4.787E-04 V/m
 * -e) 5.266E-04 V/m

4) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * -a) 1.65E-04 s
 * +b) 2.00E-04 s
 * -c) 2.43E-04 s
 * -d) 2.94E-04 s
 * -e) 3.56E-04 s

5) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 7.396E-08 N
 * -b) 8.136E-08 N
 * +c) 8.950E-08 N
 * -d) 9.845E-08 N
 * -e) 1.083E-07 N

6) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.944E-05 T
 * -b) 2.138E-05 T
 * -c) 2.352E-05 T
 * -d) 2.587E-05 T
 * -e) 2.846E-05 T

7) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 24 &mu;C.  What is the electric field between the plates?


 * -a) 4.24E+04 N/C (or V/m)
 * +b) 5.13E+04 N/C (or V/m)
 * -c) 6.22E+04 N/C (or V/m)
 * -d) 7.53E+04 N/C (or V/m)
 * -e) 9.13E+04 N/C (or V/m)

8) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if &epsilon; = 5.95 V, R = 7.26 &Omega;, and L = 1.29 H?


 * -a) -3.114E-01 s
 * -b) -3.425E-01 s
 * +c) -3.767E-01 s
 * -d) -4.144E-01 s
 * -e) -4.559E-01 s

9) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.157 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?


 * -a) 8.608E-01 MeV
 * -b) 9.468E-01 MeV
 * -c) 1.042E+00 MeV
 * -d) 1.146E+00 MeV
 * +e) 1.260E+00 MeV

10) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.25 V. The resistance, inductance, and capacitance are R =7 &Omega;, L= 5.00E-03H, and C=7.70E-04 F, respectively. What is the amplitude of the current?


 * -a) 2.439E-02 A
 * -b) 2.683E-02 A
 * -c) 2.952E-02 A
 * -d) 3.247E-02 A
 * +e) 3.571E-02 A

11) A parallel plate capacitor with a capicatnce C=6.80E-06 F whose plates have an area A=6.60E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 62 &Omega; resistor and a battery of voltage V0=36 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * -a) 8.288E-02 A
 * -b) 9.117E-02 A
 * -c) 1.003E-01 A
 * -d) 1.103E-01 A
 * +e) 1.213E-01 A

Key: C0
1) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 3.43 mT and 4.670E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 1.362E+06 m/s
 * -b) 1.498E+06 m/s
 * -c) 1.647E+06 m/s
 * -d) 1.812E+06 m/s
 * -e) 1.993E+06 m/s

2) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23&deg; away from the wire?


 * +a) 5.205E-01 N/m
 * -b) 5.725E-01 N/m
 * -c) 6.297E-01 N/m
 * -d) 6.927E-01 N/m
 * -e) 7.620E-01 N/m

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.907E+03

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.549 m and $$B_{max}=\,$$ 0.599 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.29 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 5.581E+05 A
 * -b) 6.139E+05 A
 * +c) 6.752E+05 A
 * -d) 7.428E+05 A
 * -e) 8.170E+05 A

5) A long solenoid has a radius of 0.591 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1 A and $$\alpha=$$30 s&minus;1.What is the induced electric fied at a distance 0.234 m from the axis at time t=0.0208 s ?


 * -a) 6.618E-05 V/m
 * -b) 7.280E-05 V/m
 * -c) 8.008E-05 V/m
 * -d) 8.809E-05 V/m
 * +e) 9.689E-05 V/m

6) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.230E-04 s
 * -b) 6.853E-04 s
 * -c) 7.538E-04 s
 * -d) 8.292E-04 s
 * +e) 9.121E-04 s

7) A step-down transformer steps 19 kV down to 220 V. The high-voltage input is provided by a 230 &Omega; power line that carries 5 A of currentWhat is the output current (at the 220 V side ?)


 * -a) 3.244E+02 A
 * -b) 3.569E+02 A
 * -c) 3.926E+02 A
 * +d) 4.318E+02 A
 * -e) 4.750E+02 A

8) A parallel plate capacitor with a capicatnce C=7.30E-06 F whose plates have an area A=6.10E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 18 &Omega; resistor and a battery of voltage V0=8 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.20E-04?


 * -a) 6.259E-02 A
 * -b) 6.885E-02 A
 * -c) 7.573E-02 A
 * +d) 8.331E-02 A
 * -e) 9.164E-02 A

9) A parallel plate capacitor with a capicatnce C=7.40E-06 F whose plates have an area A=5.30E+03 m2 and separation d=6.30E-03 m is connected via a swith to a 5 &Omega; resistor and a battery of voltage V0=58 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.10E-04?


 * -a) 4.548E+01 V
 * -b) 5.003E+01 V
 * +c) 5.503E+01 V
 * -d) 6.054E+01 V
 * -e) 6.659E+01 V

10) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is the decay time?


 * +a) 2.57E-04 s
 * -b) 3.11E-04 s
 * -c) 3.77E-04 s
 * -d) 4.57E-04 s
 * -e) 5.53E-04 s

11) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.95E-09 Tesla
 * -b) 4.97E-09 Tesla
 * +c) 6.26E-09 Tesla
 * -d) 7.88E-09 Tesla
 * -e) 9.92E-09 Tesla

Key: C1
1) A circlular capactitor of radius 3.2 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * +a) 2.49E-04 s
 * -b) 3.02E-04 s
 * -c) 3.66E-04 s
 * -d) 4.43E-04 s
 * -e) 5.37E-04 s

2) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * -a) 7.315E-02 A
 * +b) 8.047E-02 A
 * -c) 8.851E-02 A
 * -d) 9.737E-02 A
 * -e) 1.071E-01 A

3) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * +a) 7.693E+01 V
 * -b) 8.463E+01 V
 * -c) 9.309E+01 V
 * -d) 1.024E+02 V
 * -e) 1.126E+02 V

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 22 turns per centimeter and the current applied to the solenoid is 568 mA, the net magnetic field is measured to be 1.29 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 8.205E+02
 * -b) $$\chi \text{ (chi) }=$$ 9.026E+02
 * -c) $$\chi \text{ (chi) }=$$ 9.928E+02
 * -d) $$\chi \text{ (chi) }=$$ 1.092E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.201E+03

5) A step-down transformer steps 18 kV down to 170 V. The high-voltage input is provided by a 240 &Omega; power line that carries 5 A of currentWhat is the output current (at the 170 V side ?)


 * +a) 5.294E+02 A
 * -b) 5.824E+02 A
 * -c) 6.406E+02 A
 * -d) 7.046E+02 A
 * -e) 7.751E+02 A

6) A long solenoid has a radius of 0.857 m and 58 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 0.144 m from the axis at time t=0.0898 s ?


 * -a) 1.256E-05 V/m
 * -b) 1.382E-05 V/m
 * -c) 1.520E-05 V/m
 * +d) 1.672E-05 V/m
 * -e) 1.839E-05 V/m

7) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 2.82E-09 Tesla
 * -b) 3.54E-09 Tesla
 * -c) 4.46E-09 Tesla
 * -d) 5.62E-09 Tesla
 * +e) 7.07E-09 Tesla

8) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * -a) 1.131E+00 N/m
 * -b) 1.244E+00 N/m
 * -c) 1.368E+00 N/m
 * +d) 1.505E+00 N/m
 * -e) 1.655E+00 N/m

9) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.571 m and $$B_{max}=\,$$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.321 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.226E+05 A
 * -b) 3.549E+05 A
 * -c) 3.904E+05 A
 * +d) 4.294E+05 A
 * -e) 4.724E+05 A

10) In an LC circuit, the self-inductance is 0.0735 H and the capacitance is 2.300E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.220E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 4.411E-04 s
 * -b) 4.852E-04 s
 * -c) 5.338E-04 s
 * -d) 5.871E-04 s
 * +e) 6.458E-04 s

11) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 5.49 mT and 5.570E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 9.223E+05 m/s
 * +b) 1.015E+06 m/s
 * -c) 1.116E+06 m/s
 * -d) 1.228E+06 m/s
 * -e) 1.350E+06 m/s

Key: C2
1) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 5.04 mT and 7.820E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 1.060E+06 m/s
 * -b) 1.166E+06 m/s
 * -c) 1.282E+06 m/s
 * -d) 1.411E+06 m/s
 * +e) 1.552E+06 m/s

2) A step-down transformer steps 9 kV down to 210 V. The high-voltage input is provided by a 170 &Omega; power line that carries 5 A of currentWhat is the output current (at the 210 V side ?)


 * -a) 1.948E+02 A
 * +b) 2.143E+02 A
 * -c) 2.357E+02 A
 * -d) 2.593E+02 A
 * -e) 2.852E+02 A

3) A long solenoid has a radius of 0.596 m and 19 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5 A and $$\alpha=$$29 s&minus;1.What is the induced electric fied at a distance 0.209 m from the axis at time t=0.0604 s ?


 * +a) 6.277E-05 V/m
 * -b) 6.904E-05 V/m
 * -c) 7.595E-05 V/m
 * -d) 8.354E-05 V/m
 * -e) 9.190E-05 V/m

4) A long rigid wire carries a 3 A current. What is the magnetic force per unit length on the wire if a 0.534 T magnetic field is directed 18&deg; away from the wire?


 * +a) 4.950E-01 N/m
 * -b) 5.445E-01 N/m
 * -c) 5.990E-01 N/m
 * -d) 6.589E-01 N/m
 * -e) 7.248E-01 N/m

5) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.230E-04 s
 * -b) 6.853E-04 s
 * -c) 7.538E-04 s
 * -d) 8.292E-04 s
 * +e) 9.121E-04 s

6) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.248 m and $$B_{max}=\,$$ 0.459 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.152 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 2.228E+05 A
 * -b) 2.451E+05 A
 * -c) 2.696E+05 A
 * +d) 2.966E+05 A
 * -e) 3.262E+05 A

7) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * +a) 5.017E+01 V
 * -b) 5.519E+01 V
 * -c) 6.071E+01 V
 * -d) 6.678E+01 V
 * -e) 7.345E+01 V

8) A circlular capactitor of radius 3.6 m has a gap of 19 mm, and a charge of 98 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 1.90E-08 Tesla
 * -b) 2.40E-08 Tesla
 * -c) 3.02E-08 Tesla
 * -d) 3.80E-08 Tesla
 * +e) 4.78E-08 Tesla

9) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * +a) 6.624E-02 A
 * -b) 7.287E-02 A
 * -c) 8.016E-02 A
 * -d) 8.817E-02 A
 * -e) 9.699E-02 A

10) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.188E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.307E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.438E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.582E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.740E+03

11) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is the decay time?


 * +a) 2.57E-04 s
 * -b) 3.11E-04 s
 * -c) 3.77E-04 s
 * -d) 4.57E-04 s
 * -e) 5.53E-04 s

Key: D0
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * +a) 3.575E+00 N/m
 * -b) 3.932E+00 N/m
 * -c) 4.325E+00 N/m
 * -d) 4.758E+00 N/m
 * -e) 5.234E+00 N/m

2) A 76 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 13 g, and the magnitude of the magnetic field is 0.367 T. What current is required to maintain this balance?


 * -a) 3.432E-01 A
 * -b) 3.775E-01 A
 * -c) 4.152E-01 A
 * +d) 4.568E-01 A
 * -e) 5.024E-01 A

3) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.76 cm to z=+1.99 cm


 * -a) 2.762E-04 T-m
 * +b) 3.038E-04 T-m
 * -c) 3.342E-04 T-m
 * -d) 3.676E-04 T-m
 * -e) 4.043E-04 T-m

4) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 7.035E-05 T
 * -b) By= 7.739E-05 T
 * -c) By= 8.512E-05 T
 * +d) By= 9.364E-05 T
 * -e) By= 1.030E-04 T

5) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * +a) 6.040E-05 V/m
 * -b) 6.644E-05 V/m
 * -c) 7.309E-05 V/m
 * -d) 8.039E-05 V/m
 * -e) 8.843E-05 V/m

6) An induced emf of 1.92V is measured across a coil of 74 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.38A in 0.69s. What is the self-inductance of the coil?


 * -a) 1.560E-01 H
 * -b) 1.716E-01 H
 * -c) 1.888E-01 H
 * +d) 2.076E-01 H
 * -e) 2.284E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 480 Hz and an amplitude of 0.63 V;. If R =7 &Omega;, L= 3.80E-03H, and C=5.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * +a) 9.972E-01 &rad;
 * -b) 1.097E+00 &rad;
 * -c) 1.207E+00 &rad;
 * -d) 1.327E+00 &rad;
 * -e) 1.460E+00 &rad;

8) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 8.969E-08 N
 * -b) 9.866E-08 N
 * -c) 1.085E-07 N
 * -d) 1.194E-07 N
 * +e) 1.313E-07 N

9) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * +a) 5.017E+01 V
 * -b) 5.519E+01 V
 * -c) 6.071E+01 V
 * -d) 6.678E+01 V
 * -e) 7.345E+01 V

10) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.30E-09 Tesla
 * -b) 4.15E-09 Tesla
 * -c) 5.23E-09 Tesla
 * +d) 6.58E-09 Tesla
 * -e) 8.29E-09 Tesla

11) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 62 &mu;C.  What is the electric field between the plates?


 * -a) 9.50E+04 N/C (or V/m)
 * +b) 1.15E+05 N/C (or V/m)
 * -c) 1.39E+05 N/C (or V/m)
 * -d) 1.69E+05 N/C (or V/m)
 * -e) 2.05E+05 N/C (or V/m)

Key: D1
1) An induced emf of 1.7V is measured across a coil of 81 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.07A in 0.174s. What is the self-inductance of the coil?


 * -a) 3.458E-02 H
 * -b) 3.804E-02 H
 * +c) 4.184E-02 H
 * -d) 4.602E-02 H
 * -e) 5.062E-02 H

2) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 &Omega;, L= 7.70E-03H, and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 1.329E+00 &rad;
 * +b) 1.462E+00 &rad;
 * -c) 1.608E+00 &rad;
 * -d) 1.769E+00 &rad;
 * -e) 1.946E+00 &rad;

3) A circlular capactitor of radius 4.9 m has a gap of 11 mm, and a charge of 85 &mu;C.  What is the electric field between the plates?


 * +a) 1.27E+05 N/C (or V/m)
 * -b) 1.54E+05 N/C (or V/m)
 * -c) 1.87E+05 N/C (or V/m)
 * -d) 2.26E+05 N/C (or V/m)
 * -e) 2.74E+05 N/C (or V/m)

4) Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 5.930E-05 T
 * +b) By= 6.523E-05 T
 * -c) By= 7.175E-05 T
 * -d) By= 7.892E-05 T
 * -e) By= 8.682E-05 T

5) A long solenoid has a radius of 0.757 m and 90 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$30 s&minus;1.What is the induced electric fied at a distance 2.08 m from the axis at time t=0.0442 s ?


 * -a) 6.527E-04 V/m
 * -b) 7.180E-04 V/m
 * -c) 7.898E-04 V/m
 * +d) 8.688E-04 V/m
 * -e) 9.556E-04 V/m

6) A 17 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.768 T. What current is required to maintain this balance?


 * -a) 4.963E-01 A
 * -b) 5.459E-01 A
 * +c) 6.005E-01 A
 * -d) 6.605E-01 A
 * -e) 7.266E-01 A

7) A circlular capactitor of radius 4.6 m has a gap of 18 mm, and a charge of 44 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 6.64E-09 Tesla
 * +b) 8.36E-09 Tesla
 * -c) 1.05E-08 Tesla
 * -d) 1.32E-08 Tesla
 * -e) 1.67E-08 Tesla

8) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * +a) 3.575E+00 N/m
 * -b) 3.932E+00 N/m
 * -c) 4.325E+00 N/m
 * -d) 4.758E+00 N/m
 * -e) 5.234E+00 N/m

9) A parallel plate capacitor with a capicatnce C=8.30E-06 F whose plates have an area A=7.00E+03 m2 and separation d=7.50E-03 m is connected via a swith to a 51 &Omega; resistor and a battery of voltage V0=81 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.20E-03?


 * -a) 5.728E+01 V
 * -b) 6.301E+01 V
 * -c) 6.931E+01 V
 * +d) 7.624E+01 V
 * -e) 8.387E+01 V

10) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.11 cm to z=+2.76 cm


 * -a) 1.068E-04 T-m
 * -b) 1.175E-04 T-m
 * -c) 1.292E-04 T-m
 * -d) 1.421E-04 T-m
 * +e) 1.563E-04 T-m

11) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.673E-07 N
 * -b) 2.940E-07 N
 * -c) 3.234E-07 N
 * -d) 3.558E-07 N
 * -e) 3.913E-07 N

Key: D2
1) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * +a) 8.32E-09 Tesla
 * -b) 1.05E-08 Tesla
 * -c) 1.32E-08 Tesla
 * -d) 1.66E-08 Tesla
 * -e) 2.09E-08 Tesla

2) A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?


 * -a) 5.131E+01 V
 * -b) 5.644E+01 V
 * -c) 6.209E+01 V
 * -d) 6.830E+01 V
 * +e) 7.513E+01 V

3) An induced emf of 6.29V is measured across a coil of 85 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.15A in 0.913s. What is the self-inductance of the coil?


 * -a) 2.428E+00 H
 * +b) 2.671E+00 H
 * -c) 2.938E+00 H
 * -d) 3.232E+00 H
 * -e) 3.555E+00 H

4) A long solenoid has a radius of 0.583 m and 38 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$24 s&minus;1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?


 * -a) 1.655E-04 V/m
 * -b) 1.821E-04 V/m
 * -c) 2.003E-04 V/m
 * +d) 2.203E-04 V/m
 * -e) 2.424E-04 V/m

5) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 &Omega;, L= 9.50E-03H, and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.646E-01 &rad;
 * -b) 9.511E-01 &rad;
 * -c) 1.046E+00 &rad;
 * -d) 1.151E+00 &rad;
 * +e) 1.266E+00 &rad;

6) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * +a) 3.575E+00 N/m
 * -b) 3.932E+00 N/m
 * -c) 4.325E+00 N/m
 * -d) 4.758E+00 N/m
 * -e) 5.234E+00 N/m

7) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.275E-07 N
 * -b) 5.803E-07 N
 * +c) 6.383E-07 N
 * -d) 7.021E-07 N
 * -e) 7.723E-07 N

8) A 96 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.325 T. What current is required to maintain this balance?


 * -a) 2.596E-01 A
 * -b) 2.855E-01 A
 * +c) 3.141E-01 A
 * -d) 3.455E-01 A
 * -e) 3.801E-01 A

9) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * -a) 2.44E+05 N/C (or V/m)
 * +b) 2.95E+05 N/C (or V/m)
 * -c) 3.58E+05 N/C (or V/m)
 * -d) 4.34E+05 N/C (or V/m)
 * -e) 5.25E+05 N/C (or V/m)

10) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 7.035E-05 T
 * -b) By= 7.739E-05 T
 * -c) By= 8.512E-05 T
 * +d) By= 9.364E-05 T
 * -e) By= 1.030E-04 T

11) A solenoid has 8.890E+04 turns wound around a cylinder of diameter 1.32 cm and length 15 m. The current through the coils is 0.297 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.41 cm to z=+2.56 cm


 * -a) 7.257E-05 T-m
 * -b) 7.983E-05 T-m
 * +c) 8.781E-05 T-m
 * -d) 9.660E-05 T-m
 * -e) 1.063E-04 T-m

Key: E0
1) The silver ribbon shown are a=4.81 cm, b=3.96 cm, and c= 1.3 cm. The current carries a current of 274 A and it lies in a uniform magnetic field of 3.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 7.202E-06 V
 * -b) 7.922E-06 V
 * -c) 8.714E-06 V
 * -d) 9.586E-06 V
 * -e) 1.054E-05 V

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0887 T . It emerges after being deflected by 69&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 2.561E-07 s
 * +b) 2.817E-07 s
 * -c) 3.099E-07 s
 * -d) 3.409E-07 s
 * -e) 3.750E-07 s

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.82 kA, I2=0.964 kA, and I3=2.21 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.069E-03 T-m
 * -b) 1.176E-03 T-m
 * -c) 1.294E-03 T-m
 * -d) 1.423E-03 T-m
 * +e) 1.566E-03 T-m

4) Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.171E-05 T
 * +b) Bx= 6.788E-05 T
 * -c) Bx= 7.467E-05 T
 * -d) Bx= 8.213E-05 T
 * -e) Bx= 9.035E-05 T

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * -a) 1.605E-04 V/m
 * +b) 1.766E-04 V/m
 * -c) 1.942E-04 V/m
 * -d) 2.136E-04 V/m
 * -e) 2.350E-04 V/m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if &epsilon; = 6.08 V, R = 1.88 &Omega;, and L = 4.67 H?


 * +a) -5.192E+00 s
 * -b) -5.711E+00 s
 * -c) -6.282E+00 s
 * -d) -6.910E+00 s
 * -e) -7.601E+00 s

7) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a  99 mF capacitor?


 * -a) 1.644E+00 A
 * +b) 1.808E+00 A
 * -c) 1.989E+00 A
 * -d) 2.188E+00 A
 * -e) 2.407E+00 A

8) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * +a) 6.624E-02 A
 * -b) 7.287E-02 A
 * -c) 8.016E-02 A
 * -d) 8.817E-02 A
 * -e) 9.699E-02 A

9) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.673E-07 N
 * -b) 2.940E-07 N
 * -c) 3.234E-07 N
 * -d) 3.558E-07 N
 * -e) 3.913E-07 N

10) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.28E-11 Vs2m-1
 * -b) 8.82E-11 Vs2m-1
 * +c) 1.07E-10 Vs2m-1
 * -d) 1.29E-10 Vs2m-1
 * -e) 1.57E-10 Vs2m-1

11) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * -a) 3.07E-04 s
 * -b) 3.71E-04 s
 * +c) 4.50E-04 s
 * -d) 5.45E-04 s
 * -e) 6.61E-04 s

Key: E1
1) A circlular capactitor of radius 4.4 m has a gap of 17 mm, and a charge of 65 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.56E-11 Vs2m-1
 * -b) 6.74E-11 Vs2m-1
 * +c) 8.17E-11 Vs2m-1
 * -d) 9.90E-11 Vs2m-1
 * -e) 1.20E-10 Vs2m-1

2) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.63% of its maximum value if &epsilon; = 8.7 V, R = 8.35 &Omega;, and L = 1.44 H?


 * +a) -3.137E-01 s
 * -b) -3.451E-01 s
 * -c) -3.796E-01 s
 * -d) -4.176E-01 s
 * -e) -4.593E-01 s

3) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.075 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 5.002E-08 N
 * -b) 5.502E-08 N
 * -c) 6.052E-08 N
 * -d) 6.657E-08 N
 * -e) 7.323E-08 N

4) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * -a) 1.16E-04 s
 * -b) 1.41E-04 s
 * -c) 1.71E-04 s
 * -d) 2.07E-04 s
 * +e) 2.50E-04 s

5) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0582 T . It emerges after being deflected by 77&deg; from its original direction. How much time did it spend in that magnetic field?


 * +a) 4.791E-07 s
 * -b) 5.271E-07 s
 * -c) 5.798E-07 s
 * -d) 6.377E-07 s
 * -e) 7.015E-07 s

6) Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 3.394E-05 T
 * -b) Bx= 3.733E-05 T
 * -c) Bx= 4.106E-05 T
 * -d) Bx= 4.517E-05 T
 * +e) Bx= 4.969E-05 T

7) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?


 * +a) 6.182E-04 V/m
 * -b) 6.801E-04 V/m
 * -c) 7.481E-04 V/m
 * -d) 8.229E-04 V/m
 * -e) 9.052E-04 V/m

8) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * -a) 7.315E-02 A
 * +b) 8.047E-02 A
 * -c) 8.851E-02 A
 * -d) 9.737E-02 A
 * -e) 1.071E-01 A

9) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a  59 mF capacitor?


 * +a) 5.042E+00 A
 * -b) 5.546E+00 A
 * -c) 6.100E+00 A
 * -d) 6.710E+00 A
 * -e) 7.381E+00 A

10) The silver ribbon shown are a=3.68 cm, b=2.66 cm, and c= 0.505 cm. The current carries a current of 113 A and it lies in a uniform magnetic field of 3.12 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 6.104E-06 V
 * -b) 6.714E-06 V
 * +c) 7.385E-06 V
 * -d) 8.124E-06 V
 * -e) 8.936E-06 V

11) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.55 kA, I2=1.02 kA, and I3=1.81 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 8.204E-04 T-m
 * -b) 9.025E-04 T-m
 * +c) 9.927E-04 T-m
 * -d) 1.092E-03 T-m
 * -e) 1.201E-03 T-m

Key: E2
1) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a  6 mF capacitor?


 * -a) 5.253E-02 A
 * -b) 5.778E-02 A
 * -c) 6.356E-02 A
 * -d) 6.991E-02 A
 * +e) 7.691E-02 A

2) The silver ribbon shown are a=4.14 cm, b=3.69 cm, and c= 1.13 cm. The current carries a current of 291 A and it lies in a uniform magnetic field of 3.32 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 6.795E-06 V
 * -b) 7.475E-06 V
 * -c) 8.222E-06 V
 * +d) 9.045E-06 V
 * -e) 9.949E-06 V

3) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=1.00E+04 m2 and separation d=9.00E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * -a) 6.394E-02 A
 * +b) 7.033E-02 A
 * -c) 7.736E-02 A
 * -d) 8.510E-02 A
 * -e) 9.361E-02 A

4) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?


 * +a) 6.182E-04 V/m
 * -b) 6.801E-04 V/m
 * -c) 7.481E-04 V/m
 * -d) 8.229E-04 V/m
 * -e) 9.052E-04 V/m

5) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.51 kA, I2=1.32 kA, and I3=2.73 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.331E-03 T-m
 * -b) 1.464E-03 T-m
 * -c) 1.611E-03 T-m
 * +d) 1.772E-03 T-m
 * -e) 1.949E-03 T-m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.59% of its maximum value if &epsilon; = 1.14 V, R = 6.17 &Omega;, and L = 5.45 H?


 * +a) -1.614E+00 s
 * -b) -1.775E+00 s
 * -c) -1.952E+00 s
 * -d) -2.148E+00 s
 * -e) -2.362E+00 s

7) What is the radiation force on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 1.630E-08 N
 * -b) 1.793E-08 N
 * -c) 1.972E-08 N
 * -d) 2.169E-08 N
 * -e) 2.386E-08 N

8) Three wires sit at the corners of a square of length 0.75 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.1 A, 1.11 A, 2.26 A), respectively. What is the x-component of the magnetic field at point P?


 * +a) Bx= 7.507E-05 T
 * -b) Bx= 8.257E-05 T
 * -c) Bx= 9.083E-05 T
 * -d) Bx= 9.991E-05 T
 * -e) Bx= 1.099E-04 T

9) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * +a) 3.62E-04 s
 * -b) 4.38E-04 s
 * -c) 5.31E-04 s
 * -d) 6.43E-04 s
 * -e) 7.79E-04 s

10) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0883 T . It emerges after being deflected by 74&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 2.280E-07 s
 * -b) 2.508E-07 s
 * -c) 2.759E-07 s
 * +d) 3.035E-07 s
 * -e) 3.339E-07 s

11) A circlular capactitor of radius 4.1 m has a gap of 8 mm, and a charge of 24 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 2.05E-11 Vs2m-1
 * -b) 2.49E-11 Vs2m-1
 * +c) 3.02E-11 Vs2m-1
 * -d) 3.65E-11 Vs2m-1
 * -e) 4.43E-11 Vs2m-1

Key: F0
1) A charged particle in a magnetic field of 4.910E-04 T is moving perpendicular to the magnetic field with a speed of 3.000E+05 m/s. What is the period of orbit if orbital radius is 0.507 m?


 * +a) 1.062E-05 s
 * -b) 1.168E-05 s
 * -c) 1.285E-05 s
 * -d) 1.413E-05 s
 * -e) 1.555E-05 s

2) A 24 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.706 T. What current is required to maintain this balance?


 * -a) 5.258E-01 A
 * +b) 5.784E-01 A
 * -c) 6.362E-01 A
 * -d) 6.998E-01 A
 * -e) 7.698E-01 A

3) A wire carries a current of 332 A in a circular arc with radius 2.47 cm swept through 44 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * +a) 3.389E+00 Tesla
 * -b) 3.727E+00 Tesla
 * -c) 4.100E+00 Tesla
 * -d) 4.510E+00 Tesla
 * -e) 4.961E+00 Tesla

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.45 kA, I2=2.68 kA, and I3=5.5 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 3.544E-03 T-m
 * -b) 3.898E-03 T-m
 * -c) 4.288E-03 T-m
 * -d) 4.717E-03 T-m
 * -e) 5.188E-03 T-m

5) The current through the windings of a solenoid with n= 1.850E+03 turns per meter is changing at a rate dI/dt=17 A/s. The solenoid is 98 cm long and has a cross-sectional diameter of 3.38 cm.  A small coil consisting of N=23turns wraped in a circle of diameter 1.72 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 1.587E-04 V
 * -b) 1.745E-04 V
 * -c) 1.920E-04 V
 * +d) 2.112E-04 V
 * -e) 2.323E-04 V

6) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =2.47 s if &epsilon; = 7.04 V, R = 7.69 &Omega;, and L = 5.78 H?


 * -a) 4.249E-01 V
 * -b) 5.099E-01 V
 * -c) 6.118E-01 V
 * -d) 7.342E-01 V
 * +e) 8.810E-01 V

7) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 6.60E-03H, and C=5.30E-06 F, what is the rms power transferred to the resistor?


 * -a) 2.007E-03 Watts
 * -b) 2.208E-03 Watts
 * -c) 2.429E-03 Watts
 * +d) 2.672E-03 Watts
 * -e) 2.939E-03 Watts

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.003E+02 km
 * -b) 1.103E+02 km
 * -c) 1.213E+02 km
 * +d) 1.335E+02 km
 * -e) 1.468E+02 km

9) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m2 and separation d=3.50E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?


 * -a) 3.751E+03 V/m
 * +b) 4.126E+03 V/m
 * -c) 4.539E+03 V/m
 * -d) 4.993E+03 V/m
 * -e) 5.492E+03 V/m

10) A circlular capactitor of radius 3.3 m has a gap of 12 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * -a) 9.94E-05 s
 * -b) 1.20E-04 s
 * -c) 1.46E-04 s
 * +d) 1.77E-04 s
 * -e) 2.14E-04 s

11) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 8.75E-12 Vs2m-1
 * -b) 1.06E-11 Vs2m-1
 * -c) 1.28E-11 Vs2m-1
 * -d) 1.56E-11 Vs2m-1
 * +e) 1.88E-11 Vs2m-1

Key: F1
1) A circlular capactitor of radius 4.5 m has a gap of 18 mm, and a charge of 92 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.88E-11 Vs2m-1
 * -b) 9.54E-11 Vs2m-1
 * +c) 1.16E-10 Vs2m-1
 * -d) 1.40E-10 Vs2m-1
 * -e) 1.70E-10 Vs2m-1

2) A charged particle in a magnetic field of 3.600E-04 T is moving perpendicular to the magnetic field with a speed of 5.960E+05 m/s. What is the period of orbit if orbital radius is 0.397 m?


 * -a) 3.805E-06 s
 * +b) 4.185E-06 s
 * -c) 4.604E-06 s
 * -d) 5.064E-06 s
 * -e) 5.571E-06 s

3) The output of an ac generator connected to an RLC series combination has a frequency of 6.10E+04 Hz and an amplitude of 8 V. If R =5 &Omega;, L= 9.10E-03H, and C=8.80E-06 F, what is the rms power transferred to the resistor?


 * -a) 4.320E-04 Watts
 * -b) 4.752E-04 Watts
 * +c) 5.227E-04 Watts
 * -d) 5.750E-04 Watts
 * -e) 6.325E-04 Watts

4) A 14 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 11 g, and the magnitude of the magnetic field is 0.448 T. What current is required to maintain this balance?


 * -a) 1.174E+00 A
 * -b) 1.291E+00 A
 * -c) 1.420E+00 A
 * -d) 1.562E+00 A
 * +e) 1.719E+00 A

5) A circlular capactitor of radius 3.6 m has a gap of 14 mm, and a charge of 98 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * -a) 1.40E-04 s
 * -b) 1.70E-04 s
 * +c) 2.06E-04 s
 * -d) 2.50E-04 s
 * -e) 3.02E-04 s

6) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.250E-03 T-m
 * +b) 1.375E-03 T-m
 * -c) 1.512E-03 T-m
 * -d) 1.663E-03 T-m
 * -e) 1.830E-03 T-m

7) A 57 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.020E+02 km
 * -b) 1.122E+02 km
 * -c) 1.235E+02 km
 * +d) 1.358E+02 km
 * -e) 1.494E+02 km

8) The current through the windings of a solenoid with n= 2.040E+03 turns per meter is changing at a rate dI/dt=19 A/s. The solenoid is 76 cm long and has a cross-sectional diameter of 3.23 cm.  A small coil consisting of N=25turns wraped in a circle of diameter 1.67 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 2.204E-04 V
 * -b) 2.425E-04 V
 * +c) 2.667E-04 V
 * -d) 2.934E-04 V
 * -e) 3.227E-04 V

9) A parallel plate capacitor with a capicatnce C=5.20E-06 F whose plates have an area A=2.90E+03 m2 and separation d=4.90E-03 m is connected via a swith to a 93 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.20E-03?


 * -a) 6.896E+02 V/m
 * -b) 7.585E+02 V/m
 * -c) 8.344E+02 V/m
 * -d) 9.178E+02 V/m
 * +e) 1.010E+03 V/m

10) A wire carries a current of 106 A in a circular arc with radius 1.32 cm swept through 38 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * -a) 1.589E+00 Tesla
 * +b) 1.748E+00 Tesla
 * -c) 1.923E+00 Tesla
 * -d) 2.116E+00 Tesla
 * -e) 2.327E+00 Tesla

11) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =0.741 s if &epsilon; = 7.36 V, R = 5.33 &Omega;, and L = 1.27 H?


 * -a) 7.635E-01 V
 * -b) 9.162E-01 V
 * -c) 1.099E+00 V
 * +d) 1.319E+00 V
 * -e) 1.583E+00 V

Key: F2
1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.51 kA, I2=2.33 kA, and I3=5.35 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 3.795E-03 T-m
 * -b) 4.175E-03 T-m
 * -c) 4.592E-03 T-m
 * -d) 5.051E-03 T-m
 * -e) 5.556E-03 T-m

2) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * -a) 1.753E+02 km
 * -b) 1.928E+02 km
 * +c) 2.121E+02 km
 * -d) 2.333E+02 km
 * -e) 2.567E+02 km

3) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 7.00E-03H, and C=6.60E-06 F, what is the rms power transferred to the resistor?


 * -a) 1.146E-03 Watts
 * -b) 1.260E-03 Watts
 * -c) 1.386E-03 Watts
 * -d) 1.525E-03 Watts
 * +e) 1.677E-03 Watts

4) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm.  A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 1.407E-04 V
 * +b) 1.548E-04 V
 * -c) 1.703E-04 V
 * -d) 1.873E-04 V
 * -e) 2.061E-04 V

5) A 25 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.702 T. What current is required to maintain this balance?


 * -a) 5.076E-01 A
 * +b) 5.584E-01 A
 * -c) 6.142E-01 A
 * -d) 6.757E-01 A
 * -e) 7.432E-01 A

6) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =20.1 s if &epsilon; = 5.77 V, R = 1.38 &Omega;, and L = 5.45 H?


 * -a) 3.463E+00 V
 * +b) 4.156E+00 V
 * -c) 4.987E+00 V
 * -d) 5.984E+00 V
 * -e) 7.181E+00 V

7) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * +a) 3.62E-04 s
 * -b) 4.38E-04 s
 * -c) 5.31E-04 s
 * -d) 6.43E-04 s
 * -e) 7.79E-04 s

8) A wire carries a current of 303 A in a circular arc with radius 2.2 cm swept through 72 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * -a) 3.881E+00 Tesla
 * -b) 4.269E+00 Tesla
 * -c) 4.696E+00 Tesla
 * -d) 5.165E+00 Tesla
 * +e) 5.682E+00 Tesla

9) A charged particle in a magnetic field of 3.600E-04 T is moving perpendicular to the magnetic field with a speed of 5.960E+05 m/s. What is the period of orbit if orbital radius is 0.397 m?


 * -a) 3.805E-06 s
 * +b) 4.185E-06 s
 * -c) 4.604E-06 s
 * -d) 5.064E-06 s
 * -e) 5.571E-06 s

10) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 8.75E-12 Vs2m-1
 * -b) 1.06E-11 Vs2m-1
 * -c) 1.28E-11 Vs2m-1
 * -d) 1.56E-11 Vs2m-1
 * +e) 1.88E-11 Vs2m-1

11) A parallel plate capacitor with a capicatnce C=4.50E-06 F whose plates have an area A=3.30E+03 m2 and separation d=6.40E-03 m is connected via a swith to a 83 &Omega; resistor and a battery of voltage V0=56 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.40E-03?


 * -a) 7.767E+03 V/m
 * +b) 8.544E+03 V/m
 * -c) 9.398E+03 V/m
 * -d) 1.034E+04 V/m
 * -e) 1.137E+04 V/m

Key: G0
1) A charged particle in a magnetic field of 6.400E-04 T is moving perpendicular to the magnetic field with a speed of 1.360E+05 m/s. What is the period of orbit if orbital radius is 0.751 m?


 * -a) 3.154E-05 s
 * +b) 3.470E-05 s
 * -c) 3.817E-05 s
 * -d) 4.198E-05 s
 * -e) 4.618E-05 s

2) A circular current loop of radius 1.94 cm carries a current of 1.83 mA. What is the magnitude of the torque if the dipole is oriented at 43 &deg; to a uniform magnetic fied of 0.156 T?


 * -a) 1.903E-07 N m
 * -b) 2.093E-07 N m
 * +c) 2.302E-07 N m
 * -d) 2.532E-07 N m
 * -e) 2.785E-07 N m

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.250E-03 T-m
 * +b) 1.375E-03 T-m
 * -c) 1.512E-03 T-m
 * -d) 1.663E-03 T-m
 * -e) 1.830E-03 T-m

4) Three wires sit at the corners of a square of length 0.532 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.11 A, 1.25 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 5.930E-05 T
 * +b) By= 6.523E-05 T
 * -c) By= 7.175E-05 T
 * -d) By= 7.892E-05 T
 * -e) By= 8.682E-05 T

5) A cylinder of height 1.68 cm and radius 3.44 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.28 cm from point O and moves at a speed of 1.41 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * -a) 7.479E+00 cm3/s
 * -b) 8.227E+00 cm3/s
 * -c) 9.049E+00 cm3/s
 * -d) 9.954E+00 cm3/s
 * +e) 1.095E+01 cm3/s

6) In an LC circuit, the self-inductance is 0.0126 H and the capacitance is 3.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.420E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 2.204E-04 s
 * -b) 2.425E-04 s
 * -c) 2.667E-04 s
 * -d) 2.934E-04 s
 * +e) 3.227E-04 s

7) An ac generator produces an emf of amplitude 73 V at a frequency of 110 Hz. What is the maximum amplitude of the current if the generator is connected to a  70 mF inductor?


 * -a) 1.134E+00 A
 * -b) 1.247E+00 A
 * -c) 1.372E+00 A
 * +d) 1.509E+00 A
 * -e) 1.660E+00 A

8) A parallel plate capacitor with a capicatnce C=7.50E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=77 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.70E-03?


 * -a) 5.131E+01 V
 * -b) 5.644E+01 V
 * -c) 6.209E+01 V
 * -d) 6.830E+01 V
 * +e) 7.513E+01 V

9) What is the radiation pressure on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.057 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 3.075E-07 N/m2
 * -b) 3.382E-07 N/m2
 * -c) 3.720E-07 N/m2
 * -d) 4.092E-07 N/m2
 * -e) 4.502E-07 N/m2

10) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * +a) 8.32E-09 Tesla
 * -b) 1.05E-08 Tesla
 * -c) 1.32E-08 Tesla
 * -d) 1.66E-08 Tesla
 * -e) 2.09E-08 Tesla

11) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 45 &mu;C.  What is the electric field between the plates?


 * -a) 6.31E+04 N/C (or V/m)
 * +b) 7.65E+04 N/C (or V/m)
 * -c) 9.26E+04 N/C (or V/m)
 * -d) 1.12E+05 N/C (or V/m)
 * -e) 1.36E+05 N/C (or V/m)

Key: G1
1) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * -a) 2.44E+05 N/C (or V/m)
 * +b) 2.95E+05 N/C (or V/m)
 * -c) 3.58E+05 N/C (or V/m)
 * -d) 4.34E+05 N/C (or V/m)
 * -e) 5.25E+05 N/C (or V/m)

2) Three wires sit at the corners of a square of length 0.703 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.49 A, 1.32 A, 1.75 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 8.962E-05 T
 * -b) By= 9.858E-05 T
 * -c) By= 1.084E-04 T
 * -d) By= 1.193E-04 T
 * -e) By= 1.312E-04 T

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.250E-03 T-m
 * +b) 1.375E-03 T-m
 * -c) 1.512E-03 T-m
 * -d) 1.663E-03 T-m
 * -e) 1.830E-03 T-m

4) A circular current loop of radius 3.0 cm carries a current of 1.58 mA. What is the magnitude of the torque if the dipole is oriented at 63 &deg; to a uniform magnetic fied of 0.408 T?


 * -a) 1.476E-06 N m
 * +b) 1.624E-06 N m
 * -c) 1.786E-06 N m
 * -d) 1.965E-06 N m
 * -e) 2.162E-06 N m

5) A cylinder of height 3.82 cm and radius 5.6 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.89 cm from point O and moves at a speed of 4.25 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * -a) 7.280E+01 cm3/s
 * -b) 8.008E+01 cm3/s
 * +c) 8.808E+01 cm3/s
 * -d) 9.689E+01 cm3/s
 * -e) 1.066E+02 cm3/s

6) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.048 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.253E-05 N/m2
 * -b) 1.378E-05 N/m2
 * -c) 1.516E-05 N/m2
 * +d) 1.667E-05 N/m2
 * -e) 1.834E-05 N/m2

7) In an LC circuit, the self-inductance is 0.0273 H and the capacitance is 6.440E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.620E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 5.443E-04 s
 * -b) 5.988E-04 s
 * +c) 6.586E-04 s
 * -d) 7.245E-04 s
 * -e) 7.969E-04 s

8) A charged particle in a magnetic field of 4.970E-04 T is moving perpendicular to the magnetic field with a speed of 2.950E+05 m/s. What is the period of orbit if orbital radius is 0.344 m?


 * +a) 7.327E-06 s
 * -b) 8.060E-06 s
 * -c) 8.865E-06 s
 * -d) 9.752E-06 s
 * -e) 1.073E-05 s

9) A parallel plate capacitor with a capicatnce C=1.80E-06 F whose plates have an area A=670.0 m2 and separation d=3.30E-03 m is connected via a swith to a 40 &Omega; resistor and a battery of voltage V0=97 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.40E-04?


 * -a) 7.731E+01 V
 * -b) 8.504E+01 V
 * +c) 9.354E+01 V
 * -d) 1.029E+02 V
 * -e) 1.132E+02 V

10) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.95E-09 Tesla
 * -b) 4.97E-09 Tesla
 * +c) 6.26E-09 Tesla
 * -d) 7.88E-09 Tesla
 * -e) 9.92E-09 Tesla

11) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a  97 mF inductor?


 * -a) 4.972E-01 A
 * -b) 5.469E-01 A
 * +c) 6.016E-01 A
 * -d) 6.618E-01 A
 * -e) 7.280E-01 A

Key: G2
1) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * -a) 2.80E+04 N/C (or V/m)
 * -b) 3.40E+04 N/C (or V/m)
 * +c) 4.12E+04 N/C (or V/m)
 * -d) 4.99E+04 N/C (or V/m)
 * -e) 6.04E+04 N/C (or V/m)

2) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?


 * +a) 1.141E-05 s
 * -b) 1.255E-05 s
 * -c) 1.381E-05 s
 * -d) 1.519E-05 s
 * -e) 1.671E-05 s

3) Three wires sit at the corners of a square of length 0.76 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.91 A, 1.34 A, 1.05 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 5.611E-05 T
 * -b) By= 6.172E-05 T
 * +c) By= 6.789E-05 T
 * -d) By= 7.468E-05 T
 * -e) By= 8.215E-05 T

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.66 kA, I2=1.25 kA, and I3=2.74 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.547E-03 T-m
 * -b) 1.702E-03 T-m
 * +c) 1.872E-03 T-m
 * -d) 2.060E-03 T-m
 * -e) 2.266E-03 T-m

5) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a  35 mF inductor?


 * -a) 2.422E+00 A
 * +b) 2.664E+00 A
 * -c) 2.930E+00 A
 * -d) 3.224E+00 A
 * -e) 3.546E+00 A

6) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 88 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 1.86E-08 Tesla
 * -b) 2.34E-08 Tesla
 * +c) 2.95E-08 Tesla
 * -d) 3.72E-08 Tesla
 * -e) 4.68E-08 Tesla

7) What is the radiation pressure on an object that is 8.30E+11 m away from the sun and has cross-sectional area of 0.097 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.928E-07 N/m2
 * -b) 3.221E-07 N/m2
 * -c) 3.543E-07 N/m2
 * -d) 3.898E-07 N/m2
 * -e) 4.287E-07 N/m2

8) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.166E-04 s
 * -b) 6.783E-04 s
 * -c) 7.461E-04 s
 * -d) 8.207E-04 s
 * +e) 9.028E-04 s

9) A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * -a) 3.093E+01 cm3/s
 * -b) 3.403E+01 cm3/s
 * +c) 3.743E+01 cm3/s
 * -d) 4.117E+01 cm3/s
 * -e) 4.529E+01 cm3/s

10) A parallel plate capacitor with a capicatnce C=9.60E-06 F whose plates have an area A=5.40E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 29 &Omega; resistor and a battery of voltage V0=50 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.30E-04?


 * -a) 3.923E+01 V
 * -b) 4.315E+01 V
 * +c) 4.746E+01 V
 * -d) 5.221E+01 V
 * -e) 5.743E+01 V

11) A circular current loop of radius 2.48 cm carries a current of 3.67 mA. What is the magnitude of the torque if the dipole is oriented at 21 &deg; to a uniform magnetic fied of 0.402 T?


 * +a) 1.022E-06 N m
 * -b) 1.124E-06 N m
 * -c) 1.236E-06 N m
 * -d) 1.360E-06 N m
 * -e) 1.496E-06 N m

Key: H0
1) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.83 T magnetic field is directed 22&deg; away from the wire?


 * -a) 1.062E+00 N/m
 * -b) 1.168E+00 N/m
 * -c) 1.285E+00 N/m
 * -d) 1.413E+00 N/m
 * +e) 1.555E+00 N/m

2) A circular current loop of radius 1.17 cm carries a current of 3.68 mA. What is the magnitude of the torque if the dipole is oriented at 55 &deg; to a uniform magnetic fied of 0.179 T?


 * -a) 1.585E-07 N m
 * -b) 1.743E-07 N m
 * -c) 1.918E-07 N m
 * -d) 2.110E-07 N m
 * +e) 2.321E-07 N m

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.04 mm from the center of a wire of radius 5 mm if the current is 1A?


 * -a) 1.115E-05 T
 * -b) 1.226E-05 T
 * -c) 1.349E-05 T
 * -d) 1.484E-05 T
 * +e) 1.632E-05 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.736 m and $$B_{max}=\,$$ 0.204 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.532 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.764E+05 A
 * -b) 4.140E+05 A
 * -c) 4.554E+05 A
 * +d) 5.010E+05 A
 * -e) 5.510E+05 A

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.75 T and $$\omega=$$9.800E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.22 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 4.198E+04 V
 * -b) 4.618E+04 V
 * +c) 5.080E+04 V
 * -d) 5.588E+04 V
 * -e) 6.147E+04 V

6) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.7mm$$, and $$n=2.76$$. What is the volume of the washer?


 * -a) 1.038E+00 cm3
 * -b) 1.142E+00 cm3
 * +c) 1.256E+00 cm3
 * -d) 1.381E+00 cm3
 * -e) 1.520E+00 cm3

7) An ac generator produces an emf of amplitude 46 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a  63 mF inductor?


 * -a) 4.961E-01 A
 * -b) 5.457E-01 A
 * -c) 6.002E-01 A
 * -d) 6.603E-01 A
 * +e) 7.263E-01 A

8) A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=3.20E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 27 &Omega; resistor and a battery of voltage V0=80 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.60E-04?


 * -a) 9.524E-01 A
 * +b) 1.048E+00 A
 * -c) 1.152E+00 A
 * -d) 1.268E+00 A
 * -e) 1.394E+00 A

9) What is the radiation pressure on an object that is 8.10E+11 m away from the sun and has cross-sectional area of 0.057 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 3.075E-07 N/m2
 * -b) 3.382E-07 N/m2
 * -c) 3.720E-07 N/m2
 * -d) 4.092E-07 N/m2
 * -e) 4.502E-07 N/m2

10) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * -a) 2.44E+05 N/C (or V/m)
 * +b) 2.95E+05 N/C (or V/m)
 * -c) 3.58E+05 N/C (or V/m)
 * -d) 4.34E+05 N/C (or V/m)
 * -e) 5.25E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.3 m has a gap of 11 mm, and a charge of 66 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 6.85E-11 Vs2m-1
 * +b) 8.29E-11 Vs2m-1
 * -c) 1.00E-10 Vs2m-1
 * -d) 1.22E-10 Vs2m-1
 * -e) 1.47E-10 Vs2m-1

Key: H1
1) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.355 T magnetic field is directed 53&deg; away from the wire?


 * -a) 8.520E-01 N/m
 * -b) 9.372E-01 N/m
 * -c) 1.031E+00 N/m
 * +d) 1.134E+00 N/m
 * -e) 1.247E+00 N/m

2) A circlular capactitor of radius 3.7 m has a gap of 10 mm, and a charge of 12 &mu;C.  What is the electric field between the plates?


 * -a) 2.15E+04 N/C (or V/m)
 * -b) 2.60E+04 N/C (or V/m)
 * +c) 3.15E+04 N/C (or V/m)
 * -d) 3.82E+04 N/C (or V/m)
 * -e) 4.63E+04 N/C (or V/m)

3) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.39mm$$, and $$n=2.55$$. What is the volume of the washer?


 * -a) 7.754E-01 cm3
 * -b) 8.530E-01 cm3
 * -c) 9.383E-01 cm3
 * -d) 1.032E+00 cm3
 * +e) 1.135E+00 cm3

4) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.315E-07 N/m2
 * +b) 2.547E-07 N/m2
 * -c) 2.801E-07 N/m2
 * -d) 3.082E-07 N/m2
 * -e) 3.390E-07 N/m2

5) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?


 * -a) 1.791E-05 T
 * -b) 1.970E-05 T
 * -c) 2.167E-05 T
 * -d) 2.384E-05 T
 * +e) 2.622E-05 T

6) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * +a) 6.624E-02 A
 * -b) 7.287E-02 A
 * -c) 8.016E-02 A
 * -d) 8.817E-02 A
 * -e) 9.699E-02 A

7) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.58 T and $$\omega=$$4.310E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.879 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 7.043E+04 V
 * -b) 7.747E+04 V
 * +c) 8.522E+04 V
 * -d) 9.374E+04 V
 * -e) 1.031E+05 V

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.645 m and $$B_{max}=\,$$ 0.469 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.26 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 2.949E+05 A
 * -b) 3.244E+05 A
 * -c) 3.568E+05 A
 * +d) 3.925E+05 A
 * -e) 4.317E+05 A

9) An ac generator produces an emf of amplitude 8 V at a frequency of 80 Hz. What is the maximum amplitude of the current if the generator is connected to a  14 mF inductor?


 * -a) 8.541E-01 A
 * -b) 9.395E-01 A
 * -c) 1.033E+00 A
 * +d) 1.137E+00 A
 * -e) 1.251E+00 A

10) A circular current loop of radius 1.59 cm carries a current of 1.13 mA. What is the magnitude of the torque if the dipole is oriented at 41 &deg; to a uniform magnetic fied of 0.189 T?


 * +a) 1.113E-07 N m
 * -b) 1.224E-07 N m
 * -c) 1.347E-07 N m
 * -d) 1.481E-07 N m
 * -e) 1.629E-07 N m

11) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.11E-11 Vs2m-1
 * -b) 8.61E-11 Vs2m-1
 * +c) 1.04E-10 Vs2m-1
 * -d) 1.26E-10 Vs2m-1
 * -e) 1.53E-10 Vs2m-1

Key: H2
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * +a) 3.575E+00 N/m
 * -b) 3.932E+00 N/m
 * -c) 4.325E+00 N/m
 * -d) 4.758E+00 N/m
 * -e) 5.234E+00 N/m

2) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=7.30E+03 m2 and separation d=7.00E-03 m is connected via a swith to a 75 &Omega; resistor and a battery of voltage V0=78 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.90E-03?


 * +a) 6.624E-02 A
 * -b) 7.287E-02 A
 * -c) 8.016E-02 A
 * -d) 8.817E-02 A
 * -e) 9.699E-02 A

3) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.14mm$$, and $$n=2.86$$. What is the volume of the washer?


 * +a) 1.071E+00 cm3
 * -b) 1.178E+00 cm3
 * -c) 1.296E+00 cm3
 * -d) 1.425E+00 cm3
 * -e) 1.568E+00 cm3

4) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 78 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 4.55E-11 Vs2m-1
 * -b) 5.51E-11 Vs2m-1
 * -c) 6.68E-11 Vs2m-1
 * -d) 8.09E-11 Vs2m-1
 * +e) 9.80E-11 Vs2m-1

5) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.66 mm from the center of a wire of radius 4 mm if the current is 1A?


 * +a) 3.325E-05 T
 * -b) 3.658E-05 T
 * -c) 4.023E-05 T
 * -d) 4.426E-05 T
 * -e) 4.868E-05 T

6) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.036 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.378E-05 N/m2
 * -b) 1.516E-05 N/m2
 * +c) 1.667E-05 N/m2
 * -d) 1.834E-05 N/m2
 * -e) 2.017E-05 N/m2

7) A circlular capactitor of radius 4.3 m has a gap of 7 mm, and a charge of 47 &mu;C.  What is the electric field between the plates?


 * -a) 7.54E+04 N/C (or V/m)
 * +b) 9.14E+04 N/C (or V/m)
 * -c) 1.11E+05 N/C (or V/m)
 * -d) 1.34E+05 N/C (or V/m)
 * -e) 1.63E+05 N/C (or V/m)

8) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.54 T and $$\omega=$$1.860E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.642 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 2.415E+04 V
 * +b) 2.656E+04 V
 * -c) 2.922E+04 V
 * -d) 3.214E+04 V
 * -e) 3.535E+04 V

9) An ac generator produces an emf of amplitude 66 V at a frequency of 180 Hz. What is the maximum amplitude of the current if the generator is connected to a  97 mF inductor?


 * -a) 4.972E-01 A
 * -b) 5.469E-01 A
 * +c) 6.016E-01 A
 * -d) 6.618E-01 A
 * -e) 7.280E-01 A

10) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.52 m and $$B_{max}=\,$$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?


 * +a) 7.876E+05 A
 * -b) 8.664E+05 A
 * -c) 9.530E+05 A
 * -d) 1.048E+06 A
 * -e) 1.153E+06 A

11) A circular current loop of radius 2.1 cm carries a current of 5.02 mA. What is the magnitude of the torque if the dipole is oriented at 26 &deg; to a uniform magnetic fied of 0.184 T?


 * +a) 5.610E-07 N m
 * -b) 6.171E-07 N m
 * -c) 6.788E-07 N m
 * -d) 7.467E-07 N m
 * -e) 8.213E-07 N m

Key: I0
1) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.559 T magnetic field is directed 46&deg; away from the wire?


 * -a) 2.417E+00 N/m
 * -b) 2.659E+00 N/m
 * -c) 2.924E+00 N/m
 * +d) 3.217E+00 N/m
 * -e) 3.539E+00 N/m

2) A charged particle in a magnetic field of 3.820E-04 T is moving perpendicular to the magnetic field with a speed of 3.890E+05 m/s. What is the period of orbit if orbital radius is 0.718 m?


 * -a) 8.713E-06 s
 * -b) 9.584E-06 s
 * -c) 1.054E-05 s
 * +d) 1.160E-05 s
 * -e) 1.276E-05 s

3) A solenoid has 9.880E+04 turns wound around a cylinder of diameter 1.5 cm and length 15 m. The current through the coils is 0.981 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.56 cm to z=+3.22 cm


 * -a) 2.916E-04 T-m
 * -b) 3.208E-04 T-m
 * -c) 3.528E-04 T-m
 * +d) 3.881E-04 T-m
 * -e) 4.269E-04 T-m

4) Three wires sit at the corners of a square of length 0.716 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.94 A, 2.04 A, 2.41 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 6.833E-05 T
 * -b) By= 7.517E-05 T
 * +c) By= 8.268E-05 T
 * -d) By= 9.095E-05 T
 * -e) By= 1.000E-04 T

5) A long solenoid has a radius of 0.777 m and 67 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$20 s&minus;1.What is the induced electric fied at a distance 2.39 m from the axis at time t=0.0399 s ?


 * -a) 3.924E-04 V/m
 * -b) 4.317E-04 V/m
 * -c) 4.748E-04 V/m
 * -d) 5.223E-04 V/m
 * +e) 5.745E-04 V/m

6) An induced emf of 7.94V is measured across a coil of 94 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.65A in 0.478s. What is the self-inductance of the coil?


 * -a) 5.047E-01 H
 * -b) 5.552E-01 H
 * -c) 6.107E-01 H
 * +d) 6.717E-01 H
 * -e) 7.389E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 5.50E+04 Hz and an amplitude of 2 V. If R =8 &Omega;, L= 9.60E-03H, and C=8.30E-06 F, what is the rms power transferred to the resistor?


 * -a) 4.347E-05 Watts
 * -b) 4.782E-05 Watts
 * -c) 5.260E-05 Watts
 * +d) 5.786E-05 Watts
 * -e) 6.364E-05 Watts

8) A parallel plate capacitor with a capicatnce C=8.90E-06 F whose plates have an area A=6.90E+03 m2 and separation d=6.90E-03 m is connected via a swith to a 89 &Omega; resistor and a battery of voltage V0=89 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-03?


 * -a) 6.595E+01 V
 * -b) 7.255E+01 V
 * -c) 7.980E+01 V
 * +d) 8.778E+01 V
 * -e) 9.656E+01 V

9) What is the radiation pressure on an object that is 9.30E+11 m away from the sun and has cross-sectional area of 0.019 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.332E-07 N/m2
 * -b) 2.566E-07 N/m2
 * -c) 2.822E-07 N/m2
 * -d) 3.104E-07 N/m2
 * -e) 3.415E-07 N/m2

10) A circlular capactitor of radius 3.2 m has a gap of 18 mm, and a charge of 82 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.79E-11 Vs2m-1
 * -b) 7.02E-11 Vs2m-1
 * -c) 8.51E-11 Vs2m-1
 * +d) 1.03E-10 Vs2m-1
 * -e) 1.25E-10 Vs2m-1

11) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 &mu;C.  What is the electric field between the plates?


 * +a) 1.92E+05 N/C (or V/m)
 * -b) 2.32E+05 N/C (or V/m)
 * -c) 2.81E+05 N/C (or V/m)
 * -d) 3.41E+05 N/C (or V/m)
 * -e) 4.13E+05 N/C (or V/m)

Key: I1
1) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.28E-11 Vs2m-1
 * -b) 8.82E-11 Vs2m-1
 * +c) 1.07E-10 Vs2m-1
 * -d) 1.29E-10 Vs2m-1
 * -e) 1.57E-10 Vs2m-1

2) An induced emf of 6.75V is measured across a coil of 79 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.76A in 0.115s. What is the self-inductance of the coil?


 * -a) 9.094E-02 H
 * +b) 1.000E-01 H
 * -c) 1.100E-01 H
 * -d) 1.210E-01 H
 * -e) 1.331E-01 H

3) Three wires sit at the corners of a square of length 0.66 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.82 A, 1.35 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 7.035E-05 T
 * -b) By= 7.739E-05 T
 * -c) By= 8.512E-05 T
 * +d) By= 9.364E-05 T
 * -e) By= 1.030E-04 T

4) The output of an ac generator connected to an RLC series combination has a frequency of 3.60E+04 Hz and an amplitude of 9 V. If R =2 &Omega;, L= 7.60E-03H, and C=7.50E-06 F, what is the rms power transferred to the resistor?


 * -a) 1.011E-03 Watts
 * +b) 1.112E-03 Watts
 * -c) 1.223E-03 Watts
 * -d) 1.345E-03 Watts
 * -e) 1.480E-03 Watts

5) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * -a) 1.131E+00 N/m
 * -b) 1.244E+00 N/m
 * -c) 1.368E+00 N/m
 * +d) 1.505E+00 N/m
 * -e) 1.655E+00 N/m

6) A solenoid has 5.980E+04 turns wound around a cylinder of diameter 1.8 cm and length 17 m. The current through the coils is 0.933 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;3.68 cm to z=+1.29 cm


 * -a) 1.863E-04 T-m
 * +b) 2.050E-04 T-m
 * -c) 2.255E-04 T-m
 * -d) 2.480E-04 T-m
 * -e) 2.728E-04 T-m

7) What is the radiation pressure on an object that is 1.10E+11 m away from the sun and has cross-sectional area of 0.036 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.378E-05 N/m2
 * -b) 1.516E-05 N/m2
 * +c) 1.667E-05 N/m2
 * -d) 1.834E-05 N/m2
 * -e) 2.017E-05 N/m2

8) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=2.70E+03 m2 and separation d=6.30E-03 m is connected via a swith to a 4 &Omega; resistor and a battery of voltage V0=7 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-05?


 * +a) 6.252E+00 V
 * -b) 6.878E+00 V
 * -c) 7.565E+00 V
 * -d) 8.322E+00 V
 * -e) 9.154E+00 V

9) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 75 &mu;C.  What is the electric field between the plates?


 * -a) 5.43E+04 N/C (or V/m)
 * -b) 6.58E+04 N/C (or V/m)
 * -c) 7.97E+04 N/C (or V/m)
 * -d) 9.66E+04 N/C (or V/m)
 * +e) 1.17E+05 N/C (or V/m)

10) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?


 * -a) 1.616E-04 V/m
 * -b) 1.778E-04 V/m
 * -c) 1.955E-04 V/m
 * -d) 2.151E-04 V/m
 * +e) 2.366E-04 V/m

11) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?


 * -a) 5.792E-06 s
 * +b) 6.371E-06 s
 * -c) 7.008E-06 s
 * -d) 7.709E-06 s
 * -e) 8.480E-06 s

Key: I2
1) A charged particle in a magnetic field of 3.720E-04 T is moving perpendicular to the magnetic field with a speed of 4.780E+05 m/s. What is the period of orbit if orbital radius is 0.868 m?


 * -a) 7.793E-06 s
 * -b) 8.572E-06 s
 * -c) 9.429E-06 s
 * -d) 1.037E-05 s
 * +e) 1.141E-05 s

2) A circlular capactitor of radius 3.2 m has a gap of 19 mm, and a charge of 46 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * +a) 5.78E-11 Vs2m-1
 * -b) 7.00E-11 Vs2m-1
 * -c) 8.48E-11 Vs2m-1
 * -d) 1.03E-10 Vs2m-1
 * -e) 1.25E-10 Vs2m-1

3) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 55 &mu;C.  What is the electric field between the plates?


 * -a) 6.37E+04 N/C (or V/m)
 * -b) 7.71E+04 N/C (or V/m)
 * +c) 9.34E+04 N/C (or V/m)
 * -d) 1.13E+05 N/C (or V/m)
 * -e) 1.37E+05 N/C (or V/m)

4) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.559 T magnetic field is directed 46&deg; away from the wire?


 * -a) 2.417E+00 N/m
 * -b) 2.659E+00 N/m
 * -c) 2.924E+00 N/m
 * +d) 3.217E+00 N/m
 * -e) 3.539E+00 N/m

5) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 3 V. If R =5 &Omega;, L= 3.90E-03H, and C=9.00E-06 F, what is the rms power transferred to the resistor?


 * -a) 2.339E-03 Watts
 * -b) 2.573E-03 Watts
 * -c) 2.830E-03 Watts
 * +d) 3.113E-03 Watts
 * -e) 3.424E-03 Watts

6) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.025 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.511E-07 N/m2
 * -b) 6.063E-07 N/m2
 * +c) 6.669E-07 N/m2
 * -d) 7.336E-07 N/m2
 * -e) 8.069E-07 N/m2

7) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * +a) 6.040E-05 V/m
 * -b) 6.644E-05 V/m
 * -c) 7.309E-05 V/m
 * -d) 8.039E-05 V/m
 * -e) 8.843E-05 V/m

8) An induced emf of 7.87V is measured across a coil of 66 closely wound turns while the current throuth it increases uniformly from 0.0 to 7.05A in 0.781s. What is the self-inductance of the coil?


 * -a) 7.926E-01 H
 * +b) 8.718E-01 H
 * -c) 9.590E-01 H
 * -d) 1.055E+00 H
 * -e) 1.160E+00 H

9) A solenoid has 7.610E+04 turns wound around a cylinder of diameter 1.21 cm and length 9 m. The current through the coils is 0.696 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.52 cm to z=+2.04 cm


 * -a) 2.176E-04 T-m
 * -b) 2.393E-04 T-m
 * +c) 2.633E-04 T-m
 * -d) 2.896E-04 T-m
 * -e) 3.186E-04 T-m

10) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * +a) 7.693E+01 V
 * -b) 8.463E+01 V
 * -c) 9.309E+01 V
 * -d) 1.024E+02 V
 * -e) 1.126E+02 V

11) Three wires sit at the corners of a square of length 0.534 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.45 A, 2.44 A, 1.61 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 9.388E-05 T
 * -b) By= 1.033E-04 T
 * -c) By= 1.136E-04 T
 * -d) By= 1.250E-04 T
 * +e) By= 1.375E-04 T

Key: J0
1) A circular current loop of radius 1.17 cm carries a current of 3.68 mA. What is the magnitude of the torque if the dipole is oriented at 55 &deg; to a uniform magnetic fied of 0.179 T?


 * -a) 1.585E-07 N m
 * -b) 1.743E-07 N m
 * -c) 1.918E-07 N m
 * -d) 2.110E-07 N m
 * +e) 2.321E-07 N m

2) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?


 * -a) 5.792E-06 s
 * +b) 6.371E-06 s
 * -c) 7.008E-06 s
 * -d) 7.709E-06 s
 * -e) 8.480E-06 s

3) Three wires sit at the corners of a square of length 0.819 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.01 A, 1.09 A, 1.56 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 4.688E-05 T
 * -b) By= 5.156E-05 T
 * -c) By= 5.672E-05 T
 * +d) By= 6.239E-05 T
 * -e) By= 6.863E-05 T

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.386E-03 T-m
 * -b) 4.825E-03 T-m
 * -c) 5.307E-03 T-m
 * -d) 5.838E-03 T-m
 * +e) 6.421E-03 T-m

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * -a) 1.605E-04 V/m
 * +b) 1.766E-04 V/m
 * -c) 1.942E-04 V/m
 * -d) 2.136E-04 V/m
 * -e) 2.350E-04 V/m

6) In an LC circuit, the self-inductance is 0.0116 H and the capacitance is 7.040E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.140E-05 C. How long does it take for the capacitor to become completely discharged?


 * +a) 4.489E-04 s
 * -b) 4.938E-04 s
 * -c) 5.432E-04 s
 * -d) 5.975E-04 s
 * -e) 6.572E-04 s

7) An ac generator produces an emf of amplitude 85 V at a frequency of 160 Hz. What is the maximum amplitude of the current if the generator is connected to a  59 mF capacitor?


 * +a) 5.042E+00 A
 * -b) 5.546E+00 A
 * -c) 6.100E+00 A
 * -d) 6.710E+00 A
 * -e) 7.381E+00 A

8) What is the radiation force on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.044 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 7.088E-09 N
 * -b) 7.796E-09 N
 * -c) 8.576E-09 N
 * +d) 9.434E-09 N
 * -e) 1.038E-08 N

9) A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 41 &Omega; resistor and a battery of voltage V0=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?


 * -a) 6.755E+01 V
 * -b) 7.431E+01 V
 * -c) 8.174E+01 V
 * +d) 8.991E+01 V
 * -e) 9.890E+01 V

10) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.28E-11 Vs2m-1
 * -b) 8.82E-11 Vs2m-1
 * +c) 1.07E-10 Vs2m-1
 * -d) 1.29E-10 Vs2m-1
 * -e) 1.57E-10 Vs2m-1

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * -a) 2.80E+04 N/C (or V/m)
 * -b) 3.40E+04 N/C (or V/m)
 * +c) 4.12E+04 N/C (or V/m)
 * -d) 4.99E+04 N/C (or V/m)
 * -e) 6.04E+04 N/C (or V/m)

Key: J1
1) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?


 * -a) 2.730E-06 s
 * +b) 3.003E-06 s
 * -c) 3.303E-06 s
 * -d) 3.633E-06 s
 * -e) 3.997E-06 s

2) An ac generator produces an emf of amplitude 17 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a  6 mF capacitor?


 * -a) 5.253E-02 A
 * -b) 5.778E-02 A
 * -c) 6.356E-02 A
 * -d) 6.991E-02 A
 * +e) 7.691E-02 A

3) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 4.028E-05 T
 * -b) By= 4.431E-05 T
 * -c) By= 4.874E-05 T
 * -d) By= 5.361E-05 T
 * -e) By= 5.897E-05 T

4) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 21 &mu;C.  What is the electric field between the plates?


 * +a) 6.16E+04 N/C (or V/m)
 * -b) 7.47E+04 N/C (or V/m)
 * -c) 9.05E+04 N/C (or V/m)
 * -d) 1.10E+05 N/C (or V/m)
 * -e) 1.33E+05 N/C (or V/m)

5) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.230E-04 s
 * -b) 6.853E-04 s
 * -c) 7.538E-04 s
 * -d) 8.292E-04 s
 * +e) 9.121E-04 s

6) A circlular capactitor of radius 4.5 m has a gap of 19 mm, and a charge of 13 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 1.35E-11 Vs2m-1
 * +b) 1.63E-11 Vs2m-1
 * -c) 1.98E-11 Vs2m-1
 * -d) 2.40E-11 Vs2m-1
 * -e) 2.91E-11 Vs2m-1

7) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=5.60E+03 m2 and separation d=5.10E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=54 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.50E-04?


 * -a) 3.015E+01 V
 * -b) 3.316E+01 V
 * -c) 3.648E+01 V
 * -d) 4.013E+01 V
 * +e) 4.414E+01 V

8) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.075 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 5.002E-08 N
 * -b) 5.502E-08 N
 * -c) 6.052E-08 N
 * -d) 6.657E-08 N
 * -e) 7.323E-08 N

9) A long solenoid has a radius of 0.8 m and 77 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.2 m from the axis at time t=0.0757 s ?


 * -a) 1.616E-04 V/m
 * -b) 1.778E-04 V/m
 * -c) 1.955E-04 V/m
 * -d) 2.151E-04 V/m
 * +e) 2.366E-04 V/m

10) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.42 kA, I2=0.904 kA, and I3=1.34 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 2.696E-03 T-m
 * -b) 2.966E-03 T-m
 * -c) 3.263E-03 T-m
 * +d) 3.589E-03 T-m
 * -e) 3.948E-03 T-m

11) A circular current loop of radius 1.63 cm carries a current of 2.38 mA. What is the magnitude of the torque if the dipole is oriented at 54 &deg; to a uniform magnetic fied of 0.125 T?


 * +a) 2.009E-07 N m
 * -b) 2.210E-07 N m
 * -c) 2.431E-07 N m
 * -d) 2.674E-07 N m
 * -e) 2.941E-07 N m

Key: J2
1) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.167E-08 N
 * -b) 1.284E-08 N
 * -c) 1.412E-08 N
 * -d) 1.553E-08 N
 * +e) 1.708E-08 N

2) Three wires sit at the corners of a square of length 0.793 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.32 A, 1.4 A, 2.27 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 3.480E-05 T
 * -b) By= 3.828E-05 T
 * -c) By= 4.210E-05 T
 * -d) By= 4.631E-05 T
 * +e) By= 5.095E-05 T

3) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * +a) 5.017E+01 V
 * -b) 5.519E+01 V
 * -c) 6.071E+01 V
 * -d) 6.678E+01 V
 * -e) 7.345E+01 V

4) In an LC circuit, the self-inductance is 0.0464 H and the capacitance is 7.350E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.280E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 8.339E-04 s
 * +b) 9.173E-04 s
 * -c) 1.009E-03 s
 * -d) 1.110E-03 s
 * -e) 1.221E-03 s

5) A long solenoid has a radius of 0.583 m and 38 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6 A and $$\alpha=$$24 s&minus;1.What is the induced electric fied at a distance 2.09 m from the axis at time t=0.0388 s ?


 * -a) 1.655E-04 V/m
 * -b) 1.821E-04 V/m
 * -c) 2.003E-04 V/m
 * +d) 2.203E-04 V/m
 * -e) 2.424E-04 V/m

6) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?


 * +a) 1.141E-05 s
 * -b) 1.255E-05 s
 * -c) 1.381E-05 s
 * -d) 1.519E-05 s
 * -e) 1.671E-05 s

7) A circular current loop of radius 1.11 cm carries a current of 4.0 mA. What is the magnitude of the torque if the dipole is oriented at 68 &deg; to a uniform magnetic fied of 0.173 T?


 * -a) 1.866E-07 N m
 * -b) 2.052E-07 N m
 * -c) 2.258E-07 N m
 * +d) 2.484E-07 N m
 * -e) 2.732E-07 N m

8) An ac generator produces an emf of amplitude 51 V at a frequency of 57 Hz. What is the maximum amplitude of the current if the generator is connected to a  99 mF capacitor?


 * -a) 1.644E+00 A
 * +b) 1.808E+00 A
 * -c) 1.989E+00 A
 * -d) 2.188E+00 A
 * -e) 2.407E+00 A

9) A circlular capactitor of radius 4.9 m has a gap of 11 mm, and a charge of 85 &mu;C.  What is the electric field between the plates?


 * +a) 1.27E+05 N/C (or V/m)
 * -b) 1.54E+05 N/C (or V/m)
 * -c) 1.87E+05 N/C (or V/m)
 * -d) 2.26E+05 N/C (or V/m)
 * -e) 2.74E+05 N/C (or V/m)

10) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 2.05E-11 Vs2m-1
 * -b) 2.48E-11 Vs2m-1
 * -c) 3.01E-11 Vs2m-1
 * +d) 3.64E-11 Vs2m-1
 * -e) 4.42E-11 Vs2m-1

11) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.46 kA, I2=2.14 kA, and I3=4.44 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.943E-03 T-m
 * -b) 5.438E-03 T-m
 * +c) 5.982E-03 T-m
 * -d) 6.580E-03 T-m
 * -e) 7.238E-03 T-m

Key: K0
1) The silver ribbon shown are a=4.23 cm, b=3.7 cm, and c= 0.721 cm. The current carries a current of 144 A and it lies in a uniform magnetic field of 1.21 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.746E-06 V
 * -b) 1.921E-06 V
 * -c) 2.113E-06 V
 * -d) 2.324E-06 V
 * +e) 2.557E-06 V

2) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.394 T magnetic field is directed 14&deg; away from the wire?


 * -a) 6.302E-01 N/m
 * -b) 6.932E-01 N/m
 * +c) 7.625E-01 N/m
 * -d) 8.388E-01 N/m
 * -e) 9.227E-01 N/m

3) Two loops of wire carry the same current of 43 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.516 m while the other has a radius of 1.22 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.565 m from the first (smaller) loopif the disance between the loops is 1.78 m?


 * -a) 1.798E-02 T
 * -b) 1.978E-02 T
 * -c) 2.176E-02 T
 * +d) 2.394E-02 T
 * -e) 2.633E-02 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 595 mA, the net magnetic field is measured to be 1.46 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 6.716E+02
 * -b) $$\chi \text{ (chi) }=$$ 7.387E+02
 * +c) $$\chi \text{ (chi) }=$$ 8.126E+02
 * -d) $$\chi \text{ (chi) }=$$ 8.939E+02
 * -e) $$\chi \text{ (chi) }=$$ 9.833E+02

5) A square coil has sides that are L= 0.727 m long and is tightly wound with N=376 turns of wire. The resistance of the coil is R=5.59 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 1.567E+00 A
 * +b) 1.724E+00 A
 * -c) 1.897E+00 A
 * -d) 2.086E+00 A
 * -e) 2.295E+00 A

6) An induced emf of 3.78V is measured across a coil of 99 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.36A in 0.821s. What is the self-inductance of the coil?


 * -a) 4.033E-01 H
 * -b) 4.436E-01 H
 * +c) 4.880E-01 H
 * -d) 5.367E-01 H
 * -e) 5.904E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 &Omega;, L= 2.80E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.759E-01 &rad;
 * -b) 9.635E-01 &rad;
 * +c) 1.060E+00 &rad;
 * -d) 1.166E+00 &rad;
 * -e) 1.282E+00 &rad;

8) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.099 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.464E-07 N/m2
 * -b) 1.611E-07 N/m2
 * -c) 1.772E-07 N/m2
 * -d) 1.949E-07 N/m2
 * +e) 2.144E-07 N/m2

9) A 46 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 78 kW?


 * +a) 1.563E+02 km
 * -b) 1.719E+02 km
 * -c) 1.891E+02 km
 * -d) 2.080E+02 km
 * -e) 2.288E+02 km

10) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * -a) 6.62E-05 s
 * -b) 8.02E-05 s
 * -c) 9.71E-05 s
 * -d) 1.18E-04 s
 * +e) 1.43E-04 s

11) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 &mu;C.  What is the electric field between the plates?


 * -a) 1.29E+05 N/C (or V/m)
 * +b) 1.56E+05 N/C (or V/m)
 * -c) 1.89E+05 N/C (or V/m)
 * -d) 2.29E+05 N/C (or V/m)
 * -e) 2.77E+05 N/C (or V/m)

Key: K1
1) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 &Omega;, L= 8.20E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.146E-01 &rad;
 * -b) 8.960E-01 &rad;
 * +c) 9.856E-01 &rad;
 * -d) 1.084E+00 &rad;
 * -e) 1.193E+00 &rad;

2) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * -a) 4.55E+04 N/C (or V/m)
 * -b) 5.52E+04 N/C (or V/m)
 * +c) 6.68E+04 N/C (or V/m)
 * -d) 8.10E+04 N/C (or V/m)
 * -e) 9.81E+04 N/C (or V/m)

3) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * -a) 2.094E+02 km
 * +b) 2.304E+02 km
 * -c) 2.534E+02 km
 * -d) 2.788E+02 km
 * -e) 3.066E+02 km

4) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.025 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.511E-07 N/m2
 * -b) 6.063E-07 N/m2
 * +c) 6.669E-07 N/m2
 * -d) 7.336E-07 N/m2
 * -e) 8.069E-07 N/m2

5) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 23 turns per centimeter and the current applied to the solenoid is 534 mA, the net magnetic field is measured to be 1.48 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 7.917E+02
 * -b) $$\chi \text{ (chi) }=$$ 8.708E+02
 * +c) $$\chi \text{ (chi) }=$$ 9.579E+02
 * -d) $$\chi \text{ (chi) }=$$ 1.054E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.159E+03

6) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.355 T magnetic field is directed 53&deg; away from the wire?


 * -a) 8.520E-01 N/m
 * -b) 9.372E-01 N/m
 * -c) 1.031E+00 N/m
 * +d) 1.134E+00 N/m
 * -e) 1.247E+00 N/m

7) Two loops of wire carry the same current of 20 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.776 m while the other has a radius of 1.2 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.517 m from the first (smaller) loopif the disance between the loops is 1.37 m?


 * -a) 1.127E-02 T
 * -b) 1.240E-02 T
 * -c) 1.364E-02 T
 * +d) 1.500E-02 T
 * -e) 1.650E-02 T

8) An induced emf of 5.08V is measured across a coil of 78 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.07A in 0.681s. What is the self-inductance of the coil?


 * -a) 4.660E-01 H
 * -b) 5.127E-01 H
 * -c) 5.639E-01 H
 * -d) 6.203E-01 H
 * +e) 6.823E-01 H

9) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.080E-06 V
 * -b) 1.188E-06 V
 * -c) 1.306E-06 V
 * -d) 1.437E-06 V
 * +e) 1.581E-06 V

10) A square coil has sides that are L= 0.465 m long and is tightly wound with N=954 turns of wire. The resistance of the coil is R=6.06 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0367 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 1.136E+00 A
 * +b) 1.249E+00 A
 * -c) 1.374E+00 A
 * -d) 1.512E+00 A
 * -e) 1.663E+00 A

11) A circlular capactitor of radius 4.8 m has a gap of 16 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * -a) 1.98E-04 s
 * +b) 2.40E-04 s
 * -c) 2.91E-04 s
 * -d) 3.53E-04 s
 * -e) 4.27E-04 s

Key: K2
1) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * -a) 2.094E+02 km
 * +b) 2.304E+02 km
 * -c) 2.534E+02 km
 * -d) 2.788E+02 km
 * -e) 3.066E+02 km

2) An induced emf of 4.7V is measured across a coil of 52 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.08A in 0.961s. What is the self-inductance of the coil?


 * -a) 1.102E+00 H
 * -b) 1.212E+00 H
 * -c) 1.333E+00 H
 * +d) 1.466E+00 H
 * -e) 1.613E+00 H

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 525 mA, the net magnetic field is measured to be 1.45 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 8.249E+02
 * -b) $$\chi \text{ (chi) }=$$ 9.074E+02
 * -c) $$\chi \text{ (chi) }=$$ 9.981E+02
 * +d) $$\chi \text{ (chi) }=$$ 1.098E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.208E+03

4) A circlular capactitor of radius 3.7 m has a gap of 10 mm, and a charge of 41 &mu;C.  What is the electric field between the plates?


 * +a) 1.08E+05 N/C (or V/m)
 * -b) 1.30E+05 N/C (or V/m)
 * -c) 1.58E+05 N/C (or V/m)
 * -d) 1.91E+05 N/C (or V/m)
 * -e) 2.32E+05 N/C (or V/m)

5) Two loops of wire carry the same current of 66 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.485 m while the other has a radius of 1.27 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.507 m from the first (smaller) loopif the disance between the loops is 1.76 m?


 * -a) 2.733E-02 T
 * -b) 3.007E-02 T
 * -c) 3.307E-02 T
 * -d) 3.638E-02 T
 * +e) 4.002E-02 T

6) A circlular capactitor of radius 3.7 m has a gap of 15 mm, and a charge of 36 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * -a) 1.04E-04 s
 * -b) 1.26E-04 s
 * +c) 1.52E-04 s
 * -d) 1.85E-04 s
 * -e) 2.24E-04 s

7) A square coil has sides that are L= 0.819 m long and is tightly wound with N=887 turns of wire. The resistance of the coil is R=5.69 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 4.414E+00 A
 * -b) 4.855E+00 A
 * -c) 5.341E+00 A
 * -d) 5.875E+00 A
 * +e) 6.462E+00 A

8) The output of an ac generator connected to an RLC series combination has a frequency of 200 Hz and an amplitude of 0.14 V;. If R =3 &Omega;, L= 1.70E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 3.691E-01 &rad;
 * +b) 4.060E-01 &rad;
 * -c) 4.466E-01 &rad;
 * -d) 4.913E-01 &rad;
 * -e) 5.404E-01 &rad;

9) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * +a) 3.575E+00 N/m
 * -b) 3.932E+00 N/m
 * -c) 4.325E+00 N/m
 * -d) 4.758E+00 N/m
 * -e) 5.234E+00 N/m

10) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.144E-07 N/m2
 * -b) 2.358E-07 N/m2
 * -c) 2.594E-07 N/m2
 * -d) 2.854E-07 N/m2
 * -e) 3.139E-07 N/m2

11) The silver ribbon shown are a=3.89 cm, b=2.94 cm, and c= 0.58 cm. The current carries a current of 242 A and it lies in a uniform magnetic field of 2.47 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 9.911E-06 V
 * +b) 1.090E-05 V
 * -c) 1.199E-05 V
 * -d) 1.319E-05 V
 * -e) 1.451E-05 V

Key: L0
1) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.88 T magnetic field is directed 47&deg; away from the wire?


 * -a) 4.096E+00 N/m
 * +b) 4.505E+00 N/m
 * -c) 4.956E+00 N/m
 * -d) 5.451E+00 N/m
 * -e) 5.996E+00 N/m

2) A 27 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.85 T. What current is required to maintain this balance?


 * -a) 3.106E-01 A
 * +b) 3.416E-01 A
 * -c) 3.758E-01 A
 * -d) 4.134E-01 A
 * -e) 4.547E-01 A

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.51 kA, I2=1.32 kA, and I3=2.73 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.331E-03 T-m
 * -b) 1.464E-03 T-m
 * -c) 1.611E-03 T-m
 * +d) 1.772E-03 T-m
 * -e) 1.949E-03 T-m

4) Three wires sit at the corners of a square of length 0.687 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 7.134E-05 T
 * -b) Bx= 7.847E-05 T
 * +c) Bx= 8.632E-05 T
 * -d) Bx= 9.495E-05 T
 * -e) Bx= 1.044E-04 T

5) A cylinder of height 1.3 cm and radius 6.01 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.61 cm from point O and moves at a speed of 2.11 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * +a) 1.372E+01 cm3/s
 * -b) 1.509E+01 cm3/s
 * -c) 1.660E+01 cm3/s
 * -d) 1.826E+01 cm3/s
 * -e) 2.009E+01 cm3/s

6) In an LC circuit, the self-inductance is 0.0399 H and the capacitance is 8.450E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.480E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.230E-04 s
 * -b) 6.853E-04 s
 * -c) 7.538E-04 s
 * -d) 8.292E-04 s
 * +e) 9.121E-04 s

7) The output of an ac generator connected to an RLC series combination has a frequency of 910 Hz and an amplitude of 0.88 V;. If R =7 &Omega;, L= 6.80E-03H, and C=9.60E-04 F, what is the impedance?


 * -a) 3.575E+01 &Omega;
 * +b) 3.933E+01 &Omega;
 * -c) 4.326E+01 &Omega;
 * -d) 4.758E+01 &Omega;
 * -e) 5.234E+01 &Omega;

8) A 55 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 93 kW?


 * -a) 1.270E+02 km
 * -b) 1.397E+02 km
 * -c) 1.537E+02 km
 * +d) 1.690E+02 km
 * -e) 1.859E+02 km

9) What is the radiation force on an object that is 4.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 7.396E-08 N
 * -b) 8.136E-08 N
 * +c) 8.950E-08 N
 * -d) 9.845E-08 N
 * -e) 1.083E-07 N

10) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 8.75E-12 Vs2m-1
 * -b) 1.06E-11 Vs2m-1
 * -c) 1.28E-11 Vs2m-1
 * -d) 1.56E-11 Vs2m-1
 * +e) 1.88E-11 Vs2m-1

11) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.95E-09 Tesla
 * -b) 4.97E-09 Tesla
 * +c) 6.26E-09 Tesla
 * -d) 7.88E-09 Tesla
 * -e) 9.92E-09 Tesla

Key: L1
1) A cylinder of height 1.27 cm and radius 8.63 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.15 cm from point O and moves at a speed of 1.26 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * +a) 1.892E+01 cm3/s
 * -b) 2.081E+01 cm3/s
 * -c) 2.289E+01 cm3/s
 * -d) 2.518E+01 cm3/s
 * -e) 2.770E+01 cm3/s

2) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.166E-04 s
 * -b) 6.783E-04 s
 * -c) 7.461E-04 s
 * -d) 8.207E-04 s
 * +e) 9.028E-04 s

3) The output of an ac generator connected to an RLC series combination has a frequency of 1.00E+03 Hz and an amplitude of 0.6 V;. If R =3 &Omega;, L= 1.70E-03H, and C=5.40E-04 F, what is the impedance?


 * -a) 8.123E+00 &Omega;
 * -b) 8.935E+00 &Omega;
 * -c) 9.828E+00 &Omega;
 * +d) 1.081E+01 &Omega;
 * -e) 1.189E+01 &Omega;

4) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.275E-07 N
 * -b) 5.803E-07 N
 * +c) 6.383E-07 N
 * -d) 7.021E-07 N
 * -e) 7.723E-07 N

5) A 42 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * -a) 1.641E+02 km
 * -b) 1.805E+02 km
 * +c) 1.986E+02 km
 * -d) 2.184E+02 km
 * -e) 2.403E+02 km

6) A circlular capactitor of radius 3.2 m has a gap of 19 mm, and a charge of 46 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * +a) 5.78E-11 Vs2m-1
 * -b) 7.00E-11 Vs2m-1
 * -c) 8.48E-11 Vs2m-1
 * -d) 1.03E-10 Vs2m-1
 * -e) 1.25E-10 Vs2m-1

7) Three wires sit at the corners of a square of length 0.518 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.31 A, 1.32 A, 1.62 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.013E-05 T
 * -b) Bx= 6.614E-05 T
 * -c) Bx= 7.275E-05 T
 * -d) Bx= 8.003E-05 T
 * +e) Bx= 8.803E-05 T

8) A 42 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 7 g, and the magnitude of the magnetic field is 0.48 T. What current is required to maintain this balance?


 * -a) 2.812E-01 A
 * -b) 3.093E-01 A
 * +c) 3.403E-01 A
 * -d) 3.743E-01 A
 * -e) 4.117E-01 A

9) A circlular capactitor of radius 4.6 m has a gap of 18 mm, and a charge of 44 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 6.64E-09 Tesla
 * +b) 8.36E-09 Tesla
 * -c) 1.05E-08 Tesla
 * -d) 1.32E-08 Tesla
 * -e) 1.67E-08 Tesla

10) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.55 kA, I2=1.02 kA, and I3=1.81 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 8.204E-04 T-m
 * -b) 9.025E-04 T-m
 * +c) 9.927E-04 T-m
 * -d) 1.092E-03 T-m
 * -e) 1.201E-03 T-m

11) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.623 T magnetic field is directed 73&deg; away from the wire?


 * +a) 3.575E+00 N/m
 * -b) 3.932E+00 N/m
 * -c) 4.325E+00 N/m
 * -d) 4.758E+00 N/m
 * -e) 5.234E+00 N/m

Key: L2
1) A 92 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 15 g, and the magnitude of the magnetic field is 0.713 T. What current is required to maintain this balance?


 * -a) 2.037E-01 A
 * +b) 2.241E-01 A
 * -c) 2.465E-01 A
 * -d) 2.712E-01 A
 * -e) 2.983E-01 A

2) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * -a) 2.094E+02 km
 * +b) 2.304E+02 km
 * -c) 2.534E+02 km
 * -d) 2.788E+02 km
 * -e) 3.066E+02 km

3) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 34 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 2.40E-11 Vs2m-1
 * -b) 2.91E-11 Vs2m-1
 * -c) 3.53E-11 Vs2m-1
 * +d) 4.27E-11 Vs2m-1
 * -e) 5.18E-11 Vs2m-1

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.84 kA, I2=0.476 kA, and I3=1.57 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.250E-03 T-m
 * +b) 1.375E-03 T-m
 * -c) 1.512E-03 T-m
 * -d) 1.663E-03 T-m
 * -e) 1.830E-03 T-m

5) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.18 V;. If R =6 &Omega;, L= 7.50E-03H, and C=7.50E-04 F, what is the impedance?


 * -a) 2.708E+01 &Omega;
 * -b) 2.978E+01 &Omega;
 * -c) 3.276E+01 &Omega;
 * +d) 3.604E+01 &Omega;
 * -e) 3.964E+01 &Omega;

6) A cylinder of height 2.12 cm and radius 2.28 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.52 cm from point O and moves at a speed of 8.21 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * +a) 2.976E+01 cm3/s
 * -b) 3.274E+01 cm3/s
 * -c) 3.601E+01 cm3/s
 * -d) 3.961E+01 cm3/s
 * -e) 4.358E+01 cm3/s

7) Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 8.371E-05 T
 * -b) Bx= 9.208E-05 T
 * +c) Bx= 1.013E-04 T
 * -d) Bx= 1.114E-04 T
 * -e) Bx= 1.226E-04 T

8) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.30E-09 Tesla
 * -b) 4.15E-09 Tesla
 * -c) 5.23E-09 Tesla
 * +d) 6.58E-09 Tesla
 * -e) 8.29E-09 Tesla

9) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.275E-07 N
 * -b) 5.803E-07 N
 * +c) 6.383E-07 N
 * -d) 7.021E-07 N
 * -e) 7.723E-07 N

10) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.761 T magnetic field is directed 44&deg; away from the wire?


 * -a) 2.527E+00 N/m
 * -b) 2.780E+00 N/m
 * -c) 3.058E+00 N/m
 * -d) 3.364E+00 N/m
 * +e) 3.700E+00 N/m

11) In an LC circuit, the self-inductance is 0.0424 H and the capacitance is 7.790E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 6.230E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 6.166E-04 s
 * -b) 6.783E-04 s
 * -c) 7.461E-04 s
 * -d) 8.207E-04 s
 * +e) 9.028E-04 s

Key: M0
1) The silver ribbon shown are a=3.52 cm, b=2.88 cm, and c= 0.515 cm. The current carries a current of 137 A and it lies in a uniform magnetic field of 2.02 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 5.685E-06 V
 * -b) 6.253E-06 V
 * -c) 6.878E-06 V
 * -d) 7.566E-06 V
 * -e) 8.323E-06 V

2) A circular current loop of radius 1.88 cm carries a current of 3.41 mA. What is the magnitude of the torque if the dipole is oriented at 62 &deg; to a uniform magnetic fied of 0.415 T?


 * +a) 1.387E-06 N m
 * -b) 1.526E-06 N m
 * -c) 1.679E-06 N m
 * -d) 1.847E-06 N m
 * -e) 2.031E-06 N m

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.58 kA, I2=1.27 kA, and I3=1.99 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 3.770E-03 T-m
 * +b) 4.147E-03 T-m
 * -c) 4.562E-03 T-m
 * -d) 5.018E-03 T-m
 * -e) 5.520E-03 T-m

4) Three wires sit at the corners of a square of length 0.832 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.03 A, 1.95 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.545E-05 T
 * +b) Bx= 7.200E-05 T
 * -c) Bx= 7.919E-05 T
 * -d) Bx= 8.711E-05 T
 * -e) Bx= 9.583E-05 T

5) The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15 A/s. The solenoid is 89 cm long and has a cross-sectional diameter of 3.48 cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.5 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 2.081E-04 V
 * -b) 2.289E-04 V
 * -c) 2.518E-04 V
 * +d) 2.770E-04 V
 * -e) 3.047E-04 V

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.96% of its maximum value if &epsilon; = 2.64 V, R = 6.37 &Omega;, and L = 7.33 H?


 * -a) -1.700E+00 s
 * -b) -1.870E+00 s
 * -c) -2.057E+00 s
 * +d) -2.262E+00 s
 * -e) -2.489E+00 s

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * -a) Q = 1.288E+02
 * +b) Q = 1.482E+02
 * -c) Q = 1.704E+02
 * -d) Q = 1.959E+02
 * -e) Q = 2.253E+02

8) What is the radiation pressure on an object that is 2.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 3.131E-06 N/m2
 * -b) 3.445E-06 N/m2
 * -c) 3.789E-06 N/m2
 * +d) 4.168E-06 N/m2
 * -e) 4.585E-06 N/m2

9) A 46 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 78 kW?


 * +a) 1.563E+02 km
 * -b) 1.719E+02 km
 * -c) 1.891E+02 km
 * -d) 2.080E+02 km
 * -e) 2.288E+02 km

10) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 33 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * +a) 1.42E-04 s
 * -b) 1.73E-04 s
 * -c) 2.09E-04 s
 * -d) 2.53E-04 s
 * -e) 3.07E-04 s

11) A circlular capactitor of radius 3.9 m has a gap of 8 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 5.30E-09 Tesla
 * +b) 6.67E-09 Tesla
 * -c) 8.39E-09 Tesla
 * -d) 1.06E-08 Tesla
 * -e) 1.33E-08 Tesla

Key: M1
1) The silver ribbon shown are a=3.55 cm, b=2.99 cm, and c= 1.03 cm. The current carries a current of 135 A and it lies in a uniform magnetic field of 1.26 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.193E-06 V
 * -b) 1.313E-06 V
 * -c) 1.444E-06 V
 * -d) 1.588E-06 V
 * +e) 1.747E-06 V

2) A circlular capactitor of radius 4 m has a gap of 14 mm, and a charge of 78 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 9.77E-09 Tesla
 * -b) 1.23E-08 Tesla
 * -c) 1.55E-08 Tesla
 * -d) 1.95E-08 Tesla
 * +e) 2.45E-08 Tesla

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 &Omega;, L= 4.90E-03H, and C=2.10E-06 F, respectively.


 * -a) Q = 1.381E+02
 * -b) Q = 1.588E+02
 * -c) Q = 1.826E+02
 * -d) Q = 2.100E+02
 * +e) Q = 2.415E+02

4) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.019 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.392E-06 N/m2
 * -b) 2.631E-06 N/m2
 * -c) 2.894E-06 N/m2
 * -d) 3.184E-06 N/m2
 * +e) 3.502E-06 N/m2

5) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if &epsilon; = 6.08 V, R = 1.88 &Omega;, and L = 4.67 H?


 * +a) -5.192E+00 s
 * -b) -5.711E+00 s
 * -c) -6.282E+00 s
 * -d) -6.910E+00 s
 * -e) -7.601E+00 s

6) The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8 A/s. The solenoid is 74 cm long and has a cross-sectional diameter of 2.57 cm.  A small coil consisting of N=32turns wraped in a circle of diameter 1.49 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 1.407E-04 V
 * +b) 1.548E-04 V
 * -c) 1.703E-04 V
 * -d) 1.873E-04 V
 * -e) 2.061E-04 V

7) A 56 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 72 kW?


 * -a) 1.084E+02 km
 * -b) 1.193E+02 km
 * -c) 1.312E+02 km
 * -d) 1.443E+02 km
 * +e) 1.587E+02 km

8) A circlular capactitor of radius 3.3 m has a gap of 12 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * -a) 9.94E-05 s
 * -b) 1.20E-04 s
 * -c) 1.46E-04 s
 * +d) 1.77E-04 s
 * -e) 2.14E-04 s

9) A circular current loop of radius 2.21 cm carries a current of 1.43 mA. What is the magnitude of the torque if the dipole is oriented at 67 &deg; to a uniform magnetic fied of 0.276 T?


 * -a) 4.188E-07 N m
 * -b) 4.607E-07 N m
 * -c) 5.068E-07 N m
 * +d) 5.574E-07 N m
 * -e) 6.132E-07 N m

10) Three wires sit at the corners of a square of length 0.51 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.16 A, 2.46 A, 2.15 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 9.053E-05 T
 * -b) Bx= 9.959E-05 T
 * -c) Bx= 1.095E-04 T
 * -d) Bx= 1.205E-04 T
 * +e) Bx= 1.325E-04 T

11) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 2.812E-03 T-m
 * -b) 3.093E-03 T-m
 * -c) 3.402E-03 T-m
 * -d) 3.742E-03 T-m
 * +e) 4.117E-03 T-m

Key: M2
1) What is the radiation pressure on an object that is 1.20E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 9.568E-06 N/m2
 * -b) 1.053E-05 N/m2
 * -c) 1.158E-05 N/m2
 * -d) 1.274E-05 N/m2
 * +e) 1.401E-05 N/m2

2) A 48 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 80 kW?


 * +a) 1.678E+02 km
 * -b) 1.846E+02 km
 * -c) 2.031E+02 km
 * -d) 2.234E+02 km
 * -e) 2.457E+02 km

3) Three wires sit at the corners of a square of length 0.64 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.76 A, 1.02 A, 1.08 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 3.394E-05 T
 * -b) Bx= 3.733E-05 T
 * -c) Bx= 4.106E-05 T
 * -d) Bx= 4.517E-05 T
 * +e) Bx= 4.969E-05 T

4) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 88 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 1.86E-08 Tesla
 * -b) 2.34E-08 Tesla
 * +c) 2.95E-08 Tesla
 * -d) 3.72E-08 Tesla
 * -e) 4.68E-08 Tesla

5) A circular current loop of radius 2.99 cm carries a current of 4.54 mA. What is the magnitude of the torque if the dipole is oriented at 34 &deg; to a uniform magnetic fied of 0.107 T?


 * +a) 7.629E-07 N m
 * -b) 8.392E-07 N m
 * -c) 9.232E-07 N m
 * -d) 1.015E-06 N m
 * -e) 1.117E-06 N m

6) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * +a) 3.62E-04 s
 * -b) 4.38E-04 s
 * -c) 5.31E-04 s
 * -d) 6.43E-04 s
 * -e) 7.79E-04 s

7) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 1.066E-04 V
 * -b) 1.173E-04 V
 * +c) 1.290E-04 V
 * -d) 1.419E-04 V
 * -e) 1.561E-04 V

8) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.81 kA, I2=1.2 kA, and I3=1.84 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 3.583E-03 T-m
 * -b) 3.941E-03 T-m
 * +c) 4.335E-03 T-m
 * -d) 4.769E-03 T-m
 * -e) 5.246E-03 T-m

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 &Omega;, L= 4.90E-03H, and C=2.10E-06 F, respectively.


 * -a) Q = 1.381E+02
 * -b) Q = 1.588E+02
 * -c) Q = 1.826E+02
 * -d) Q = 2.100E+02
 * +e) Q = 2.415E+02

10) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.69% of its maximum value if &epsilon; = 4.79 V, R = 4.18 &Omega;, and L = 2.7 H?


 * -a) -8.773E-01 s
 * -b) -9.651E-01 s
 * -c) -1.062E+00 s
 * +d) -1.168E+00 s
 * -e) -1.284E+00 s

11) The silver ribbon shown are a=4.14 cm, b=3.69 cm, and c= 1.13 cm. The current carries a current of 291 A and it lies in a uniform magnetic field of 3.32 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 6.795E-06 V
 * -b) 7.475E-06 V
 * -c) 8.222E-06 V
 * +d) 9.045E-06 V
 * -e) 9.949E-06 V

Key: N0
1) A charged particle in a magnetic field of 4.660E-04 T is moving perpendicular to the magnetic field with a speed of 7.720E+05 m/s. What is the period of orbit if orbital radius is 0.747 m?


 * +a) 6.080E-06 s
 * -b) 6.688E-06 s
 * -c) 7.356E-06 s
 * -d) 8.092E-06 s
 * -e) 8.901E-06 s

2) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 4.13 mT and 2.810E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 6.804E+05 m/s
 * -b) 7.484E+05 m/s
 * -c) 8.233E+05 m/s
 * -d) 9.056E+05 m/s
 * -e) 9.962E+05 m/s

3) Two loops of wire carry the same current of 14 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.835 m while the other has a radius of 1.29 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.607 m from the first (smaller) loopif the disance between the loops is 1.61 m?


 * -a) 6.099E-03 T
 * -b) 6.709E-03 T
 * -c) 7.380E-03 T
 * -d) 8.118E-03 T
 * +e) 8.930E-03 T

4) A solenoid has 5.640E+04 turns wound around a cylinder of diameter 1.35 cm and length 16 m. The current through the coils is 0.912 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;1.11 cm to z=+2.76 cm


 * -a) 1.068E-04 T-m
 * -b) 1.175E-04 T-m
 * -c) 1.292E-04 T-m
 * -d) 1.421E-04 T-m
 * +e) 1.563E-04 T-m

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * -a) 1.605E-04 V/m
 * +b) 1.766E-04 V/m
 * -c) 1.942E-04 V/m
 * -d) 2.136E-04 V/m
 * -e) 2.350E-04 V/m

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.65% of its maximum value if &epsilon; = 3.62 V, R = 4.07 &Omega;, and L = 7.19 H?


 * -a) -2.476E+00 s
 * -b) -2.724E+00 s
 * -c) -2.996E+00 s
 * -d) -3.296E+00 s
 * +e) -3.625E+00 s

7) An ac generator produces an emf of amplitude 40 V at a frequency of 130 Hz. What is the maximum amplitude of the current if the generator is connected to a  52 mF inductor?


 * -a) 7.783E-01 A
 * -b) 8.561E-01 A
 * +c) 9.417E-01 A
 * -d) 1.036E+00 A
 * -e) 1.140E+00 A

8) A parallel plate capacitor with a capicatnce C=4.50E-06 F whose plates have an area A=3.30E+03 m2 and separation d=6.40E-03 m is connected via a swith to a 83 &Omega; resistor and a battery of voltage V0=56 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.40E-03?


 * -a) 7.767E+03 V/m
 * +b) 8.544E+03 V/m
 * -c) 9.398E+03 V/m
 * -d) 1.034E+04 V/m
 * -e) 1.137E+04 V/m

9) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.275E-07 N
 * -b) 5.803E-07 N
 * +c) 6.383E-07 N
 * -d) 7.021E-07 N
 * -e) 7.723E-07 N

10) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * -a) 6.62E-05 s
 * -b) 8.02E-05 s
 * -c) 9.71E-05 s
 * -d) 1.18E-04 s
 * +e) 1.43E-04 s

11) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 2.82E-09 Tesla
 * -b) 3.54E-09 Tesla
 * -c) 4.46E-09 Tesla
 * -d) 5.62E-09 Tesla
 * +e) 7.07E-09 Tesla

Key: N1
1) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.673E-07 N
 * -b) 2.940E-07 N
 * -c) 3.234E-07 N
 * -d) 3.558E-07 N
 * -e) 3.913E-07 N

2) An ac generator produces an emf of amplitude 24 V at a frequency of 120 Hz. What is the maximum amplitude of the current if the generator is connected to a  96 mF inductor?


 * -a) 3.014E-01 A
 * +b) 3.316E-01 A
 * -c) 3.647E-01 A
 * -d) 4.012E-01 A
 * -e) 4.413E-01 A

3) A charged particle in a magnetic field of 2.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.120E+05 m/s. What is the period of orbit if orbital radius is 0.385 m?


 * +a) 1.141E-05 s
 * -b) 1.255E-05 s
 * -c) 1.381E-05 s
 * -d) 1.519E-05 s
 * -e) 1.671E-05 s

4) A solenoid has 5.160E+04 turns wound around a cylinder of diameter 1.55 cm and length 18 m. The current through the coils is 0.57 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.88 cm to z=+1.52 cm


 * -a) 6.788E-05 T-m
 * -b) 7.467E-05 T-m
 * -c) 8.213E-05 T-m
 * +d) 9.035E-05 T-m
 * -e) 9.938E-05 T-m

5) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 2.62 mT and 2.120E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 8.092E+05 m/s
 * -b) 8.901E+05 m/s
 * -c) 9.791E+05 m/s
 * -d) 1.077E+06 m/s
 * -e) 1.185E+06 m/s

6) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.95E-09 Tesla
 * -b) 4.97E-09 Tesla
 * +c) 6.26E-09 Tesla
 * -d) 7.88E-09 Tesla
 * -e) 9.92E-09 Tesla

7) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 43 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * +a) 1.95E-04 s
 * -b) 2.36E-04 s
 * -c) 2.86E-04 s
 * -d) 3.46E-04 s
 * -e) 4.20E-04 s

8) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.53% of its maximum value if &epsilon; = 6.08 V, R = 1.88 &Omega;, and L = 4.67 H?


 * +a) -5.192E+00 s
 * -b) -5.711E+00 s
 * -c) -6.282E+00 s
 * -d) -6.910E+00 s
 * -e) -7.601E+00 s

9) A long solenoid has a radius of 0.434 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.28 m from the axis at time t=0.0392 s ?


 * -a) 1.479E-04 V/m
 * -b) 1.627E-04 V/m
 * +c) 1.789E-04 V/m
 * -d) 1.968E-04 V/m
 * -e) 2.165E-04 V/m

10) A parallel plate capacitor with a capicatnce C=1.30E-06 F whose plates have an area A=1.10E+03 m2 and separation d=7.60E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.30E-04?


 * -a) 4.842E+02 V/m
 * -b) 5.326E+02 V/m
 * +c) 5.858E+02 V/m
 * -d) 6.444E+02 V/m
 * -e) 7.089E+02 V/m

11) Two loops of wire carry the same current of 99 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.798 m while the other has a radius of 1.29 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.394 m from the first (smaller) loopif the disance between the loops is 1.29 m?


 * +a) 8.291E-02 T
 * -b) 9.120E-02 T
 * -c) 1.003E-01 T
 * -d) 1.104E-01 T
 * -e) 1.214E-01 T

Key: N2
1) A charged particle in a magnetic field of 3.330E-04 T is moving perpendicular to the magnetic field with a speed of 4.800E+05 m/s. What is the period of orbit if orbital radius is 0.402 m?


 * -a) 4.784E-06 s
 * +b) 5.262E-06 s
 * -c) 5.788E-06 s
 * -d) 6.367E-06 s
 * -e) 7.004E-06 s

2) A circlular capactitor of radius 4 m has a gap of 13 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 8.62E-09 Tesla
 * -b) 1.09E-08 Tesla
 * -c) 1.37E-08 Tesla
 * -d) 1.72E-08 Tesla
 * +e) 2.17E-08 Tesla

3) Two loops of wire carry the same current of 67 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.847 m while the other has a radius of 1.15 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.408 m from the first (smaller) loopif the disance between the loops is 1.15 m?


 * -a) 4.799E-02 T
 * -b) 5.278E-02 T
 * +c) 5.806E-02 T
 * -d) 6.387E-02 T
 * -e) 7.026E-02 T

4) A long solenoid has a radius of 0.806 m and 41 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0701 s ?


 * +a) 6.040E-05 V/m
 * -b) 6.644E-05 V/m
 * -c) 7.309E-05 V/m
 * -d) 8.039E-05 V/m
 * -e) 8.843E-05 V/m

5) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 2.16% of its maximum value if &epsilon; = 4.79 V, R = 4.37 &Omega;, and L = 5.29 H?


 * -a) -2.110E+00 s
 * +b) -2.321E+00 s
 * -c) -2.553E+00 s
 * -d) -2.809E+00 s
 * -e) -3.090E+00 s

6) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 9.23 mT and 6.120E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 4.982E+05 m/s
 * -b) 5.480E+05 m/s
 * -c) 6.028E+05 m/s
 * +d) 6.631E+05 m/s
 * -e) 7.294E+05 m/s

7) A solenoid has 4.380E+04 turns wound around a cylinder of diameter 1.77 cm and length 16 m. The current through the coils is 0.916 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;4.39 cm to z=+4.26 cm


 * -a) 2.478E-04 T-m
 * +b) 2.726E-04 T-m
 * -c) 2.998E-04 T-m
 * -d) 3.298E-04 T-m
 * -e) 3.628E-04 T-m

8) What is the radiation force on an object that is 2.00E+11 m away from the sun and has cross-sectional area of 0.053 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.673E-07 N
 * -b) 2.940E-07 N
 * -c) 3.234E-07 N
 * -d) 3.558E-07 N
 * -e) 3.913E-07 N

9) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * -a) 1.65E-04 s
 * +b) 2.00E-04 s
 * -c) 2.43E-04 s
 * -d) 2.94E-04 s
 * -e) 3.56E-04 s

10) A parallel plate capacitor with a capicatnce C=1.30E-06 F whose plates have an area A=1.10E+03 m2 and separation d=7.60E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.30E-04?


 * -a) 4.842E+02 V/m
 * -b) 5.326E+02 V/m
 * +c) 5.858E+02 V/m
 * -d) 6.444E+02 V/m
 * -e) 7.089E+02 V/m

11) An ac generator produces an emf of amplitude 58 V at a frequency of 99 Hz. What is the maximum amplitude of the current if the generator is connected to a  35 mF inductor?


 * -a) 2.422E+00 A
 * +b) 2.664E+00 A
 * -c) 2.930E+00 A
 * -d) 3.224E+00 A
 * -e) 3.546E+00 A

Key: O0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0631 T . It emerges after being deflected by 44&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 1.897E-07 s
 * -b) 2.087E-07 s
 * -c) 2.296E-07 s
 * +d) 2.525E-07 s
 * -e) 2.778E-07 s

2) A charged particle in a magnetic field of 3.820E-04 T is moving perpendicular to the magnetic field with a speed of 3.890E+05 m/s. What is the period of orbit if orbital radius is 0.718 m?


 * -a) 8.713E-06 s
 * -b) 9.584E-06 s
 * -c) 1.054E-05 s
 * +d) 1.160E-05 s
 * -e) 1.276E-05 s

3) A solenoid has 7.690E+04 turns wound around a cylinder of diameter 1.63 cm and length 11 m. The current through the coils is 0.728 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.76 cm to z=+1.99 cm


 * -a) 2.762E-04 T-m
 * +b) 3.038E-04 T-m
 * -c) 3.342E-04 T-m
 * -d) 3.676E-04 T-m
 * -e) 4.043E-04 T-m

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.89 kA, I2=1.19 kA, and I3=3.5 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 6.535E-03 T-m
 * -b) 7.188E-03 T-m
 * -c) 7.907E-03 T-m
 * -d) 8.697E-03 T-m
 * -e) 9.567E-03 T-m

5) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 6.581E-01 A
 * -b) 7.239E-01 A
 * -c) 7.963E-01 A
 * -d) 8.759E-01 A
 * +e) 9.635E-01 A

6) In an LC circuit, the self-inductance is 0.0237 H and the capacitance is 6.140E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 8.260E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 4.093E-04 s
 * -b) 4.502E-04 s
 * -c) 4.952E-04 s
 * -d) 5.447E-04 s
 * +e) 5.992E-04 s

7) A step-down transformer steps 12 kV down to 170 V. The high-voltage input is provided by a 140 &Omega; power line that carries 9 A of currentWhat is the output current (at the 170 V side ?)


 * -a) 4.773E+02 A
 * -b) 5.250E+02 A
 * -c) 5.775E+02 A
 * +d) 6.353E+02 A
 * -e) 6.988E+02 A

8) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.517E+02 km
 * +b) 1.669E+02 km
 * -c) 1.835E+02 km
 * -d) 2.019E+02 km
 * -e) 2.221E+02 km

9) A parallel plate capacitor with a capicatnce C=4.90E-06 F whose plates have an area A=3.00E+03 m2 and separation d=5.40E-03 m is connected via a swith to a 10 &Omega; resistor and a battery of voltage V0=12 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.00E-04?


 * -a) 1.841E-02 A
 * +b) 2.026E-02 A
 * -c) 2.228E-02 A
 * -d) 2.451E-02 A
 * -e) 2.696E-02 A

10) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 6.62E-10 Tesla
 * -b) 8.33E-10 Tesla
 * -c) 1.05E-09 Tesla
 * -d) 1.32E-09 Tesla
 * +e) 1.66E-09 Tesla

11) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.11E-11 Vs2m-1
 * -b) 8.61E-11 Vs2m-1
 * +c) 1.04E-10 Vs2m-1
 * -d) 1.26E-10 Vs2m-1
 * -e) 1.53E-10 Vs2m-1

Key: O1
1) A step-down transformer steps 19 kV down to 260 V. The high-voltage input is provided by a 290 &Omega; power line that carries 6 A of currentWhat is the output current (at the 260 V side ?)


 * -a) 3.294E+02 A
 * -b) 3.624E+02 A
 * -c) 3.986E+02 A
 * +d) 4.385E+02 A
 * -e) 4.823E+02 A

2) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.003E+02 km
 * -b) 1.103E+02 km
 * -c) 1.213E+02 km
 * +d) 1.335E+02 km
 * -e) 1.468E+02 km

3) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 6.62E-10 Tesla
 * -b) 8.33E-10 Tesla
 * -c) 1.05E-09 Tesla
 * -d) 1.32E-09 Tesla
 * +e) 1.66E-09 Tesla

4) In an LC circuit, the self-inductance is 0.0776 H and the capacitance is 6.940E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 3.400E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 1.048E-03 s
 * +b) 1.153E-03 s
 * -c) 1.268E-03 s
 * -d) 1.395E-03 s
 * -e) 1.534E-03 s

5) A square coil has sides that are L= 0.219 m long and is tightly wound with N=508 turns of wire. The resistance of the coil is R=8.42 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * +a) 1.791E-01 A
 * -b) 1.970E-01 A
 * -c) 2.167E-01 A
 * -d) 2.384E-01 A
 * -e) 2.622E-01 A

6) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.89 kA, I2=1.19 kA, and I3=3.5 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 6.535E-03 T-m
 * -b) 7.188E-03 T-m
 * -c) 7.907E-03 T-m
 * -d) 8.697E-03 T-m
 * -e) 9.567E-03 T-m

7) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=3.00E+03 m2 and separation d=7.10E-03 m is connected via a swith to a 78 &Omega; resistor and a battery of voltage V0=25 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.30E-03?


 * -a) 2.998E-03 A
 * -b) 3.298E-03 A
 * -c) 3.628E-03 A
 * +d) 3.991E-03 A
 * -e) 4.390E-03 A

8) A solenoid has 7.170E+04 turns wound around a cylinder of diameter 1.56 cm and length 9 m. The current through the coils is 0.391 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;2.73 cm to z=+2.56 cm


 * -a) 1.414E-04 T-m
 * -b) 1.556E-04 T-m
 * -c) 1.711E-04 T-m
 * -d) 1.882E-04 T-m
 * +e) 2.071E-04 T-m

9) A circlular capactitor of radius 4.8 m has a gap of 17 mm, and a charge of 73 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * +a) 9.17E-11 Vs2m-1
 * -b) 1.11E-10 Vs2m-1
 * -c) 1.35E-10 Vs2m-1
 * -d) 1.63E-10 Vs2m-1
 * -e) 1.98E-10 Vs2m-1

10) A charged particle in a magnetic field of 2.740E-04 T is moving perpendicular to the magnetic field with a speed of 1.390E+05 m/s. What is the period of orbit if orbital radius is 0.776 m?


 * -a) 2.899E-05 s
 * -b) 3.189E-05 s
 * +c) 3.508E-05 s
 * -d) 3.859E-05 s
 * -e) 4.244E-05 s

11) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0327 T . It emerges after being deflected by 89&deg; from its original direction. How much time did it spend in that magnetic field?


 * +a) 9.857E-07 s
 * -b) 1.084E-06 s
 * -c) 1.193E-06 s
 * -d) 1.312E-06 s
 * -e) 1.443E-06 s

Key: O2
1) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 2.609E+00 A
 * -b) 2.870E+00 A
 * +c) 3.157E+00 A
 * -d) 3.473E+00 A
 * -e) 3.820E+00 A

2) A circlular capactitor of radius 4.8 m has a gap of 9 mm, and a charge of 53 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.26E-09 Tesla
 * -b) 4.11E-09 Tesla
 * +c) 5.17E-09 Tesla
 * -d) 6.51E-09 Tesla
 * -e) 8.19E-09 Tesla

3) In an LC circuit, the self-inductance is 0.025 H and the capacitance is 3.530E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 7.770E-05 C. How long does it take for the capacitor to become completely discharged?


 * -a) 3.856E-04 s
 * -b) 4.242E-04 s
 * +c) 4.666E-04 s
 * -d) 5.133E-04 s
 * -e) 5.646E-04 s

4) A 56 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 72 kW?


 * -a) 1.084E+02 km
 * -b) 1.193E+02 km
 * -c) 1.312E+02 km
 * -d) 1.443E+02 km
 * +e) 1.587E+02 km

5) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.78 kA, I2=2.61 kA, and I3=3.76 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 4.939E-03 T-m
 * -b) 5.432E-03 T-m
 * -c) 5.976E-03 T-m
 * -d) 6.573E-03 T-m
 * -e) 7.231E-03 T-m

6) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0631 T . It emerges after being deflected by 44&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 1.897E-07 s
 * -b) 2.087E-07 s
 * -c) 2.296E-07 s
 * +d) 2.525E-07 s
 * -e) 2.778E-07 s

7) A parallel plate capacitor with a capicatnce C=6.80E-06 F whose plates have an area A=6.60E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 62 &Omega; resistor and a battery of voltage V0=36 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * -a) 8.288E-02 A
 * -b) 9.117E-02 A
 * -c) 1.003E-01 A
 * -d) 1.103E-01 A
 * +e) 1.213E-01 A

8) A solenoid has 9.560E+04 turns wound around a cylinder of diameter 1.18 cm and length 12 m. The current through the coils is 0.664 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;4.49 cm to z=+3.61 cm


 * -a) 4.895E-04 T-m
 * +b) 5.384E-04 T-m
 * -c) 5.923E-04 T-m
 * -d) 6.515E-04 T-m
 * -e) 7.167E-04 T-m

9) A step-down transformer steps 9 kV down to 160 V. The high-voltage input is provided by a 260 &Omega; power line that carries 7 A of currentWhat is the output current (at the 160 V side ?)


 * +a) 3.938E+02 A
 * -b) 4.331E+02 A
 * -c) 4.764E+02 A
 * -d) 5.241E+02 A
 * -e) 5.765E+02 A

10) A circlular capactitor of radius 4.4 m has a gap of 16 mm, and a charge of 41 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 3.51E-11 Vs2m-1
 * -b) 4.25E-11 Vs2m-1
 * +c) 5.15E-11 Vs2m-1
 * -d) 6.24E-11 Vs2m-1
 * -e) 7.56E-11 Vs2m-1

11) A charged particle in a magnetic field of 4.970E-04 T is moving perpendicular to the magnetic field with a speed of 2.950E+05 m/s. What is the period of orbit if orbital radius is 0.344 m?


 * +a) 7.327E-06 s
 * -b) 8.060E-06 s
 * -c) 8.865E-06 s
 * -d) 9.752E-06 s
 * -e) 1.073E-05 s

Key: P0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0883 T . It emerges after being deflected by 74&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 2.280E-07 s
 * -b) 2.508E-07 s
 * -c) 2.759E-07 s
 * +d) 3.035E-07 s
 * -e) 3.339E-07 s

2) A charged particle in a magnetic field of 2.740E-04 T is moving perpendicular to the magnetic field with a speed of 1.390E+05 m/s. What is the period of orbit if orbital radius is 0.776 m?


 * -a) 2.899E-05 s
 * -b) 3.189E-05 s
 * +c) 3.508E-05 s
 * -d) 3.859E-05 s
 * -e) 4.244E-05 s

3) Two parallel wires each carry a 8.75 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.66 cm, 1.4 cm), while the other is located at (5.64 cm, 5.66 cm). What is the force per unit length between the wires?


 * -a) 2.449E-10 N/m
 * -b) 2.694E-10 N/m
 * -c) 2.963E-10 N/m
 * +d) 3.260E-10 N/m
 * -e) 3.586E-10 N/m

4) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 4.028E-05 T
 * -b) By= 4.431E-05 T
 * -c) By= 4.874E-05 T
 * -d) By= 5.361E-05 T
 * -e) By= 5.897E-05 T

5) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 6.581E-01 A
 * -b) 7.239E-01 A
 * -c) 7.963E-01 A
 * -d) 8.759E-01 A
 * +e) 9.635E-01 A

6) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.28mm$$, and $$n=2.4$$. What is the volume of the washer?


 * +a) 1.097E+00 cm3
 * -b) 1.207E+00 cm3
 * -c) 1.328E+00 cm3
 * -d) 1.460E+00 cm3
 * -e) 1.606E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 720 Hz and an amplitude of 0.63 V;. If R =5 &Omega;, L= 4.20E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 1.081E+00 &rad;
 * -b) 1.189E+00 &rad;
 * +c) 1.308E+00 &rad;
 * -d) 1.439E+00 &rad;
 * -e) 1.583E+00 &rad;

8) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=4.20E+03 m2 and separation d=8.00E-03 m is connected via a swith to a 6 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.60E-05?


 * -a) 7.253E+03 V/m
 * -b) 7.978E+03 V/m
 * -c) 8.776E+03 V/m
 * -d) 9.653E+03 V/m
 * +e) 1.062E+04 V/m

9) A parallel plate capacitor with a capicatnce C=7.60E-06 F whose plates have an area A=2.90E+03 m2 and separation d=3.40E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.20E-04?


 * +a) 7.693E+01 V
 * -b) 8.463E+01 V
 * -c) 9.309E+01 V
 * -d) 1.024E+02 V
 * -e) 1.126E+02 V

10) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.30E-09 Tesla
 * -b) 4.15E-09 Tesla
 * -c) 5.23E-09 Tesla
 * +d) 6.58E-09 Tesla
 * -e) 8.29E-09 Tesla

11) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 43 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * +a) 1.95E-04 s
 * -b) 2.36E-04 s
 * -c) 2.86E-04 s
 * -d) 3.46E-04 s
 * -e) 4.20E-04 s

Key: P1
1) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?


 * -a) 1.283E-10 N/m
 * -b) 1.411E-10 N/m
 * -c) 1.552E-10 N/m
 * -d) 1.708E-10 N/m
 * +e) 1.878E-10 N/m

2) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 4.028E-05 T
 * -b) By= 4.431E-05 T
 * -c) By= 4.874E-05 T
 * -d) By= 5.361E-05 T
 * -e) By= 5.897E-05 T

3) A circlular capactitor of radius 4.1 m has a gap of 11 mm, and a charge of 51 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * +a) 3.40E-04 s
 * -b) 4.12E-04 s
 * -c) 4.99E-04 s
 * -d) 6.05E-04 s
 * -e) 7.33E-04 s

4) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 &Omega;, L= 8.20E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.146E-01 &rad;
 * -b) 8.960E-01 &rad;
 * +c) 9.856E-01 &rad;
 * -d) 1.084E+00 &rad;
 * -e) 1.193E+00 &rad;

5) A parallel plate capacitor with a capicatnce C=7.10E-06 F whose plates have an area A=5.10E+03 m2 and separation d=6.40E-03 m is connected via a swith to a 54 &Omega; resistor and a battery of voltage V0=83 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.50E-03?


 * -a) 6.111E+01 V
 * -b) 6.722E+01 V
 * -c) 7.395E+01 V
 * +d) 8.134E+01 V
 * -e) 8.947E+01 V

6) A square coil has sides that are L= 0.888 m long and is tightly wound with N=604 turns of wire. The resistance of the coil is R=4.31 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 3.661E+00 A
 * -b) 4.028E+00 A
 * -c) 4.430E+00 A
 * +d) 4.873E+00 A
 * -e) 5.361E+00 A

7) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.47mm$$, and $$n=2.8$$. What is the volume of the washer?


 * -a) 8.932E-01 cm3
 * -b) 9.825E-01 cm3
 * -c) 1.081E+00 cm3
 * +d) 1.189E+00 cm3
 * -e) 1.308E+00 cm3

8) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0393 T . It emerges after being deflected by 49&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 4.105E-07 s
 * +b) 4.515E-07 s
 * -c) 4.967E-07 s
 * -d) 5.464E-07 s
 * -e) 6.010E-07 s

9) A circlular capactitor of radius 4 m has a gap of 13 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 8.62E-09 Tesla
 * -b) 1.09E-08 Tesla
 * -c) 1.37E-08 Tesla
 * -d) 1.72E-08 Tesla
 * +e) 2.17E-08 Tesla

10) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m2 and separation d=3.50E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?


 * -a) 3.751E+03 V/m
 * +b) 4.126E+03 V/m
 * -c) 4.539E+03 V/m
 * -d) 4.993E+03 V/m
 * -e) 5.492E+03 V/m

11) A charged particle in a magnetic field of 1.480E-04 T is moving perpendicular to the magnetic field with a speed of 4.520E+05 m/s. What is the period of orbit if orbital radius is 0.4 m?


 * +a) 5.560E-06 s
 * -b) 6.116E-06 s
 * -c) 6.728E-06 s
 * -d) 7.401E-06 s
 * -e) 8.141E-06 s

Key: P2
1) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * -a) 1.118E+00 cm3
 * +b) 1.229E+00 cm3
 * -c) 1.352E+00 cm3
 * -d) 1.487E+00 cm3
 * -e) 1.636E+00 cm3

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0454 T . It emerges after being deflected by 74&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 4.878E-07 s
 * -b) 5.366E-07 s
 * +c) 5.903E-07 s
 * -d) 6.493E-07 s
 * -e) 7.143E-07 s

3) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * -a) 6.62E-05 s
 * -b) 8.02E-05 s
 * -c) 9.71E-05 s
 * -d) 1.18E-04 s
 * +e) 1.43E-04 s

4) The output of an ac generator connected to an RLC series combination has a frequency of 220 Hz and an amplitude of 0.71 V;. If R =7 &Omega;, L= 8.20E-03H, and C=9.40E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.146E-01 &rad;
 * -b) 8.960E-01 &rad;
 * +c) 9.856E-01 &rad;
 * -d) 1.084E+00 &rad;
 * -e) 1.193E+00 &rad;

5) A charged particle in a magnetic field of 3.350E-04 T is moving perpendicular to the magnetic field with a speed of 4.350E+05 m/s. What is the period of orbit if orbital radius is 0.841 m?


 * -a) 1.004E-05 s
 * -b) 1.104E-05 s
 * +c) 1.215E-05 s
 * -d) 1.336E-05 s
 * -e) 1.470E-05 s

6) A square coil has sides that are L= 0.568 m long and is tightly wound with N=482 turns of wire. The resistance of the coil is R=8.78 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 6.581E-01 A
 * -b) 7.239E-01 A
 * -c) 7.963E-01 A
 * -d) 8.759E-01 A
 * +e) 9.635E-01 A

7) A parallel plate capacitor with a capicatnce C=2.00E-06 F whose plates have an area A=1.90E+03 m2 and separation d=8.60E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=45 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.30E-04?


 * -a) 3.223E+03 V/m
 * -b) 3.546E+03 V/m
 * -c) 3.900E+03 V/m
 * -d) 4.290E+03 V/m
 * +e) 4.719E+03 V/m

8) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 55 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.95E-09 Tesla
 * -b) 4.97E-09 Tesla
 * +c) 6.26E-09 Tesla
 * -d) 7.88E-09 Tesla
 * -e) 9.92E-09 Tesla

9) Three wires sit at the corners of a square of length 0.703 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.49 A, 1.32 A, 1.75 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 8.962E-05 T
 * -b) By= 9.858E-05 T
 * -c) By= 1.084E-04 T
 * -d) By= 1.193E-04 T
 * -e) By= 1.312E-04 T

10) A parallel plate capacitor with a capicatnce C=2.90E-06 F whose plates have an area A=1.60E+03 m2 and separation d=5.00E-03 m is connected via a swith to a 41 &Omega; resistor and a battery of voltage V0=92 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=4.50E-04?


 * -a) 6.755E+01 V
 * -b) 7.431E+01 V
 * -c) 8.174E+01 V
 * +d) 8.991E+01 V
 * -e) 9.890E+01 V

11) Two parallel wires each carry a 7.59 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.98 cm, 0.969 cm), while the other is located at (5.13 cm, 5.53 cm). What is the force per unit length between the wires?


 * -a) 1.840E-10 N/m
 * -b) 2.024E-10 N/m
 * -c) 2.227E-10 N/m
 * +d) 2.449E-10 N/m
 * -e) 2.694E-10 N/m

Key: Q0
1) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.379 T magnetic field is directed 53&deg; away from the wire?


 * -a) 1.001E+00 N/m
 * -b) 1.101E+00 N/m
 * +c) 1.211E+00 N/m
 * -d) 1.332E+00 N/m
 * -e) 1.465E+00 N/m

2) A charged particle in a magnetic field of 3.410E-04 T is moving perpendicular to the magnetic field with a speed of 5.010E+05 m/s. What is the period of orbit if orbital radius is 0.508 m?


 * -a) 5.792E-06 s
 * +b) 6.371E-06 s
 * -c) 7.008E-06 s
 * -d) 7.709E-06 s
 * -e) 8.480E-06 s

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.39 kA, I2=0.414 kA, and I3=1.3 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 2.812E-03 T-m
 * -b) 3.093E-03 T-m
 * -c) 3.402E-03 T-m
 * -d) 3.742E-03 T-m
 * +e) 4.117E-03 T-m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.432 m and $$B_{max}=\,$$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.277E+05 A
 * -b) 3.604E+05 A
 * -c) 3.965E+05 A
 * -d) 4.361E+05 A
 * +e) 4.797E+05 A

5) A square coil has sides that are L= 0.458 m long and is tightly wound with N=742 turns of wire. The resistance of the coil is R=6.81 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 1.056E+00 A
 * -b) 1.161E+00 A
 * +c) 1.278E+00 A
 * -d) 1.405E+00 A
 * -e) 1.546E+00 A

6) A washer has an inner diameter of 2.3 cm and an outer diamter of 4.44 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.31mm$$, and $$n=2.66$$. What is the volume of the washer?


 * -a) 1.089E+00 cm3
 * -b) 1.198E+00 cm3
 * +c) 1.318E+00 cm3
 * -d) 1.449E+00 cm3
 * -e) 1.594E+00 cm3

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=5 V. The resistance, inductance, and capacitance are R =0.27 &Omega;, L= 4.30E-03H, and C=2.20E-06 F, respectively.


 * -a) Q = 1.238E+02
 * -b) Q = 1.424E+02
 * +c) Q = 1.637E+02
 * -d) Q = 1.883E+02
 * -e) Q = 2.165E+02

8) What is the radiation pressure on an object that is 8.30E+11 m away from the sun and has cross-sectional area of 0.097 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.928E-07 N/m2
 * -b) 3.221E-07 N/m2
 * -c) 3.543E-07 N/m2
 * -d) 3.898E-07 N/m2
 * -e) 4.287E-07 N/m2

9) A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 98 &Omega; resistor and a battery of voltage V0=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?


 * -a) 5.050E+03 V/m
 * -b) 5.555E+03 V/m
 * -c) 6.111E+03 V/m
 * -d) 6.722E+03 V/m
 * +e) 7.394E+03 V/m

10) A circlular capactitor of radius 4 m has a gap of 13 mm, and a charge of 89 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 8.62E-09 Tesla
 * -b) 1.09E-08 Tesla
 * -c) 1.37E-08 Tesla
 * -d) 1.72E-08 Tesla
 * +e) 2.17E-08 Tesla

11) A circlular capactitor of radius 3.4 m has a gap of 15 mm, and a charge of 63 &mu;C.  What is the electric field between the plates?


 * -a) 1.62E+05 N/C (or V/m)
 * +b) 1.96E+05 N/C (or V/m)
 * -c) 2.37E+05 N/C (or V/m)
 * -d) 2.88E+05 N/C (or V/m)
 * -e) 3.48E+05 N/C (or V/m)

Key: Q1
1) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * -a) 1.131E+00 N/m
 * -b) 1.244E+00 N/m
 * -c) 1.368E+00 N/m
 * +d) 1.505E+00 N/m
 * -e) 1.655E+00 N/m

2) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?


 * -a) 2.04E+04 N/C (or V/m)
 * -b) 2.47E+04 N/C (or V/m)
 * -c) 3.00E+04 N/C (or V/m)
 * +d) 3.63E+04 N/C (or V/m)
 * -e) 4.40E+04 N/C (or V/m)

3) A parallel plate capacitor with a capicatnce C=5.60E-06 F whose plates have an area A=2.00E+03 m2 and separation d=3.10E-03 m is connected via a swith to a 68 &Omega; resistor and a battery of voltage V0=73 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=8.50E-04?


 * -a) 1.579E+04 V/m
 * -b) 1.737E+04 V/m
 * -c) 1.911E+04 V/m
 * +d) 2.102E+04 V/m
 * -e) 2.312E+04 V/m

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.259 m and $$B_{max}=\,$$ 0.575 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.191 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.492E+05 A
 * -b) 3.841E+05 A
 * -c) 4.225E+05 A
 * -d) 4.648E+05 A
 * +e) 5.113E+05 A

5) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.2 &Omega;, L= 5.00E-03H, and C=3.20E-06 F, respectively.


 * -a) Q = 1.300E+02
 * -b) Q = 1.494E+02
 * -c) Q = 1.719E+02
 * +d) Q = 1.976E+02
 * -e) Q = 2.273E+02

6) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 2.82E-09 Tesla
 * -b) 3.54E-09 Tesla
 * -c) 4.46E-09 Tesla
 * -d) 5.62E-09 Tesla
 * +e) 7.07E-09 Tesla

7) What is the radiation pressure on an object that is 9.70E+11 m away from the sun and has cross-sectional area of 0.098 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 2.144E-07 N/m2
 * -b) 2.358E-07 N/m2
 * -c) 2.594E-07 N/m2
 * -d) 2.854E-07 N/m2
 * -e) 3.139E-07 N/m2

8) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 2.609E+00 A
 * -b) 2.870E+00 A
 * +c) 3.157E+00 A
 * -d) 3.473E+00 A
 * -e) 3.820E+00 A

9) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.57 kA, I2=0.708 kA, and I3=1.48 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 4.200E-03 T-m
 * -b) 4.620E-03 T-m
 * -c) 5.082E-03 T-m
 * -d) 5.590E-03 T-m
 * -e) 6.149E-03 T-m

10) A washer has an inner diameter of 2.75 cm and an outer diamter of 4.87 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.39mm$$, and $$n=2.55$$. What is the volume of the washer?


 * -a) 7.754E-01 cm3
 * -b) 8.530E-01 cm3
 * -c) 9.383E-01 cm3
 * -d) 1.032E+00 cm3
 * +e) 1.135E+00 cm3

11) A charged particle in a magnetic field of 4.480E-04 T is moving perpendicular to the magnetic field with a speed of 7.700E+05 m/s. What is the period of orbit if orbital radius is 0.368 m?


 * -a) 2.730E-06 s
 * +b) 3.003E-06 s
 * -c) 3.303E-06 s
 * -d) 3.633E-06 s
 * -e) 3.997E-06 s

Key: Q2
1) A charged particle in a magnetic field of 1.750E-04 T is moving perpendicular to the magnetic field with a speed of 2.330E+05 m/s. What is the period of orbit if orbital radius is 0.893 m?


 * -a) 2.189E-05 s
 * +b) 2.408E-05 s
 * -c) 2.649E-05 s
 * -d) 2.914E-05 s
 * -e) 3.205E-05 s

2) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.315E-07 N/m2
 * +b) 2.547E-07 N/m2
 * -c) 2.801E-07 N/m2
 * -d) 3.082E-07 N/m2
 * -e) 3.390E-07 N/m2

3) A square coil has sides that are L= 0.561 m long and is tightly wound with N=930 turns of wire. The resistance of the coil is R=5.08 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?


 * -a) 2.609E+00 A
 * -b) 2.870E+00 A
 * +c) 3.157E+00 A
 * -d) 3.473E+00 A
 * -e) 3.820E+00 A

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.38 kA, I2=1.58 kA, and I3=4.31 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.386E-03 T-m
 * -b) 4.825E-03 T-m
 * -c) 5.307E-03 T-m
 * -d) 5.838E-03 T-m
 * +e) 6.421E-03 T-m

5) A long rigid wire carries a 3 A current. What is the magnetic force per unit length on the wire if a 0.534 T magnetic field is directed 18&deg; away from the wire?


 * +a) 4.950E-01 N/m
 * -b) 5.445E-01 N/m
 * -c) 5.990E-01 N/m
 * -d) 6.589E-01 N/m
 * -e) 7.248E-01 N/m

6) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.568 m and $$B_{max}=\,$$ 0.214 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.387 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.382E+05 A
 * +b) 3.720E+05 A
 * -c) 4.092E+05 A
 * -d) 4.502E+05 A
 * -e) 4.952E+05 A

7) A circlular capactitor of radius 4.8 m has a gap of 14 mm, and a charge of 75 &mu;C.  What is the electric field between the plates?


 * -a) 5.43E+04 N/C (or V/m)
 * -b) 6.58E+04 N/C (or V/m)
 * -c) 7.97E+04 N/C (or V/m)
 * -d) 9.66E+04 N/C (or V/m)
 * +e) 1.17E+05 N/C (or V/m)

8) A parallel plate capacitor with a capicatnce C=1.30E-06 F whose plates have an area A=1.10E+03 m2 and separation d=7.60E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=5 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.30E-04?


 * -a) 4.842E+02 V/m
 * -b) 5.326E+02 V/m
 * +c) 5.858E+02 V/m
 * -d) 6.444E+02 V/m
 * -e) 7.089E+02 V/m

9) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=2 V. The resistance, inductance, and capacitance are R =0.25 &Omega;, L= 5.40E-03H, and C=3.20E-06 F, respectively.


 * -a) Q = 9.395E+01
 * -b) Q = 1.080E+02
 * -c) Q = 1.242E+02
 * -d) Q = 1.429E+02
 * +e) Q = 1.643E+02

10) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * +a) 8.32E-09 Tesla
 * -b) 1.05E-08 Tesla
 * -c) 1.32E-08 Tesla
 * -d) 1.66E-08 Tesla
 * -e) 2.09E-08 Tesla

11) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.18 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.42mm$$, and $$n=2.62$$. What is the volume of the washer?


 * +a) 1.351E+00 cm3
 * -b) 1.486E+00 cm3
 * -c) 1.635E+00 cm3
 * -d) 1.798E+00 cm3
 * -e) 1.978E+00 cm3

Key: R0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.011 T . It emerges after being deflected by 70&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 2.095E-06 s
 * +b) 2.305E-06 s
 * -c) 2.535E-06 s
 * -d) 2.789E-06 s
 * -e) 3.067E-06 s

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.232 m and a magneticfield of 1.1 T. What is their maximum kinetic energy?


 * -a) 2.853E+00 MeV
 * +b) 3.139E+00 MeV
 * -c) 3.453E+00 MeV
 * -d) 3.798E+00 MeV
 * -e) 4.178E+00 MeV

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.208E-05 T
 * -b) 1.329E-05 T
 * -c) 1.462E-05 T
 * -d) 1.608E-05 T
 * -e) 1.769E-05 T

4) Three wires sit at the corners of a square of length 0.78 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.13 A, 1.35 A, 2.02 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.282E-05 T
 * +b) Bx= 6.910E-05 T
 * -c) Bx= 7.601E-05 T
 * -d) Bx= 8.361E-05 T
 * -e) Bx= 9.198E-05 T

5) Calculate the motional emf induced along a 30.3 km conductor moving at an orbital speed of 7.76 km/s perpendicular to Earth's 5.100E-05 Tesla magnetic field.


 * -a) 1.090E+04 V
 * +b) 1.199E+04 V
 * -c) 1.319E+04 V
 * -d) 1.451E+04 V
 * -e) 1.596E+04 V

6) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.67% of its maximum value if &epsilon; = 5.07 V, R = 7.8 &Omega;, and L = 4.39 H?


 * -a) -1.047E+00 s
 * +b) -1.152E+00 s
 * -c) -1.267E+00 s
 * -d) -1.393E+00 s
 * -e) -1.533E+00 s

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 &Omega;, L= 4.60E-03H, and C=8.10E-04 F, respectively. What is the amplitude of the current?


 * -a) 1.417E-01 A
 * -b) 1.559E-01 A
 * -c) 1.715E-01 A
 * -d) 1.886E-01 A
 * +e) 2.075E-01 A

8) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=730.0 m2 and separation d=4.60E-03 m is connected via a swith to a 96 &Omega; resistor and a battery of voltage V0=90 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.30E-04?


 * -a) 7.315E-02 A
 * +b) 8.047E-02 A
 * -c) 8.851E-02 A
 * -d) 9.737E-02 A
 * -e) 1.071E-01 A

9) What is the radiation force on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.096 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 4.373E-08 N
 * -b) 4.810E-08 N
 * -c) 5.291E-08 N
 * -d) 5.820E-08 N
 * +e) 6.402E-08 N

10) A circlular capactitor of radius 4.9 m has a gap of 11 mm, and a charge of 85 &mu;C.  What is the electric field between the plates?


 * +a) 1.27E+05 N/C (or V/m)
 * -b) 1.54E+05 N/C (or V/m)
 * -c) 1.87E+05 N/C (or V/m)
 * -d) 2.26E+05 N/C (or V/m)
 * -e) 2.74E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.4 m has a gap of 17 mm, and a charge of 65 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.56E-11 Vs2m-1
 * -b) 6.74E-11 Vs2m-1
 * +c) 8.17E-11 Vs2m-1
 * -d) 9.90E-11 Vs2m-1
 * -e) 1.20E-10 Vs2m-1

Key: R1
1) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 8.969E-08 N
 * -b) 9.866E-08 N
 * -c) 1.085E-07 N
 * -d) 1.194E-07 N
 * +e) 1.313E-07 N

2) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =4 &Omega;, L= 4.60E-03H, and C=8.10E-04 F, respectively. What is the amplitude of the current?


 * -a) 1.417E-01 A
 * -b) 1.559E-01 A
 * -c) 1.715E-01 A
 * -d) 1.886E-01 A
 * +e) 2.075E-01 A

3) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 21 &mu;C.  What is the electric field between the plates?


 * +a) 6.16E+04 N/C (or V/m)
 * -b) 7.47E+04 N/C (or V/m)
 * -c) 9.05E+04 N/C (or V/m)
 * -d) 1.10E+05 N/C (or V/m)
 * -e) 1.33E+05 N/C (or V/m)

4) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.448 m and a magneticfield of 0.812 T. What is their maximum kinetic energy?


 * -a) 5.798E+00 MeV
 * +b) 6.377E+00 MeV
 * -c) 7.015E+00 MeV
 * -d) 7.717E+00 MeV
 * -e) 8.488E+00 MeV

5) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if &epsilon; = 5.95 V, R = 7.26 &Omega;, and L = 1.29 H?


 * -a) -3.114E-01 s
 * -b) -3.425E-01 s
 * +c) -3.767E-01 s
 * -d) -4.144E-01 s
 * -e) -4.559E-01 s

6) A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m2 and separation d=3.60E-03 m is connected via a swith to a 87 &Omega; resistor and a battery of voltage V0=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?


 * -a) 8.320E-02 A
 * -b) 9.152E-02 A
 * -c) 1.007E-01 A
 * -d) 1.107E-01 A
 * +e) 1.218E-01 A

7) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.18 mm from the center of a wire of radius 3 mm if the current is 1A?


 * -a) 1.791E-05 T
 * -b) 1.970E-05 T
 * -c) 2.167E-05 T
 * -d) 2.384E-05 T
 * +e) 2.622E-05 T

8) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0279 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 7.270E-07 s
 * -b) 7.997E-07 s
 * -c) 8.797E-07 s
 * -d) 9.676E-07 s
 * +e) 1.064E-06 s

9) Calculate the motional emf induced along a 27.5 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.520E-05 Tesla magnetic field.


 * -a) 8.074E+03 V
 * -b) 8.882E+03 V
 * +c) 9.770E+03 V
 * -d) 1.075E+04 V
 * -e) 1.182E+04 V

10) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.87E-11 Vs2m-1
 * -b) 7.11E-11 Vs2m-1
 * -c) 8.61E-11 Vs2m-1
 * +d) 1.04E-10 Vs2m-1
 * -e) 1.26E-10 Vs2m-1

11) Three wires sit at the corners of a square of length 0.688 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.73 A, 1.37 A, 1.65 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.171E-05 T
 * +b) Bx= 6.788E-05 T
 * -c) Bx= 7.467E-05 T
 * -d) Bx= 8.213E-05 T
 * -e) Bx= 9.035E-05 T

Key: R2
1) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.44% of its maximum value if &epsilon; = 5.95 V, R = 7.26 &Omega;, and L = 1.29 H?


 * -a) -3.114E-01 s
 * -b) -3.425E-01 s
 * +c) -3.767E-01 s
 * -d) -4.144E-01 s
 * -e) -4.559E-01 s

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0775 T . It emerges after being deflected by 73&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 2.819E-07 s
 * -b) 3.101E-07 s
 * +c) 3.411E-07 s
 * -d) 3.752E-07 s
 * -e) 4.128E-07 s

3) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=1.00E+04 m2 and separation d=9.00E-03 m is connected via a swith to a 15 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.60E-04?


 * -a) 6.394E-02 A
 * +b) 7.033E-02 A
 * -c) 7.736E-02 A
 * -d) 8.510E-02 A
 * -e) 9.361E-02 A

4) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.88 V. The resistance, inductance, and capacitance are R =7 &Omega;, L= 8.00E-03H, and C=5.50E-04 F, respectively. What is the amplitude of the current?


 * -a) 1.143E-01 A
 * +b) 1.257E-01 A
 * -c) 1.383E-01 A
 * -d) 1.521E-01 A
 * -e) 1.673E-01 A

5) A circlular capactitor of radius 4.3 m has a gap of 7 mm, and a charge of 47 &mu;C.  What is the electric field between the plates?


 * -a) 7.54E+04 N/C (or V/m)
 * +b) 9.14E+04 N/C (or V/m)
 * -c) 1.11E+05 N/C (or V/m)
 * -d) 1.34E+05 N/C (or V/m)
 * -e) 1.63E+05 N/C (or V/m)

6) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.157 m and a magneticfield of 1.03 T. What is their maximum kinetic energy?


 * -a) 8.608E-01 MeV
 * -b) 9.468E-01 MeV
 * -c) 1.042E+00 MeV
 * -d) 1.146E+00 MeV
 * +e) 1.260E+00 MeV

7) What is the radiation force on an object that is 7.40E+11 m away from the sun and has cross-sectional area of 0.082 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.063E-08 N
 * -b) 2.270E-08 N
 * -c) 2.497E-08 N
 * -d) 2.746E-08 N
 * +e) 3.021E-08 N

8) Three wires sit at the corners of a square of length 0.518 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.31 A, 1.32 A, 1.62 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.013E-05 T
 * -b) Bx= 6.614E-05 T
 * -c) Bx= 7.275E-05 T
 * -d) Bx= 8.003E-05 T
 * +e) Bx= 8.803E-05 T

9) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 3.33 mm from the center of a wire of radius 5 mm if the current is 1A?


 * -a) 2.202E-05 T
 * -b) 2.422E-05 T
 * +c) 2.664E-05 T
 * -d) 2.930E-05 T
 * -e) 3.223E-05 T

10) Calculate the motional emf induced along a 21.3 km conductor moving at an orbital speed of 7.75 km/s perpendicular to Earth's 5.320E-05 Tesla magnetic field.


 * -a) 6.598E+03 V
 * -b) 7.258E+03 V
 * -c) 7.984E+03 V
 * +d) 8.782E+03 V
 * -e) 9.660E+03 V

11) A circlular capactitor of radius 4.3 m has a gap of 11 mm, and a charge of 66 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 6.85E-11 Vs2m-1
 * +b) 8.29E-11 Vs2m-1
 * -c) 1.00E-10 Vs2m-1
 * -d) 1.22E-10 Vs2m-1
 * -e) 1.47E-10 Vs2m-1

Key: S0
1) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.080E-06 V
 * -b) 1.188E-06 V
 * -c) 1.306E-06 V
 * -d) 1.437E-06 V
 * +e) 1.581E-06 V

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0172 T . It emerges after being deflected by 85&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 1.627E-06 s
 * +b) 1.790E-06 s
 * -c) 1.969E-06 s
 * -d) 2.166E-06 s
 * -e) 2.382E-06 s

3) Three wires sit at the corners of a square of length 0.859 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.07 A, 1.32 A, 2.03 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 4.028E-05 T
 * -b) By= 4.431E-05 T
 * -c) By= 4.874E-05 T
 * -d) By= 5.361E-05 T
 * -e) By= 5.897E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 9.310E+02
 * -b) $$\chi \text{ (chi) }=$$ 1.024E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.126E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.239E+03
 * +e) $$\chi \text{ (chi) }=$$ 1.363E+03

5) The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12 A/s. The solenoid is 62 cm long and has a cross-sectional diameter of 3.37 cm.  A small coil consisting of N=23turns wraped in a circle of diameter 1.7 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 1.215E-04 V
 * -b) 1.337E-04 V
 * -c) 1.470E-04 V
 * -d) 1.617E-04 V
 * +e) 1.779E-04 V

6) An induced emf of 7.48V is measured across a coil of 95 closely wound turns while the current throuth it increases uniformly from 0.0 to 5.33A in 0.304s. What is the self-inductance of the coil?


 * -a) 2.914E-01 H
 * -b) 3.205E-01 H
 * -c) 3.526E-01 H
 * -d) 3.878E-01 H
 * +e) 4.266E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 760 Hz and an amplitude of 0.23 V;. If R =4 &Omega;, L= 7.70E-03H, and C=9.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 1.329E+00 &rad;
 * +b) 1.462E+00 &rad;
 * -c) 1.608E+00 &rad;
 * -d) 1.769E+00 &rad;
 * -e) 1.946E+00 &rad;

8) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * -a) 1.418E+02 km
 * +b) 1.560E+02 km
 * -c) 1.716E+02 km
 * -d) 1.887E+02 km
 * -e) 2.076E+02 km

9) A parallel plate capacitor with a capicatnce C=6.60E-06 F whose plates have an area A=4.90E+03 m2 and separation d=6.60E-03 m is connected via a swith to a 20 &Omega; resistor and a battery of voltage V0=59 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.70E-04?


 * +a) 8.138E-01 A
 * -b) 8.952E-01 A
 * -c) 9.847E-01 A
 * -d) 1.083E+00 A
 * -e) 1.191E+00 A

10) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 62 &mu;C.  What is the electric field between the plates?


 * -a) 9.50E+04 N/C (or V/m)
 * +b) 1.15E+05 N/C (or V/m)
 * -c) 1.39E+05 N/C (or V/m)
 * -d) 1.69E+05 N/C (or V/m)
 * -e) 2.05E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.1 m has a gap of 11 mm, and a charge of 51 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * +a) 3.40E-04 s
 * -b) 4.12E-04 s
 * -c) 4.99E-04 s
 * -d) 6.05E-04 s
 * -e) 7.33E-04 s

Key: S1
1) An induced emf of 2.9V is measured across a coil of 51 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.89A in 0.806s. What is the self-inductance of the coil?


 * -a) 2.549E-01 H
 * -b) 2.804E-01 H
 * -c) 3.084E-01 H
 * +d) 3.392E-01 H
 * -e) 3.732E-01 H

2) The current through the windings of a solenoid with n= 2.460E+03 turns per meter is changing at a rate dI/dt=7 A/s. The solenoid is 87 cm long and has a cross-sectional diameter of 3.32 cm.  A small coil consisting of N=38turns wraped in a circle of diameter 1.29 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 7.340E-05 V
 * -b) 8.075E-05 V
 * -c) 8.882E-05 V
 * -d) 9.770E-05 V
 * +e) 1.075E-04 V

3) The output of an ac generator connected to an RLC series combination has a frequency of 280 Hz and an amplitude of 0.35 V;. If R =5 &Omega;, L= 9.50E-03H, and C=6.90E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.646E-01 &rad;
 * -b) 9.511E-01 &rad;
 * -c) 1.046E+00 &rad;
 * -d) 1.151E+00 &rad;
 * +e) 1.266E+00 &rad;

4) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=3.00E+03 m2 and separation d=7.10E-03 m is connected via a swith to a 78 &Omega; resistor and a battery of voltage V0=25 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=1.30E-03?


 * -a) 2.998E-03 A
 * -b) 3.298E-03 A
 * -c) 3.628E-03 A
 * +d) 3.991E-03 A
 * -e) 4.390E-03 A

5) A 59 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 76 kW?


 * -a) 1.008E+02 km
 * -b) 1.109E+02 km
 * -c) 1.219E+02 km
 * -d) 1.341E+02 km
 * +e) 1.475E+02 km

6) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 19 turns per centimeter and the current applied to the solenoid is 421 mA, the net magnetic field is measured to be 1.31 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.302E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.432E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.576E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.733E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.907E+03

7) The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.648E-06 V
 * -b) 1.813E-06 V
 * -c) 1.994E-06 V
 * +d) 2.194E-06 V
 * -e) 2.413E-06 V

8) A circlular capactitor of radius 3.6 m has a gap of 8 mm, and a charge of 53 &mu;C.  What is the electric field between the plates?


 * -a) 6.82E+04 N/C (or V/m)
 * -b) 8.27E+04 N/C (or V/m)
 * -c) 1.00E+05 N/C (or V/m)
 * -d) 1.21E+05 N/C (or V/m)
 * +e) 1.47E+05 N/C (or V/m)

9) Three wires sit at the corners of a square of length 0.702 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.24 A, 1.37 A, 2.3 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 7.576E-05 T
 * +b) By= 8.333E-05 T
 * -c) By= 9.167E-05 T
 * -d) By= 1.008E-04 T
 * -e) By= 1.109E-04 T

10) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * -a) 1.65E-04 s
 * +b) 2.00E-04 s
 * -c) 2.43E-04 s
 * -d) 2.94E-04 s
 * -e) 3.56E-04 s

11) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0243 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * +a) 1.222E-06 s
 * -b) 1.344E-06 s
 * -c) 1.479E-06 s
 * -d) 1.627E-06 s
 * -e) 1.789E-06 s

Key: S2
1) A parallel plate capacitor with a capicatnce C=4.40E-06 F whose plates have an area A=1.80E+03 m2 and separation d=3.60E-03 m is connected via a swith to a 87 &Omega; resistor and a battery of voltage V0=61 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=6.70E-04?


 * -a) 8.320E-02 A
 * -b) 9.152E-02 A
 * -c) 1.007E-01 A
 * -d) 1.107E-01 A
 * +e) 1.218E-01 A

2) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 &Omega;, L= 2.80E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.759E-01 &rad;
 * -b) 9.635E-01 &rad;
 * +c) 1.060E+00 &rad;
 * -d) 1.166E+00 &rad;
 * -e) 1.282E+00 &rad;

3) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 84 kW?


 * -a) 9.780E+01 km
 * -b) 1.076E+02 km
 * -c) 1.183E+02 km
 * -d) 1.302E+02 km
 * +e) 1.432E+02 km

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 424 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 1.092E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.201E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.321E+03
 * +d) $$\chi \text{ (chi) }=$$ 1.454E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.599E+03

5) The silver ribbon shown are a=4.12 cm, b=3.32 cm, and c= 1.46 cm. The current carries a current of 120 A and it lies in a uniform magnetic field of 1.39 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 1.209E-06 V
 * -b) 1.329E-06 V
 * -c) 1.462E-06 V
 * -d) 1.609E-06 V
 * -e) 1.770E-06 V

6) An induced emf of 1.86V is measured across a coil of 59 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.58A in 0.89s. What is the self-inductance of the coil?


 * -a) 4.821E-01 H
 * -b) 5.303E-01 H
 * -c) 5.833E-01 H
 * +d) 6.416E-01 H
 * -e) 7.058E-01 H

7) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0837 T . It emerges after being deflected by 41&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 1.212E-07 s
 * -b) 1.333E-07 s
 * -c) 1.466E-07 s
 * -d) 1.613E-07 s
 * +e) 1.774E-07 s

8) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 62 &mu;C.  What is the electric field between the plates?


 * -a) 9.50E+04 N/C (or V/m)
 * +b) 1.15E+05 N/C (or V/m)
 * -c) 1.39E+05 N/C (or V/m)
 * -d) 1.69E+05 N/C (or V/m)
 * -e) 2.05E+05 N/C (or V/m)

9) The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10 A/s. The solenoid is 70 cm long and has a cross-sectional diameter of 2.73 cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.45 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?


 * -a) 1.066E-04 V
 * -b) 1.173E-04 V
 * +c) 1.290E-04 V
 * -d) 1.419E-04 V
 * -e) 1.561E-04 V

10) A circlular capactitor of radius 3.1 m has a gap of 15 mm, and a charge of 73 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * -a) 6.62E-05 s
 * -b) 8.02E-05 s
 * -c) 9.71E-05 s
 * -d) 1.18E-04 s
 * +e) 1.43E-04 s

11) Three wires sit at the corners of a square of length 0.495 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.45 A, 1.66 A, 1.63 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 1.205E-04 T
 * +b) By= 1.325E-04 T
 * -c) By= 1.458E-04 T
 * -d) By= 1.604E-04 T
 * -e) By= 1.764E-04 T

Key: T0
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.504 T magnetic field is directed 70&deg; away from the wire?


 * -a) 2.348E+00 N/m
 * -b) 2.583E+00 N/m
 * +c) 2.842E+00 N/m
 * -d) 3.126E+00 N/m
 * -e) 3.438E+00 N/m

2) The silver ribbon shown are a=4.81 cm, b=3.96 cm, and c= 1.3 cm. The current carries a current of 274 A and it lies in a uniform magnetic field of 3.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 7.202E-06 V
 * -b) 7.922E-06 V
 * -c) 8.714E-06 V
 * -d) 9.586E-06 V
 * -e) 1.054E-05 V

3) Three wires sit at the corners of a square of length 0.686 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.28 A, 1.27 A, 1.61 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 5.409E-05 T
 * -b) Bx= 5.950E-05 T
 * +c) Bx= 6.545E-05 T
 * -d) Bx= 7.200E-05 T
 * -e) Bx= 7.920E-05 T

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.547 m and $$B_{max}=\,$$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.158 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 1.751E+05 A
 * -b) 1.927E+05 A
 * -c) 2.119E+05 A
 * +d) 2.331E+05 A
 * -e) 2.564E+05 A

5) A long solenoid has a radius of 0.786 m and 60 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$21 s&minus;1.What is the induced electric fied at a distance 1.98 m from the axis at time t=0.049 s ?


 * -a) 1.605E-04 V/m
 * +b) 1.766E-04 V/m
 * -c) 1.942E-04 V/m
 * -d) 2.136E-04 V/m
 * -e) 2.350E-04 V/m

6) A washer has an inner diameter of 2.42 cm and an outer diamter of 4.53 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.47mm$$, and $$n=2.8$$. What is the volume of the washer?


 * -a) 8.932E-01 cm3
 * -b) 9.825E-01 cm3
 * -c) 1.081E+00 cm3
 * +d) 1.189E+00 cm3
 * -e) 1.308E+00 cm3

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=3 V. The resistance, inductance, and capacitance are R =0.14 &Omega;, L= 5.20E-03H, and C=2.90E-06 F, respectively.


 * -a) Q = 2.287E+02
 * -b) Q = 2.630E+02
 * +c) Q = 3.025E+02
 * -d) Q = 3.478E+02
 * -e) Q = 4.000E+02

8) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.392E-06 N/m2
 * -b) 2.631E-06 N/m2
 * -c) 2.894E-06 N/m2
 * -d) 3.184E-06 N/m2
 * +e) 3.502E-06 N/m2

9) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * -a) 1.753E+02 km
 * -b) 1.928E+02 km
 * +c) 2.121E+02 km
 * -d) 2.333E+02 km
 * -e) 2.567E+02 km

10) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * -a) 4.55E+04 N/C (or V/m)
 * -b) 5.52E+04 N/C (or V/m)
 * +c) 6.68E+04 N/C (or V/m)
 * -d) 8.10E+04 N/C (or V/m)
 * -e) 9.81E+04 N/C (or V/m)

11) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 61 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * +a) 7.67E-11 Vs2m-1
 * -b) 9.29E-11 Vs2m-1
 * -c) 1.13E-10 Vs2m-1
 * -d) 1.36E-10 Vs2m-1
 * -e) 1.65E-10 Vs2m-1

Key: T1
1) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 89 &mu;C.  What is the electric field between the plates?


 * -a) 1.93E+05 N/C (or V/m)
 * +b) 2.34E+05 N/C (or V/m)
 * -c) 2.83E+05 N/C (or V/m)
 * -d) 3.43E+05 N/C (or V/m)
 * -e) 4.16E+05 N/C (or V/m)

2) The silver ribbon shown are a=3.6 cm, b=2.68 cm, and c= 1.13 cm. The current carries a current of 97 A and it lies in a uniform magnetic field of 1.89 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.560E-06 V
 * +b) 1.716E-06 V
 * -c) 1.888E-06 V
 * -d) 2.077E-06 V
 * -e) 2.284E-06 V

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * -a) Q = 1.300E+02
 * -b) Q = 1.495E+02
 * +c) Q = 1.719E+02
 * -d) Q = 1.976E+02
 * -e) Q = 2.273E+02

4) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23&deg; away from the wire?


 * +a) 5.205E-01 N/m
 * -b) 5.725E-01 N/m
 * -c) 6.297E-01 N/m
 * -d) 6.927E-01 N/m
 * -e) 7.620E-01 N/m

5) What is the radiation pressure on an object that is 2.40E+11 m away from the sun and has cross-sectional area of 0.052 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.392E-06 N/m2
 * -b) 2.631E-06 N/m2
 * -c) 2.894E-06 N/m2
 * -d) 3.184E-06 N/m2
 * +e) 3.502E-06 N/m2

6) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.18 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.42mm$$, and $$n=2.62$$. What is the volume of the washer?


 * +a) 1.351E+00 cm3
 * -b) 1.486E+00 cm3
 * -c) 1.635E+00 cm3
 * -d) 1.798E+00 cm3
 * -e) 1.978E+00 cm3

7) Three wires sit at the corners of a square of length 0.467 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.29 A, 1.77 A, 1.48 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 8.371E-05 T
 * -b) Bx= 9.208E-05 T
 * +c) Bx= 1.013E-04 T
 * -d) Bx= 1.114E-04 T
 * -e) Bx= 1.226E-04 T

8) A 55 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 93 kW?


 * -a) 1.270E+02 km
 * -b) 1.397E+02 km
 * -c) 1.537E+02 km
 * +d) 1.690E+02 km
 * -e) 1.859E+02 km

9) A circlular capactitor of radius 4.3 m has a gap of 12 mm, and a charge of 85 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 7.28E-11 Vs2m-1
 * -b) 8.82E-11 Vs2m-1
 * +c) 1.07E-10 Vs2m-1
 * -d) 1.29E-10 Vs2m-1
 * -e) 1.57E-10 Vs2m-1

10) A long solenoid has a radius of 0.887 m and 43 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$28 s&minus;1.What is the induced electric fied at a distance 2.66 m from the axis at time t=0.0332 s ?


 * +a) 6.182E-04 V/m
 * -b) 6.801E-04 V/m
 * -c) 7.481E-04 V/m
 * -d) 8.229E-04 V/m
 * -e) 9.052E-04 V/m

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.407 m and $$B_{max}=\,$$ 0.605 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.196 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.583E+05 A
 * -b) 3.941E+05 A
 * +c) 4.335E+05 A
 * -d) 4.769E+05 A
 * -e) 5.246E+05 A

Key: T2
1) A long rigid wire carries a 6 A current. What is the magnetic force per unit length on the wire if a 0.222 T magnetic field is directed 23&deg; away from the wire?


 * +a) 5.205E-01 N/m
 * -b) 5.725E-01 N/m
 * -c) 6.297E-01 N/m
 * -d) 6.927E-01 N/m
 * -e) 7.620E-01 N/m

2) A circlular capactitor of radius 4.3 m has a gap of 11 mm, and a charge of 66 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 6.85E-11 Vs2m-1
 * +b) 8.29E-11 Vs2m-1
 * -c) 1.00E-10 Vs2m-1
 * -d) 1.22E-10 Vs2m-1
 * -e) 1.47E-10 Vs2m-1

3) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 &Omega;, L= 4.20E-03H, and C=3.70E-06 F, respectively.


 * -a) Q = 7.135E+01
 * -b) Q = 8.205E+01
 * -c) Q = 9.435E+01
 * -d) Q = 1.085E+02
 * +e) Q = 1.248E+02

4) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.517E+02 km
 * +b) 1.669E+02 km
 * -c) 1.835E+02 km
 * -d) 2.019E+02 km
 * -e) 2.221E+02 km

5) A long solenoid has a radius of 0.716 m and 96 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$23 s&minus;1.What is the induced electric fied at a distance 2.67 m from the axis at time t=0.0226 s ?


 * +a) 1.426E-03 V/m
 * -b) 1.568E-03 V/m
 * -c) 1.725E-03 V/m
 * -d) 1.897E-03 V/m
 * -e) 2.087E-03 V/m

6) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.547 m and $$B_{max}=\,$$ 0.597 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.158 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 1.751E+05 A
 * -b) 1.927E+05 A
 * -c) 2.119E+05 A
 * +d) 2.331E+05 A
 * -e) 2.564E+05 A

7) A washer has an inner diameter of 2.12 cm and an outer diamter of 4.47 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.7mm$$, and $$n=2.72$$. What is the volume of the washer?


 * -a) 1.228E+00 cm3
 * -b) 1.351E+00 cm3
 * -c) 1.486E+00 cm3
 * +d) 1.634E+00 cm3
 * -e) 1.798E+00 cm3

8) The silver ribbon shown are a=3.47 cm, b=2.98 cm, and c= 0.681 cm. The current carries a current of 289 A and it lies in a uniform magnetic field of 3.37 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.375E-05 V
 * +b) 1.513E-05 V
 * -c) 1.664E-05 V
 * -d) 1.831E-05 V
 * -e) 2.014E-05 V

9) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 &mu;C.  What is the electric field between the plates?


 * +a) 1.92E+05 N/C (or V/m)
 * -b) 2.32E+05 N/C (or V/m)
 * -c) 2.81E+05 N/C (or V/m)
 * -d) 3.41E+05 N/C (or V/m)
 * -e) 4.13E+05 N/C (or V/m)

10) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.016 m2? The average power output of the Sun is 3.80E+26 W.


 * +a) 6.669E-07 N/m2
 * -b) 7.336E-07 N/m2
 * -c) 8.069E-07 N/m2
 * -d) 8.876E-07 N/m2
 * -e) 9.764E-07 N/m2

11) Three wires sit at the corners of a square of length 0.687 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.38 A, 1.87 A, 2.03 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 7.134E-05 T
 * -b) Bx= 7.847E-05 T
 * +c) Bx= 8.632E-05 T
 * -d) Bx= 9.495E-05 T
 * -e) Bx= 1.044E-04 T

Key: U0
1) A long rigid wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.394 T magnetic field is directed 14&deg; away from the wire?


 * -a) 6.302E-01 N/m
 * -b) 6.932E-01 N/m
 * +c) 7.625E-01 N/m
 * -d) 8.388E-01 N/m
 * -e) 9.227E-01 N/m

2) A circular current loop of radius 1.29 cm carries a current of 1.75 mA. What is the magnitude of the torque if the dipole is oriented at 24 &deg; to a uniform magnetic fied of 0.156 T?


 * +a) 5.805E-08 N m
 * -b) 6.386E-08 N m
 * -c) 7.024E-08 N m
 * -d) 7.727E-08 N m
 * -e) 8.499E-08 N m

3) A wire carries a current of 293 A in a circular arc with radius 1.75 cm swept through 71 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * -a) 4.652E+00 Tesla
 * -b) 5.117E+00 Tesla
 * -c) 5.629E+00 Tesla
 * -d) 6.192E+00 Tesla
 * +e) 6.811E+00 Tesla

4) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.58 kA, I2=1.11 kA, and I3=2.47 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.092E-03 T-m
 * -b) 4.501E-03 T-m
 * +c) 4.951E-03 T-m
 * -d) 5.446E-03 T-m
 * -e) 5.991E-03 T-m

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.11 T and $$\omega=$$1.150E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.171 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 2.887E+03 V
 * -b) 3.176E+03 V
 * -c) 3.493E+03 V
 * +d) 3.843E+03 V
 * -e) 4.227E+03 V

6) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.67mm$$, and $$n=2.56$$. What is the volume of the washer?


 * +a) 1.570E+00 cm3
 * -b) 1.727E+00 cm3
 * -c) 1.900E+00 cm3
 * -d) 2.090E+00 cm3
 * -e) 2.299E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 5.50E+04 Hz and an amplitude of 2 V. If R =8 &Omega;, L= 9.60E-03H, and C=8.30E-06 F, what is the rms power transferred to the resistor?


 * -a) 4.347E-05 Watts
 * -b) 4.782E-05 Watts
 * -c) 5.260E-05 Watts
 * +d) 5.786E-05 Watts
 * -e) 6.364E-05 Watts

8) A 47 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 90 kW?


 * +a) 1.799E+02 km
 * -b) 1.979E+02 km
 * -c) 2.177E+02 km
 * -d) 2.394E+02 km
 * -e) 2.634E+02 km

9) What is the radiation pressure on an object that is 5.50E+11 m away from the sun and has cross-sectional area of 0.022 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 4.555E-07 N/m2
 * -b) 5.010E-07 N/m2
 * -c) 5.511E-07 N/m2
 * -d) 6.063E-07 N/m2
 * +e) 6.669E-07 N/m2

10) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 84 &mu;C.  What is the electric field between the plates?


 * -a) 1.37E+05 N/C (or V/m)
 * -b) 1.66E+05 N/C (or V/m)
 * -c) 2.01E+05 N/C (or V/m)
 * -d) 2.43E+05 N/C (or V/m)
 * +e) 2.95E+05 N/C (or V/m)

11) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.30E-09 Tesla
 * -b) 4.15E-09 Tesla
 * -c) 5.23E-09 Tesla
 * +d) 6.58E-09 Tesla
 * -e) 8.29E-09 Tesla

Key: U1
1) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * -a) 4.55E+04 N/C (or V/m)
 * -b) 5.52E+04 N/C (or V/m)
 * +c) 6.68E+04 N/C (or V/m)
 * -d) 8.10E+04 N/C (or V/m)
 * -e) 9.81E+04 N/C (or V/m)

2) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.46 kA, I2=2.14 kA, and I3=4.44 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.943E-03 T-m
 * -b) 5.438E-03 T-m
 * +c) 5.982E-03 T-m
 * -d) 6.580E-03 T-m
 * -e) 7.238E-03 T-m

3) A wire carries a current of 269 A in a circular arc with radius 2.35 cm swept through 36 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * -a) 1.613E+00 Tesla
 * -b) 1.774E+00 Tesla
 * -c) 1.951E+00 Tesla
 * -d) 2.146E+00 Tesla
 * +e) 2.361E+00 Tesla

4) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * -a) 2.094E+02 km
 * +b) 2.304E+02 km
 * -c) 2.534E+02 km
 * -d) 2.788E+02 km
 * -e) 3.066E+02 km

5) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.28mm$$, and $$n=2.4$$. What is the volume of the washer?


 * +a) 1.097E+00 cm3
 * -b) 1.207E+00 cm3
 * -c) 1.328E+00 cm3
 * -d) 1.460E+00 cm3
 * -e) 1.606E+00 cm3

6) The output of an ac generator connected to an RLC series combination has a frequency of 5.00E+04 Hz and an amplitude of 5 V. If R =6 &Omega;, L= 2.50E-03H, and C=5.20E-06 F, what is the rms power transferred to the resistor?


 * +a) 5.097E-03 Watts
 * -b) 5.607E-03 Watts
 * -c) 6.167E-03 Watts
 * -d) 6.784E-03 Watts
 * -e) 7.463E-03 Watts

7) A circular current loop of radius 1.17 cm carries a current of 3.68 mA. What is the magnitude of the torque if the dipole is oriented at 55 &deg; to a uniform magnetic fied of 0.179 T?


 * -a) 1.585E-07 N m
 * -b) 1.743E-07 N m
 * -c) 1.918E-07 N m
 * -d) 2.110E-07 N m
 * +e) 2.321E-07 N m

8) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.88 T magnetic field is directed 47&deg; away from the wire?


 * -a) 4.096E+00 N/m
 * +b) 4.505E+00 N/m
 * -c) 4.956E+00 N/m
 * -d) 5.451E+00 N/m
 * -e) 5.996E+00 N/m

9) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$2.25 T and $$\omega=$$8.280E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.227 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * +a) 2.657E+04 V
 * -b) 2.923E+04 V
 * -c) 3.215E+04 V
 * -d) 3.537E+04 V
 * -e) 3.890E+04 V

10) A circlular capactitor of radius 4.3 m has a gap of 15 mm, and a charge of 21 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 1.62E-09 Tesla
 * -b) 2.04E-09 Tesla
 * -c) 2.57E-09 Tesla
 * -d) 3.23E-09 Tesla
 * +e) 4.07E-09 Tesla

11) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.315E-07 N/m2
 * +b) 2.547E-07 N/m2
 * -c) 2.801E-07 N/m2
 * -d) 3.082E-07 N/m2
 * -e) 3.390E-07 N/m2

Key: U2
1) The output of an ac generator connected to an RLC series combination has a frequency of 3.50E+04 Hz and an amplitude of 8 V. If R =7 &Omega;, L= 9.40E-03H, and C=8.50E-06 F, what is the rms power transferred to the resistor?


 * +a) 2.111E-03 Watts
 * -b) 2.323E-03 Watts
 * -c) 2.555E-03 Watts
 * -d) 2.810E-03 Watts
 * -e) 3.091E-03 Watts

2) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 6.62E-10 Tesla
 * -b) 8.33E-10 Tesla
 * -c) 1.05E-09 Tesla
 * -d) 1.32E-09 Tesla
 * +e) 1.66E-09 Tesla

3) A 58 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * -a) 1.418E+02 km
 * +b) 1.560E+02 km
 * -c) 1.716E+02 km
 * -d) 1.887E+02 km
 * -e) 2.076E+02 km

4) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.75 T and $$\omega=$$9.800E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.22 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 4.198E+04 V
 * -b) 4.618E+04 V
 * +c) 5.080E+04 V
 * -d) 5.588E+04 V
 * -e) 6.147E+04 V

5) What is the radiation pressure on an object that is 8.90E+11 m away from the sun and has cross-sectional area of 0.013 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 2.315E-07 N/m2
 * +b) 2.547E-07 N/m2
 * -c) 2.801E-07 N/m2
 * -d) 3.082E-07 N/m2
 * -e) 3.390E-07 N/m2

6) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.31 kA, I2=1.16 kA, and I3=2.13 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 2.815E-03 T-m
 * -b) 3.097E-03 T-m
 * -c) 3.406E-03 T-m
 * -d) 3.747E-03 T-m
 * +e) 4.122E-03 T-m

7) A washer has an inner diameter of 2.16 cm and an outer diamter of 4.82 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.22mm$$, and $$n=2.8$$. What is the volume of the washer?


 * -a) 1.342E+00 cm3
 * +b) 1.477E+00 cm3
 * -c) 1.624E+00 cm3
 * -d) 1.787E+00 cm3
 * -e) 1.965E+00 cm3

8) A wire carries a current of 297 A in a circular arc with radius 2.31 cm swept through 75 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?


 * -a) 3.774E+00 Tesla
 * -b) 4.151E+00 Tesla
 * -c) 4.566E+00 Tesla
 * -d) 5.023E+00 Tesla
 * +e) 5.525E+00 Tesla

9) A circlular capactitor of radius 3.6 m has a gap of 8 mm, and a charge of 53 &mu;C.  What is the electric field between the plates?


 * -a) 6.82E+04 N/C (or V/m)
 * -b) 8.27E+04 N/C (or V/m)
 * -c) 1.00E+05 N/C (or V/m)
 * -d) 1.21E+05 N/C (or V/m)
 * +e) 1.47E+05 N/C (or V/m)

10) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.405 T magnetic field is directed 48&deg; away from the wire?


 * -a) 1.131E+00 N/m
 * -b) 1.244E+00 N/m
 * -c) 1.368E+00 N/m
 * +d) 1.505E+00 N/m
 * -e) 1.655E+00 N/m

11) A circular current loop of radius 1.67 cm carries a current of 3.81 mA. What is the magnitude of the torque if the dipole is oriented at 40 &deg; to a uniform magnetic fied of 0.884 T?


 * -a) 1.568E-06 N m
 * -b) 1.724E-06 N m
 * +c) 1.897E-06 N m
 * -d) 2.087E-06 N m
 * -e) 2.295E-06 N m

Key: V0
1) A long rigid wire carries a 5 A current. What is the magnetic force per unit length on the wire if a 0.83 T magnetic field is directed 22&deg; away from the wire?


 * -a) 1.062E+00 N/m
 * -b) 1.168E+00 N/m
 * -c) 1.285E+00 N/m
 * -d) 1.413E+00 N/m
 * +e) 1.555E+00 N/m

2) The silver ribbon shown are a=3.84 cm, b=3.45 cm, and c= 1.38 cm. The current carries a current of 92 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 7.153E-07 V
 * -b) 7.869E-07 V
 * -c) 8.655E-07 V
 * +d) 9.521E-07 V
 * -e) 1.047E-06 V

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.46 kA, I2=2.14 kA, and I3=4.44 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.943E-03 T-m
 * -b) 5.438E-03 T-m
 * +c) 5.982E-03 T-m
 * -d) 6.580E-03 T-m
 * -e) 7.238E-03 T-m

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.9 mm from the center of a wire of radius 4 mm if the current is 1A?


 * -a) 1.784E-05 T
 * -b) 1.963E-05 T
 * -c) 2.159E-05 T
 * +d) 2.375E-05 T
 * -e) 2.613E-05 T

5) A long solenoid has a radius of 0.749 m and 62 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$25 s&minus;1.What is the induced electric fied at a distance 0.139 m from the axis at time t=0.071 s ?


 * +a) 2.065E-04 V/m
 * -b) 2.271E-04 V/m
 * -c) 2.499E-04 V/m
 * -d) 2.748E-04 V/m
 * -e) 3.023E-04 V/m

6) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * -a) 1.118E+00 cm3
 * +b) 1.229E+00 cm3
 * -c) 1.352E+00 cm3
 * -d) 1.487E+00 cm3
 * -e) 1.636E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 830 Hz and an amplitude of 0.73 V;. If R =8 &Omega;, L= 2.80E-03H, and C=5.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 8.759E-01 &rad;
 * -b) 9.635E-01 &rad;
 * +c) 1.060E+00 &rad;
 * -d) 1.166E+00 &rad;
 * -e) 1.282E+00 &rad;

8) A 42 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 98 kW?


 * -a) 1.641E+02 km
 * -b) 1.805E+02 km
 * +c) 1.986E+02 km
 * -d) 2.184E+02 km
 * -e) 2.403E+02 km

9) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=2.70E+03 m2 and separation d=6.30E-03 m is connected via a swith to a 4 &Omega; resistor and a battery of voltage V0=7 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-05?


 * +a) 6.252E+00 V
 * -b) 6.878E+00 V
 * -c) 7.565E+00 V
 * -d) 8.322E+00 V
 * -e) 9.154E+00 V

10) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * -a) 1.16E-04 s
 * -b) 1.41E-04 s
 * -c) 1.71E-04 s
 * -d) 2.07E-04 s
 * +e) 2.50E-04 s

11) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 8.75E-12 Vs2m-1
 * -b) 1.06E-11 Vs2m-1
 * -c) 1.28E-11 Vs2m-1
 * -d) 1.56E-11 Vs2m-1
 * +e) 1.88E-11 Vs2m-1

Key: V1
1) A long solenoid has a radius of 0.732 m and 55 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9 A and $$\alpha=$$25 s&minus;1.What is the induced electric fied at a distance 0.203 m from the axis at time t=0.0448 s ?


 * +a) 5.150E-04 V/m
 * -b) 5.665E-04 V/m
 * -c) 6.232E-04 V/m
 * -d) 6.855E-04 V/m
 * -e) 7.540E-04 V/m

2) A circlular capactitor of radius 4.2 m has a gap of 18 mm, and a charge of 97 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * +a) 1.91E-04 s
 * -b) 2.31E-04 s
 * -c) 2.80E-04 s
 * -d) 3.39E-04 s
 * -e) 4.11E-04 s

3) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.31 kA, I2=1.16 kA, and I3=2.13 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 2.815E-03 T-m
 * -b) 3.097E-03 T-m
 * -c) 3.406E-03 T-m
 * -d) 3.747E-03 T-m
 * +e) 4.122E-03 T-m

4) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.893 T magnetic field is directed 66&deg; away from the wire?


 * -a) 2.697E+00 N/m
 * -b) 2.967E+00 N/m
 * +c) 3.263E+00 N/m
 * -d) 3.590E+00 N/m
 * -e) 3.948E+00 N/m

5) A 59 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.003E+02 km
 * -b) 1.103E+02 km
 * -c) 1.213E+02 km
 * +d) 1.335E+02 km
 * -e) 1.468E+02 km

6) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.51 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.208E-05 T
 * -b) 1.329E-05 T
 * -c) 1.462E-05 T
 * -d) 1.608E-05 T
 * -e) 1.769E-05 T

7) The output of an ac generator connected to an RLC series combination has a frequency of 890 Hz and an amplitude of 0.58 V;. If R =9 &Omega;, L= 2.90E-03H, and C=8.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 7.952E-01 &rad;
 * -b) 8.747E-01 &rad;
 * -c) 9.622E-01 &rad;
 * +d) 1.058E+00 &rad;
 * -e) 1.164E+00 &rad;

8) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.7mm$$, and $$n=2.76$$. What is the volume of the washer?


 * -a) 1.038E+00 cm3
 * -b) 1.142E+00 cm3
 * +c) 1.256E+00 cm3
 * -d) 1.381E+00 cm3
 * -e) 1.520E+00 cm3

9) A parallel plate capacitor with a capicatnce C=8.90E-06 F whose plates have an area A=6.90E+03 m2 and separation d=6.90E-03 m is connected via a swith to a 89 &Omega; resistor and a battery of voltage V0=89 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=3.40E-03?


 * -a) 6.595E+01 V
 * -b) 7.255E+01 V
 * -c) 7.980E+01 V
 * +d) 8.778E+01 V
 * -e) 9.656E+01 V

10) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 2.05E-11 Vs2m-1
 * -b) 2.48E-11 Vs2m-1
 * -c) 3.01E-11 Vs2m-1
 * +d) 3.64E-11 Vs2m-1
 * -e) 4.42E-11 Vs2m-1

11) The silver ribbon shown are a=3.74 cm, b=2.68 cm, and c= 0.415 cm. The current carries a current of 228 A and it lies in a uniform magnetic field of 1.49 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 8.660E-06 V
 * -b) 9.526E-06 V
 * -c) 1.048E-05 V
 * -d) 1.153E-05 V
 * -e) 1.268E-05 V

Key: V2
1) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.5 kA, I2=1.28 kA, and I3=3.4 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 4.362E-03 T-m
 * -b) 4.798E-03 T-m
 * -c) 5.278E-03 T-m
 * +d) 5.806E-03 T-m
 * -e) 6.386E-03 T-m

2) A circlular capactitor of radius 3.2 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * +a) 2.49E-04 s
 * -b) 3.02E-04 s
 * -c) 3.66E-04 s
 * -d) 4.43E-04 s
 * -e) 5.37E-04 s

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.944E-05 T
 * -b) 2.138E-05 T
 * -c) 2.352E-05 T
 * -d) 2.587E-05 T
 * -e) 2.846E-05 T

4) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * -a) 1.753E+02 km
 * -b) 1.928E+02 km
 * +c) 2.121E+02 km
 * -d) 2.333E+02 km
 * -e) 2.567E+02 km

5) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.080E-06 V
 * -b) 1.188E-06 V
 * -c) 1.306E-06 V
 * -d) 1.437E-06 V
 * +e) 1.581E-06 V

6) A parallel plate capacitor with a capicatnce C=8.30E-06 F whose plates have an area A=7.00E+03 m2 and separation d=7.50E-03 m is connected via a swith to a 51 &Omega; resistor and a battery of voltage V0=81 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=1.20E-03?


 * -a) 5.728E+01 V
 * -b) 6.301E+01 V
 * -c) 6.931E+01 V
 * +d) 7.624E+01 V
 * -e) 8.387E+01 V

7) A washer has an inner diameter of 2.36 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.28mm$$, and $$n=2.4$$. What is the volume of the washer?


 * +a) 1.097E+00 cm3
 * -b) 1.207E+00 cm3
 * -c) 1.328E+00 cm3
 * -d) 1.460E+00 cm3
 * -e) 1.606E+00 cm3

8) A long rigid wire carries a 4 A current. What is the magnetic force per unit length on the wire if a 0.379 T magnetic field is directed 53&deg; away from the wire?


 * -a) 1.001E+00 N/m
 * -b) 1.101E+00 N/m
 * +c) 1.211E+00 N/m
 * -d) 1.332E+00 N/m
 * -e) 1.465E+00 N/m

9) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 2.05E-11 Vs2m-1
 * -b) 2.48E-11 Vs2m-1
 * -c) 3.01E-11 Vs2m-1
 * +d) 3.64E-11 Vs2m-1
 * -e) 4.42E-11 Vs2m-1

10) A long solenoid has a radius of 0.603 m and 51 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2 A and $$\alpha=$$26 s&minus;1.What is the induced electric fied at a distance 0.105 m from the axis at time t=0.0659 s ?


 * -a) 2.154E-05 V/m
 * -b) 2.369E-05 V/m
 * -c) 2.606E-05 V/m
 * -d) 2.867E-05 V/m
 * +e) 3.154E-05 V/m

11) The output of an ac generator connected to an RLC series combination has a frequency of 860 Hz and an amplitude of 0.59 V;. If R =9 &Omega;, L= 8.40E-03H, and C=8.80E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?


 * -a) 1.032E+00 &rad;
 * -b) 1.136E+00 &rad;
 * -c) 1.249E+00 &rad;
 * +d) 1.374E+00 &rad;
 * -e) 1.512E+00 &rad;

Key: W0
1) The silver ribbon shown are a=3.74 cm, b=2.68 cm, and c= 0.415 cm. The current carries a current of 228 A and it lies in a uniform magnetic field of 1.49 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 8.660E-06 V
 * -b) 9.526E-06 V
 * -c) 1.048E-05 V
 * -d) 1.153E-05 V
 * -e) 1.268E-05 V

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.388 m and a magneticfield of 1.19 T. What is their maximum kinetic energy?


 * -a) 8.491E+00 MeV
 * -b) 9.340E+00 MeV
 * +c) 1.027E+01 MeV
 * -d) 1.130E+01 MeV
 * -e) 1.243E+01 MeV

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.86 mm from the center of a wire of radius 3 mm if the current is 1A?


 * -a) 3.416E-05 T
 * -b) 3.758E-05 T
 * +c) 4.133E-05 T
 * -d) 4.547E-05 T
 * -e) 5.001E-05 T

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 22 turns per centimeter and the current applied to the solenoid is 568 mA, the net magnetic field is measured to be 1.29 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 8.205E+02
 * -b) $$\chi \text{ (chi) }=$$ 9.026E+02
 * -c) $$\chi \text{ (chi) }=$$ 9.928E+02
 * -d) $$\chi \text{ (chi) }=$$ 1.092E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.201E+03

5) A cylinder of height 1.19 cm and radius 4.51 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 2.7 cm from point O and moves at a speed of 8.35 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * -a) 3.093E+01 cm3/s
 * -b) 3.403E+01 cm3/s
 * +c) 3.743E+01 cm3/s
 * -d) 4.117E+01 cm3/s
 * -e) 4.529E+01 cm3/s

6) A washer has an inner diameter of 2.6 cm and an outer diamter of 4.17 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.38mm$$, and $$n=2.62$$. What is the volume of the washer?


 * -a) 7.196E-01 cm3
 * -b) 7.916E-01 cm3
 * -c) 8.707E-01 cm3
 * +d) 9.578E-01 cm3
 * -e) 1.054E+00 cm3

7) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.82 V. The resistance, inductance, and capacitance are R =8 &Omega;, L= 6.40E-03H, and C=5.70E-04 F, respectively. What is the amplitude of the current?


 * -a) 7.701E-02 A
 * -b) 8.471E-02 A
 * -c) 9.318E-02 A
 * +d) 1.025E-01 A
 * -e) 1.128E-01 A

8) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=4.20E+03 m2 and separation d=8.00E-03 m is connected via a swith to a 6 &Omega; resistor and a battery of voltage V0=94 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.60E-05?


 * -a) 7.253E+03 V/m
 * -b) 7.978E+03 V/m
 * -c) 8.776E+03 V/m
 * -d) 9.653E+03 V/m
 * +e) 1.062E+04 V/m

9) A 41 kW radio transmitter on Earth sends it signal to a satellite 160 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 85 kW?


 * -a) 2.094E+02 km
 * +b) 2.304E+02 km
 * -c) 2.534E+02 km
 * -d) 2.788E+02 km
 * -e) 3.066E+02 km

10) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.87E-11 Vs2m-1
 * -b) 7.11E-11 Vs2m-1
 * -c) 8.61E-11 Vs2m-1
 * +d) 1.04E-10 Vs2m-1
 * -e) 1.26E-10 Vs2m-1

11) A circlular capactitor of radius 3.5 m has a gap of 14 mm, and a charge of 21 &mu;C.  What is the electric field between the plates?


 * +a) 6.16E+04 N/C (or V/m)
 * -b) 7.47E+04 N/C (or V/m)
 * -c) 9.05E+04 N/C (or V/m)
 * -d) 1.10E+05 N/C (or V/m)
 * -e) 1.33E+05 N/C (or V/m)

Key: W1
1) The silver ribbon shown are a=4.72 cm, b=4.17 cm, and c= 1.53 cm. The current carries a current of 235 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.648E-06 V
 * -b) 1.813E-06 V
 * -c) 1.994E-06 V
 * +d) 2.194E-06 V
 * -e) 2.413E-06 V

2) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 &mu;C.  What is the electric field between the plates?


 * -a) 2.44E+05 N/C (or V/m)
 * +b) 2.95E+05 N/C (or V/m)
 * -c) 3.58E+05 N/C (or V/m)
 * -d) 4.34E+05 N/C (or V/m)
 * -e) 5.25E+05 N/C (or V/m)

3) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * -a) 1.118E+00 cm3
 * +b) 1.229E+00 cm3
 * -c) 1.352E+00 cm3
 * -d) 1.487E+00 cm3
 * -e) 1.636E+00 cm3

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 24 turns per centimeter and the current applied to the solenoid is 242 mA, the net magnetic field is measured to be 1.38 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 1.718E+03
 * +b) $$\chi \text{ (chi) }=$$ 1.890E+03
 * -c) $$\chi \text{ (chi) }=$$ 2.079E+03
 * -d) $$\chi \text{ (chi) }=$$ 2.287E+03
 * -e) $$\chi \text{ (chi) }=$$ 2.515E+03

5) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.44 m and a magneticfield of 1.31 T. What is their maximum kinetic energy?


 * -a) 1.323E+01 MeV
 * -b) 1.456E+01 MeV
 * +c) 1.601E+01 MeV
 * -d) 1.761E+01 MeV
 * -e) 1.937E+01 MeV

6) A 56 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 72 kW?


 * -a) 1.084E+02 km
 * -b) 1.193E+02 km
 * -c) 1.312E+02 km
 * -d) 1.443E+02 km
 * +e) 1.587E+02 km

7) A parallel plate capacitor with a capicatnce C=9.20E-06 F whose plates have an area A=3.60E+03 m2 and separation d=3.50E-03 m is connected via a swith to a 28 &Omega; resistor and a battery of voltage V0=16 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=6.00E-04?


 * -a) 3.751E+03 V/m
 * +b) 4.126E+03 V/m
 * -c) 4.539E+03 V/m
 * -d) 4.993E+03 V/m
 * -e) 5.492E+03 V/m

8) A circlular capactitor of radius 4.3 m has a gap of 19 mm, and a charge of 83 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.87E-11 Vs2m-1
 * -b) 7.11E-11 Vs2m-1
 * -c) 8.61E-11 Vs2m-1
 * +d) 1.04E-10 Vs2m-1
 * -e) 1.26E-10 Vs2m-1

9) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.86 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.488E-05 T
 * -b) 1.637E-05 T
 * -c) 1.800E-05 T
 * -d) 1.981E-05 T
 * -e) 2.179E-05 T

10) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.83 V. The resistance, inductance, and capacitance are R =9 &Omega;, L= 8.50E-03H, and C=7.20E-04 F, respectively. What is the amplitude of the current?


 * -a) 8.384E-02 A
 * +b) 9.222E-02 A
 * -c) 1.014E-01 A
 * -d) 1.116E-01 A
 * -e) 1.227E-01 A

11) A cylinder of height 2.58 cm and radius 9.47 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.62 cm from point O and moves at a speed of 4.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * -a) 1.128E+02 cm3/s
 * -b) 1.241E+02 cm3/s
 * -c) 1.365E+02 cm3/s
 * +d) 1.502E+02 cm3/s
 * -e) 1.652E+02 cm3/s

Key: W2
1) A parallel plate capacitor with a capicatnce C=5.70E-06 F whose plates have an area A=5.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 98 &Omega; resistor and a battery of voltage V0=67 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=1.80E-03?


 * -a) 5.050E+03 V/m
 * -b) 5.555E+03 V/m
 * -c) 6.111E+03 V/m
 * -d) 6.722E+03 V/m
 * +e) 7.394E+03 V/m

2) A 48 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 96 kW?


 * -a) 1.753E+02 km
 * -b) 1.928E+02 km
 * +c) 2.121E+02 km
 * -d) 2.333E+02 km
 * -e) 2.567E+02 km

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 344 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 1.185E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.303E+03
 * +c) $$\chi \text{ (chi) }=$$ 1.433E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.577E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.734E+03

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.43 mm from the center of a wire of radius 5 mm if the current is 1A?


 * +a) 1.944E-05 T
 * -b) 2.138E-05 T
 * -c) 2.352E-05 T
 * -d) 2.587E-05 T
 * -e) 2.846E-05 T

5) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.12 V. The resistance, inductance, and capacitance are R =3 &Omega;, L= 8.80E-03H, and C=6.40E-04 F, respectively. What is the amplitude of the current?


 * -a) 2.732E-02 A
 * -b) 3.005E-02 A
 * -c) 3.306E-02 A
 * -d) 3.636E-02 A
 * +e) 4.000E-02 A

6) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.14mm$$, and $$n=2.86$$. What is the volume of the washer?


 * +a) 1.071E+00 cm3
 * -b) 1.178E+00 cm3
 * -c) 1.296E+00 cm3
 * -d) 1.425E+00 cm3
 * -e) 1.568E+00 cm3

7) A cylinder of height 2.58 cm and radius 9.47 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 3.62 cm from point O and moves at a speed of 4.7 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)


 * -a) 1.128E+02 cm3/s
 * -b) 1.241E+02 cm3/s
 * -c) 1.365E+02 cm3/s
 * +d) 1.502E+02 cm3/s
 * -e) 1.652E+02 cm3/s

8) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 &mu;C.  What is the electric field between the plates?


 * -a) 1.29E+05 N/C (or V/m)
 * +b) 1.56E+05 N/C (or V/m)
 * -c) 1.89E+05 N/C (or V/m)
 * -d) 2.29E+05 N/C (or V/m)
 * -e) 2.77E+05 N/C (or V/m)

9) The silver ribbon shown are a=4.12 cm, b=3.32 cm, and c= 1.46 cm. The current carries a current of 120 A and it lies in a uniform magnetic field of 1.39 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * +a) 1.209E-06 V
 * -b) 1.329E-06 V
 * -c) 1.462E-06 V
 * -d) 1.609E-06 V
 * -e) 1.770E-06 V

10) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.232 m and a magneticfield of 1.1 T. What is their maximum kinetic energy?


 * -a) 2.853E+00 MeV
 * +b) 3.139E+00 MeV
 * -c) 3.453E+00 MeV
 * -d) 3.798E+00 MeV
 * -e) 4.178E+00 MeV

11) A circlular capactitor of radius 4.4 m has a gap of 17 mm, and a charge of 65 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.


 * -a) 5.56E-11 Vs2m-1
 * -b) 6.74E-11 Vs2m-1
 * +c) 8.17E-11 Vs2m-1
 * -d) 9.90E-11 Vs2m-1
 * -e) 1.20E-10 Vs2m-1

Key: X0
1) A circular current loop of radius 2.84 cm carries a current of 3.01 mA. What is the magnitude of the torque if the dipole is oriented at 63 &deg; to a uniform magnetic fied of 0.174 T?


 * -a) 1.075E-06 N m
 * +b) 1.182E-06 N m
 * -c) 1.301E-06 N m
 * -d) 1.431E-06 N m
 * -e) 1.574E-06 N m

2) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 8.55 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.96 i + 1.68 j  + 6.92 k) x 104 m/s?


 * -a) 4.179E-14 N
 * +b) 4.596E-14 N
 * -c) 5.056E-14 N
 * -d) 5.562E-14 N
 * -e) 6.118E-14 N

3) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.259 m and $$B_{max}=\,$$ 0.575 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.191 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.492E+05 A
 * -b) 3.841E+05 A
 * -c) 4.225E+05 A
 * -d) 4.648E+05 A
 * +e) 5.113E+05 A

4) Two parallel wires each carry a 2.12 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.67 cm, 1.25 cm), while the other is located at (4.69 cm, 4.27 cm). What is the force per unit length between the wires?


 * -a) 2.119E-11 N/m
 * -b) 2.331E-11 N/m
 * -c) 2.564E-11 N/m
 * +d) 2.820E-11 N/m
 * -e) 3.102E-11 N/m

5) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$1.89 T and $$\omega=$$1.710E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.476 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 7.262E+03 V
 * -b) 7.988E+03 V
 * -c) 8.787E+03 V
 * +d) 9.666E+03 V
 * -e) 1.063E+04 V

6) A washer has an inner diameter of 2.46 cm and an outer diamter of 4.24 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.32mm$$, and $$n=2.63$$. What is the volume of the washer?


 * -a) 7.499E-01 cm3
 * -b) 8.249E-01 cm3
 * -c) 9.074E-01 cm3
 * -d) 9.982E-01 cm3
 * +e) 1.098E+00 cm3

7) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=6 V. The resistance, inductance, and capacitance are R =0.27 &Omega;, L= 4.20E-03H, and C=3.70E-06 F, respectively.


 * -a) Q = 7.135E+01
 * -b) Q = 8.205E+01
 * -c) Q = 9.435E+01
 * -d) Q = 1.085E+02
 * +e) Q = 1.248E+02

8) A parallel plate capacitor with a capicatnce C=6.90E-06 F whose plates have an area A=5.80E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 78 &Omega; resistor and a battery of voltage V0=70 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=2.50E-03?


 * -a) 5.890E-03 A
 * -b) 6.479E-03 A
 * -c) 7.126E-03 A
 * -d) 7.839E-03 A
 * +e) 8.623E-03 A

9) What is the radiation force on an object that is 3.80E+11 m away from the sun and has cross-sectional area of 0.094 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 8.969E-08 N
 * -b) 9.866E-08 N
 * -c) 1.085E-07 N
 * -d) 1.194E-07 N
 * +e) 1.313E-07 N

10) A circlular capactitor of radius 4.3 m has a gap of 15 mm, and a charge of 21 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 1.62E-09 Tesla
 * -b) 2.04E-09 Tesla
 * -c) 2.57E-09 Tesla
 * -d) 3.23E-09 Tesla
 * +e) 4.07E-09 Tesla

11) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 &mu;C.  What is the electric field between the plates?


 * -a) 1.29E+05 N/C (or V/m)
 * +b) 1.56E+05 N/C (or V/m)
 * -c) 1.89E+05 N/C (or V/m)
 * -d) 2.29E+05 N/C (or V/m)
 * -e) 2.77E+05 N/C (or V/m)

Key: X1
1) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 89 &mu;C.  What is the electric field between the plates?


 * -a) 1.93E+05 N/C (or V/m)
 * +b) 2.34E+05 N/C (or V/m)
 * -c) 2.83E+05 N/C (or V/m)
 * -d) 3.43E+05 N/C (or V/m)
 * -e) 4.16E+05 N/C (or V/m)

2) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.13 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (5.64 i + 1.93 j  + 8.71 k) x 104 m/s?


 * -a) 1.757E-14 N
 * +b) 1.933E-14 N
 * -c) 2.126E-14 N
 * -d) 2.339E-14 N
 * -e) 2.573E-14 N

3) Two parallel wires each carry a 3.38 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.46 cm, 1.76 cm), while the other is located at (5.13 cm, 5.5 cm). What is the force per unit length between the wires?


 * -a) 3.810E-11 N/m
 * -b) 4.191E-11 N/m
 * -c) 4.610E-11 N/m
 * -d) 5.071E-11 N/m
 * +e) 5.578E-11 N/m

4) What is the radiation force on an object that is 1.70E+11 m away from the sun and has cross-sectional area of 0.033 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.904E-07 N
 * -b) 2.094E-07 N
 * +c) 2.303E-07 N
 * -d) 2.534E-07 N
 * -e) 2.787E-07 N

5) A parallel plate capacitor with a capicatnce C=6.90E-06 F whose plates have an area A=5.80E+03 m2 and separation d=7.40E-03 m is connected via a swith to a 26 &Omega; resistor and a battery of voltage V0=9 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=4.70E-04?


 * -a) 1.894E-02 A
 * -b) 2.083E-02 A
 * -c) 2.291E-02 A
 * +d) 2.520E-02 A
 * -e) 2.773E-02 A

6) A circular current loop of radius 1.59 cm carries a current of 1.13 mA. What is the magnitude of the torque if the dipole is oriented at 41 &deg; to a uniform magnetic fied of 0.189 T?


 * +a) 1.113E-07 N m
 * -b) 1.224E-07 N m
 * -c) 1.347E-07 N m
 * -d) 1.481E-07 N m
 * -e) 1.629E-07 N m

7) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.31 T and $$\omega=$$8.360E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.547 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 7.145E+04 V
 * -b) 7.860E+04 V
 * -c) 8.646E+04 V
 * +d) 9.510E+04 V
 * -e) 1.046E+05 V

8) A washer has an inner diameter of 2.38 cm and an outer diamter of 4.83 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.92mm$$, and $$n=2.68$$. What is the volume of the washer?


 * -a) 1.118E+00 cm3
 * +b) 1.229E+00 cm3
 * -c) 1.352E+00 cm3
 * -d) 1.487E+00 cm3
 * -e) 1.636E+00 cm3

9) A circlular capactitor of radius 4.9 m has a gap of 18 mm, and a charge of 45 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 2.82E-09 Tesla
 * -b) 3.54E-09 Tesla
 * -c) 4.46E-09 Tesla
 * -d) 5.62E-09 Tesla
 * +e) 7.07E-09 Tesla

10) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=3 V. The resistance, inductance, and capacitance are R =0.29 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * -a) Q = 1.288E+02
 * +b) Q = 1.482E+02
 * -c) Q = 1.704E+02
 * -d) Q = 1.959E+02
 * -e) Q = 2.253E+02

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.619 m and $$B_{max}=\,$$ 0.215 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.351 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 2.534E+05 A
 * -b) 2.787E+05 A
 * +c) 3.066E+05 A
 * -d) 3.373E+05 A
 * -e) 3.710E+05 A

Key: X2
1) A circular current loop of radius 1.88 cm carries a current of 3.41 mA. What is the magnitude of the torque if the dipole is oriented at 62 &deg; to a uniform magnetic fied of 0.415 T?


 * +a) 1.387E-06 N m
 * -b) 1.526E-06 N m
 * -c) 1.679E-06 N m
 * -d) 1.847E-06 N m
 * -e) 2.031E-06 N m

2) A parallel plate capacitor with a capicatnce C=5.50E-06 F whose plates have an area A=3.00E+03 m2 and separation d=4.90E-03 m is connected via a swith to a 55 &Omega; resistor and a battery of voltage V0=37 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=9.00E-04?


 * -a) 2.580E-02 A
 * -b) 2.838E-02 A
 * -c) 3.121E-02 A
 * +d) 3.433E-02 A
 * -e) 3.777E-02 A

3) A circlular capactitor of radius 3.7 m has a gap of 10 mm, and a charge of 12 &mu;C.  What is the electric field between the plates?


 * -a) 2.15E+04 N/C (or V/m)
 * -b) 2.60E+04 N/C (or V/m)
 * +c) 3.15E+04 N/C (or V/m)
 * -d) 3.82E+04 N/C (or V/m)
 * -e) 4.63E+04 N/C (or V/m)

4) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=4 V. The resistance, inductance, and capacitance are R =0.25 &Omega;, L= 4.80E-03H, and C=2.60E-06 F, respectively.


 * -a) Q = 1.300E+02
 * -b) Q = 1.495E+02
 * +c) Q = 1.719E+02
 * -d) Q = 1.976E+02
 * -e) Q = 2.273E+02

5) Two parallel wires each carry a 9.08 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.17 cm, 1.32 cm), while the other is located at (5.72 cm, 4.47 cm). What is the force per unit length between the wires?


 * -a) 3.882E-10 N/m
 * -b) 4.270E-10 N/m
 * +c) 4.697E-10 N/m
 * -d) 5.167E-10 N/m
 * -e) 5.683E-10 N/m

6) What is the radiation force on an object that is 5.40E+11 m away from the sun and has cross-sectional area of 0.021 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 9.923E-09 N
 * -b) 1.092E-08 N
 * -c) 1.201E-08 N
 * -d) 1.321E-08 N
 * +e) 1.453E-08 N

7) A washer has an inner diameter of 2.37 cm and an outer diamter of 4.84 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.67mm$$, and $$n=2.56$$. What is the volume of the washer?


 * +a) 1.570E+00 cm3
 * -b) 1.727E+00 cm3
 * -c) 1.900E+00 cm3
 * -d) 2.090E+00 cm3
 * -e) 2.299E+00 cm3

8) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$2.34 T and $$\omega=$$2.670E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.646 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.


 * -a) 1.905E+04 V
 * -b) 2.096E+04 V
 * -c) 2.305E+04 V
 * +d) 2.536E+04 V
 * -e) 2.790E+04 V

9) A circlular capactitor of radius 4.4 m has a gap of 15 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 7.92E-09 Tesla
 * +b) 9.97E-09 Tesla
 * -c) 1.26E-08 Tesla
 * -d) 1.58E-08 Tesla
 * -e) 1.99E-08 Tesla

10) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 9.76 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (6.97 i + 8.52 j  + 9.46 k) x 104 m/s?


 * -a) 2.199E-13 N
 * -b) 2.419E-13 N
 * +c) 2.661E-13 N
 * -d) 2.927E-13 N
 * -e) 3.220E-13 N

11) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.871 m and $$B_{max}=\,$$ 0.427 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.688 m that is centered on the axis with its plane perpendicular to the axis?


 * +a) 1.404E+06 A
 * -b) 1.544E+06 A
 * -c) 1.699E+06 A
 * -d) 1.869E+06 A
 * -e) 2.056E+06 A

Key: Y0
1) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 6.96 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (7.01 i + 5.35 j  + 2.07 k) x 104 m/s?


 * +a) 1.192E-13 N
 * -b) 1.311E-13 N
 * -c) 1.442E-13 N
 * -d) 1.586E-13 N
 * -e) 1.745E-13 N

2) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.118 m and a magneticfield of 1.48 T. What is their maximum kinetic energy?


 * -a) 1.004E+00 MeV
 * -b) 1.104E+00 MeV
 * -c) 1.215E+00 MeV
 * -d) 1.336E+00 MeV
 * +e) 1.470E+00 MeV

3) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 16 turns per centimeter and the current applied to the solenoid is 536 mA, the net magnetic field is measured to be 1.47 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 9.310E+02
 * -b) $$\chi \text{ (chi) }=$$ 1.024E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.126E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.239E+03
 * +e) $$\chi \text{ (chi) }=$$ 1.363E+03

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.52 m and $$B_{max}=\,$$ 0.657 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.295 m that is centered on the axis with its plane perpendicular to the axis?


 * +a) 7.876E+05 A
 * -b) 8.664E+05 A
 * -c) 9.530E+05 A
 * -d) 1.048E+06 A
 * -e) 1.153E+06 A

5) Calculate the motional emf induced along a 14.1 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.910E-05 Tesla magnetic field.


 * -a) 3.688E+03 V
 * -b) 4.057E+03 V
 * -c) 4.463E+03 V
 * -d) 4.909E+03 V
 * +e) 5.400E+03 V

6) A washer has an inner diameter of 2.31 cm and an outer diamter of 4.19 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.14mm$$, and $$n=2.86$$. What is the volume of the washer?


 * +a) 1.071E+00 cm3
 * -b) 1.178E+00 cm3
 * -c) 1.296E+00 cm3
 * -d) 1.425E+00 cm3
 * -e) 1.568E+00 cm3

7) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 6.60E-03H, and C=5.30E-06 F, what is the rms power transferred to the resistor?


 * -a) 2.007E-03 Watts
 * -b) 2.208E-03 Watts
 * -c) 2.429E-03 Watts
 * +d) 2.672E-03 Watts
 * -e) 2.939E-03 Watts

8) A parallel plate capacitor with a capicatnce C=5.60E-06 F whose plates have an area A=2.00E+03 m2 and separation d=3.10E-03 m is connected via a swith to a 68 &Omega; resistor and a battery of voltage V0=73 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=8.50E-04?


 * -a) 1.579E+04 V/m
 * -b) 1.737E+04 V/m
 * -c) 1.911E+04 V/m
 * +d) 2.102E+04 V/m
 * -e) 2.312E+04 V/m

9) What is the radiation force on an object that is 1.60E+11 m away from the sun and has cross-sectional area of 0.081 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 5.275E-07 N
 * -b) 5.803E-07 N
 * +c) 6.383E-07 N
 * -d) 7.021E-07 N
 * -e) 7.723E-07 N

10) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * -a) 1.16E-04 s
 * -b) 1.41E-04 s
 * -c) 1.71E-04 s
 * -d) 2.07E-04 s
 * +e) 2.50E-04 s

11) A circlular capactitor of radius 4.9 m has a gap of 14 mm, and a charge of 56 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 3.18E-09 Tesla
 * -b) 4.00E-09 Tesla
 * -c) 5.04E-09 Tesla
 * -d) 6.34E-09 Tesla
 * +e) 7.99E-09 Tesla

Key: Y1
1) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.23 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (3.84 i + 8.79 j  + 9.05 k) x 104 m/s?


 * -a) 7.509E-14 N
 * -b) 8.259E-14 N
 * +c) 9.085E-14 N
 * -d) 9.994E-14 N
 * -e) 1.099E-13 N

2) A parallel plate capacitor with a capicatnce C=1.40E-06 F whose plates have an area A=980.0 m2 and separation d=6.20E-03 m is connected via a swith to a 8 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.40E-05?


 * -a) 5.154E+03 V/m
 * -b) 5.669E+03 V/m
 * -c) 6.236E+03 V/m
 * -d) 6.860E+03 V/m
 * +e) 7.545E+03 V/m

3) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.


 * -a) 1.279E+04 V
 * -b) 1.407E+04 V
 * +c) 1.547E+04 V
 * -d) 1.702E+04 V
 * -e) 1.872E+04 V

4) The output of an ac generator connected to an RLC series combination has a frequency of 4.00E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 7.00E-03H, and C=6.60E-06 F, what is the rms power transferred to the resistor?


 * -a) 1.146E-03 Watts
 * -b) 1.260E-03 Watts
 * -c) 1.386E-03 Watts
 * -d) 1.525E-03 Watts
 * +e) 1.677E-03 Watts

5) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * +a) 8.32E-09 Tesla
 * -b) 1.05E-08 Tesla
 * -c) 1.32E-08 Tesla
 * -d) 1.66E-08 Tesla
 * -e) 2.09E-08 Tesla

6) A circlular capactitor of radius 4.3 m has a gap of 8 mm, and a charge of 12 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * -a) 3.07E-04 s
 * -b) 3.71E-04 s
 * +c) 4.50E-04 s
 * -d) 5.45E-04 s
 * -e) 6.61E-04 s

7) What is the radiation force on an object that is 9.90E+11 m away from the sun and has cross-sectional area of 0.083 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 1.167E-08 N
 * -b) 1.284E-08 N
 * -c) 1.412E-08 N
 * -d) 1.553E-08 N
 * +e) 1.708E-08 N

8) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.571 m and $$B_{max}=\,$$ 0.331 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.321 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.226E+05 A
 * -b) 3.549E+05 A
 * -c) 3.904E+05 A
 * +d) 4.294E+05 A
 * -e) 4.724E+05 A

9) A washer has an inner diameter of 2.21 cm and an outer diamter of 4.5 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.29mm$$, and $$n=2.62$$. What is the volume of the washer?


 * -a) 1.325E+00 cm3
 * +b) 1.457E+00 cm3
 * -c) 1.603E+00 cm3
 * -d) 1.763E+00 cm3
 * -e) 1.939E+00 cm3

10) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.355 m and a magneticfield of 1.28 T. What is their maximum kinetic energy?


 * -a) 7.476E+00 MeV
 * -b) 8.224E+00 MeV
 * -c) 9.046E+00 MeV
 * +d) 9.951E+00 MeV
 * -e) 1.095E+01 MeV

11) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 26 turns per centimeter and the current applied to the solenoid is 359 mA, the net magnetic field is measured to be 1.32 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.124E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.237E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.360E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.497E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.646E+03

Key: Y2
1) What is the radiation force on an object that is 3.60E+11 m away from the sun and has cross-sectional area of 0.069 m2? The average power output of the Sun is 3.80E+26 W.


 * -a) 7.336E-08 N
 * -b) 8.069E-08 N
 * -c) 8.876E-08 N
 * -d) 9.764E-08 N
 * +e) 1.074E-07 N

2) A washer has an inner diameter of 2.23 cm and an outer diamter of 4.85 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=3.7mm$$, and $$n=2.76$$. What is the volume of the washer?


 * -a) 1.038E+00 cm3
 * -b) 1.142E+00 cm3
 * +c) 1.256E+00 cm3
 * -d) 1.381E+00 cm3
 * -e) 1.520E+00 cm3

3) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.41 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (6.21 i + 5.39 j  + 3.81 k) x 104 m/s?


 * -a) 4.419E-14 N
 * -b) 4.861E-14 N
 * -c) 5.347E-14 N
 * +d) 5.882E-14 N
 * -e) 6.470E-14 N

4) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.432 m and $$B_{max}=\,$$ 0.402 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.275 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 3.277E+05 A
 * -b) 3.604E+05 A
 * -c) 3.965E+05 A
 * -d) 4.361E+05 A
 * +e) 4.797E+05 A

5) The output of an ac generator connected to an RLC series combination has a frequency of 2.30E+04 Hz and an amplitude of 7 V. If R =3 &Omega;, L= 4.10E-03H, and C=8.70E-06 F, what is the rms power transferred to the resistor?


 * -a) 8.369E-03 Watts
 * +b) 9.206E-03 Watts
 * -c) 1.013E-02 Watts
 * -d) 1.114E-02 Watts
 * -e) 1.225E-02 Watts

6) A circlular capactitor of radius 4.6 m has a gap of 18 mm, and a charge of 44 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)


 * -a) 6.64E-09 Tesla
 * +b) 8.36E-09 Tesla
 * -c) 1.05E-08 Tesla
 * -d) 1.32E-08 Tesla
 * -e) 1.67E-08 Tesla

7) Calculate the motional emf induced along a 24.9 km conductor moving at an orbital speed of 7.82 km/s perpendicular to Earth's 5.040E-05 Tesla magnetic field.


 * -a) 8.111E+03 V
 * -b) 8.922E+03 V
 * +c) 9.814E+03 V
 * -d) 1.080E+04 V
 * -e) 1.187E+04 V

8) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.378 m and a magneticfield of 0.835 T. What is their maximum kinetic energy?


 * -a) 4.365E+00 MeV
 * +b) 4.801E+00 MeV
 * -c) 5.281E+00 MeV
 * -d) 5.809E+00 MeV
 * -e) 6.390E+00 MeV

9) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 27 turns per centimeter and the current applied to the solenoid is 280 mA, the net magnetic field is measured to be 1.13 T. What is the magnetic susceptibility for this case?


 * +a) $$\chi \text{ (chi) }=$$ 1.188E+03
 * -b) $$\chi \text{ (chi) }=$$ 1.307E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.438E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.582E+03
 * -e) $$\chi \text{ (chi) }=$$ 1.740E+03

10) A parallel plate capacitor with a capicatnce C=1.60E-06 F whose plates have an area A=890.0 m2 and separation d=4.90E-03 m is connected via a swith to a 80 &Omega; resistor and a battery of voltage V0=44 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=2.90E-04?


 * -a) 6.651E+03 V/m
 * -b) 7.316E+03 V/m
 * +c) 8.048E+03 V/m
 * -d) 8.853E+03 V/m
 * -e) 9.738E+03 V/m

11) A circlular capactitor of radius 4 m has a gap of 16 mm, and a charge of 48 &mu;C.  The capacitor is discharged through a  9 k&Omega; resistor.  What is the decay time?


 * -a) 1.16E-04 s
 * -b) 1.41E-04 s
 * -c) 1.71E-04 s
 * -d) 2.07E-04 s
 * +e) 2.50E-04 s

Key: Z0
1) A 24 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 10 g, and the magnitude of the magnetic field is 0.706 T. What current is required to maintain this balance?


 * -a) 5.258E-01 A
 * +b) 5.784E-01 A
 * -c) 6.362E-01 A
 * -d) 6.998E-01 A
 * -e) 7.698E-01 A

2) The silver ribbon shown are a=3.32 cm, b=2.81 cm, and c= 0.996 cm. The current carries a current of 121 A and it lies in a uniform magnetic field of 1.23 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.080E-06 V
 * -b) 1.188E-06 V
 * -c) 1.306E-06 V
 * -d) 1.437E-06 V
 * +e) 1.581E-06 V

3) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?


 * -a) 1.935E-05 T
 * +b) 2.128E-05 T
 * -c) 2.341E-05 T
 * -d) 2.575E-05 T
 * -e) 2.832E-05 T

4) Two parallel wires each carry a 2.83 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.15 cm, 1.13 cm), while the other is located at (5.14 cm, 4.22 cm). What is the force per unit length between the wires?


 * -a) 2.977E-11 N/m
 * -b) 3.274E-11 N/m
 * -c) 3.602E-11 N/m
 * -d) 3.962E-11 N/m
 * +e) 4.358E-11 N/m

5) Calculate the motional emf induced along a 34.3 km conductor moving at an orbital speed of 7.86 km/s perpendicular to Earth's 4.780E-05 Tesla magnetic field.


 * -a) 8.802E+03 V
 * -b) 9.682E+03 V
 * -c) 1.065E+04 V
 * -d) 1.172E+04 V
 * +e) 1.289E+04 V

6) An induced emf of 4.13V is measured across a coil of 70 closely wound turns while the current throuth it increases uniformly from 0.0 to 2.63A in 0.133s. What is the self-inductance of the coil?


 * -a) 1.726E-01 H
 * -b) 1.899E-01 H
 * +c) 2.089E-01 H
 * -d) 2.297E-01 H
 * -e) 2.527E-01 H

7) The output of an ac generator connected to an RLC series combination has a frequency of 3.40E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 6.60E-03H, and C=5.30E-06 F, what is the rms power transferred to the resistor?


 * -a) 2.007E-03 Watts
 * -b) 2.208E-03 Watts
 * -c) 2.429E-03 Watts
 * +d) 2.672E-03 Watts
 * -e) 2.939E-03 Watts

8) A 55 kW radio transmitter on Earth sends it signal to a satellite 130 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 93 kW?


 * -a) 1.270E+02 km
 * -b) 1.397E+02 km
 * -c) 1.537E+02 km
 * +d) 1.690E+02 km
 * -e) 1.859E+02 km

9) A parallel plate capacitor with a capicatnce C=9.80E-06 F whose plates have an area A=9.60E+03 m2 and separation d=8.70E-03 m is connected via a swith to a 23 &Omega; resistor and a battery of voltage V0=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=7.20E-04?


 * +a) 2.877E+00 V
 * -b) 3.165E+00 V
 * -c) 3.481E+00 V
 * -d) 3.829E+00 V
 * -e) 4.212E+00 V

10) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 45 &mu;C.  What is the electric field between the plates?


 * -a) 6.31E+04 N/C (or V/m)
 * +b) 7.65E+04 N/C (or V/m)
 * -c) 9.26E+04 N/C (or V/m)
 * -d) 1.12E+05 N/C (or V/m)
 * -e) 1.36E+05 N/C (or V/m)

11) A circlular capactitor of radius 4 m has a gap of 14 mm, and a charge of 24 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?


 * -a) 1.84E-04 s
 * +b) 2.23E-04 s
 * -c) 2.70E-04 s
 * -d) 3.27E-04 s
 * -e) 3.96E-04 s

Key: Z1
1) The output of an ac generator connected to an RLC series combination has a frequency of 2.70E+04 Hz and an amplitude of 8 V. If R =4 &Omega;, L= 9.10E-03H, and C=9.60E-06 F, what is the rms power transferred to the resistor?


 * +a) 2.188E-03 Watts
 * -b) 2.407E-03 Watts
 * -c) 2.647E-03 Watts
 * -d) 2.912E-03 Watts
 * -e) 3.203E-03 Watts

2) A 34 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.348 T. What current is required to maintain this balance?


 * +a) 6.626E-01 A
 * -b) 7.289E-01 A
 * -c) 8.018E-01 A
 * -d) 8.819E-01 A
 * -e) 9.701E-01 A

3) A circlular capactitor of radius 4.1 m has a gap of 14 mm, and a charge of 71 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?


 * -a) 1.65E-04 s
 * +b) 2.00E-04 s
 * -c) 2.43E-04 s
 * -d) 2.94E-04 s
 * -e) 3.56E-04 s

4) An induced emf of 3.78V is measured across a coil of 99 closely wound turns while the current throuth it increases uniformly from 0.0 to 6.36A in 0.821s. What is the self-inductance of the coil?


 * -a) 4.033E-01 H
 * -b) 4.436E-01 H
 * +c) 4.880E-01 H
 * -d) 5.367E-01 H
 * -e) 5.904E-01 H

5) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.64 mm from the center of a wire of radius 5 mm if the current is 1A?


 * -a) 1.920E-05 T
 * +b) 2.112E-05 T
 * -c) 2.323E-05 T
 * -d) 2.556E-05 T
 * -e) 2.811E-05 T

6) Calculate the motional emf induced along a 11.9 km conductor moving at an orbital speed of 7.8 km/s perpendicular to Earth's 4.870E-05 Tesla magnetic field.


 * -a) 3.736E+03 V
 * -b) 4.109E+03 V
 * +c) 4.520E+03 V
 * -d) 4.972E+03 V
 * -e) 5.470E+03 V

7) A 59 kW radio transmitter on Earth sends it signal to a satellite 150 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?


 * -a) 1.517E+02 km
 * +b) 1.669E+02 km
 * -c) 1.835E+02 km
 * -d) 2.019E+02 km
 * -e) 2.221E+02 km

8) A circlular capactitor of radius 4.4 m has a gap of 18 mm, and a charge of 36 &mu;C.  What is the electric field between the plates?


 * -a) 4.55E+04 N/C (or V/m)
 * -b) 5.52E+04 N/C (or V/m)
 * +c) 6.68E+04 N/C (or V/m)
 * -d) 8.10E+04 N/C (or V/m)
 * -e) 9.81E+04 N/C (or V/m)

9) Two parallel wires each carry a 6.26 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.4 cm, 1.42 cm), while the other is located at (5.56 cm, 4.99 cm). What is the force per unit length between the wires?


 * -a) 1.283E-10 N/m
 * -b) 1.411E-10 N/m
 * -c) 1.552E-10 N/m
 * -d) 1.708E-10 N/m
 * +e) 1.878E-10 N/m

10) The silver ribbon shown are a=3.84 cm, b=3.45 cm, and c= 1.38 cm. The current carries a current of 92 A and it lies in a uniform magnetic field of 1.35 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 7.153E-07 V
 * -b) 7.869E-07 V
 * -c) 8.655E-07 V
 * +d) 9.521E-07 V
 * -e) 1.047E-06 V

11) A parallel plate capacitor with a capicatnce C=6.50E-06 F whose plates have an area A=4.50E+03 m2 and separation d=6.10E-03 m is connected via a swith to a 4 &Omega; resistor and a battery of voltage V0=3 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.70E-05?


 * -a) 1.456E+00 V
 * -b) 1.602E+00 V
 * -c) 1.762E+00 V
 * +d) 1.938E+00 V
 * -e) 2.132E+00 V

Key: Z2
1) A parallel plate capacitor with a capicatnce C=4.70E-06 F whose plates have an area A=1.70E+03 m2 and separation d=3.20E-03 m is connected via a swith to a 61 &Omega; resistor and a battery of voltage V0=53 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=8.40E-04?


 * +a) 5.017E+01 V
 * -b) 5.519E+01 V
 * -c) 6.071E+01 V
 * -d) 6.678E+01 V
 * -e) 7.345E+01 V

2) The output of an ac generator connected to an RLC series combination has a frequency of 3.50E+04 Hz and an amplitude of 8 V. If R =7 &Omega;, L= 9.40E-03H, and C=8.50E-06 F, what is the rms power transferred to the resistor?


 * +a) 2.111E-03 Watts
 * -b) 2.323E-03 Watts
 * -c) 2.555E-03 Watts
 * -d) 2.810E-03 Watts
 * -e) 3.091E-03 Watts

3) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 45 &mu;C.  What is the electric field between the plates?


 * -a) 6.31E+04 N/C (or V/m)
 * +b) 7.65E+04 N/C (or V/m)
 * -c) 9.26E+04 N/C (or V/m)
 * -d) 1.12E+05 N/C (or V/m)
 * -e) 1.36E+05 N/C (or V/m)

4) A 46 kW radio transmitter on Earth sends it signal to a satellite 120 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 78 kW?


 * +a) 1.563E+02 km
 * -b) 1.719E+02 km
 * -c) 1.891E+02 km
 * -d) 2.080E+02 km
 * -e) 2.288E+02 km

5) A circlular capactitor of radius 3.1 m has a gap of 11 mm, and a charge of 76 &mu;C.  The capacitor is discharged through a  8 k&Omega; resistor.  What is the decay time?


 * +a) 1.94E-04 s
 * -b) 2.36E-04 s
 * -c) 2.85E-04 s
 * -d) 3.46E-04 s
 * -e) 4.19E-04 s

6) Calculate the motional emf induced along a 42.1 km conductor moving at an orbital speed of 7.77 km/s perpendicular to Earth's 4.730E-05 Tesla magnetic field.


 * -a) 1.279E+04 V
 * -b) 1.407E+04 V
 * +c) 1.547E+04 V
 * -d) 1.702E+04 V
 * -e) 1.872E+04 V

7) Two parallel wires each carry a 7.48 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.13 cm, 0.955 cm), while the other is located at (5.37 cm, 5.48 cm). What is the force per unit length between the wires?


 * -a) 2.015E-10 N/m
 * +b) 2.216E-10 N/m
 * -c) 2.438E-10 N/m
 * -d) 2.682E-10 N/m
 * -e) 2.950E-10 N/m

8) The silver ribbon shown are a=3.6 cm, b=2.68 cm, and c= 1.13 cm. The current carries a current of 97 A and it lies in a uniform magnetic field of 1.89 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.560E-06 V
 * +b) 1.716E-06 V
 * -c) 1.888E-06 V
 * -d) 2.077E-06 V
 * -e) 2.284E-06 V

9) An induced emf of 6.78V is measured across a coil of 58 closely wound turns while the current throuth it increases uniformly from 0.0 to 3.98A in 0.726s. What is the self-inductance of the coil?


 * -a) 1.022E+00 H
 * -b) 1.124E+00 H
 * +c) 1.237E+00 H
 * -d) 1.360E+00 H
 * -e) 1.496E+00 H

10) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 2.66 mm from the center of a wire of radius 5 mm if the current is 1A?


 * -a) 1.935E-05 T
 * +b) 2.128E-05 T
 * -c) 2.341E-05 T
 * -d) 2.575E-05 T
 * -e) 2.832E-05 T

11) A 44 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 7 g, and the magnitude of the magnetic field is 0.784 T. What current is required to maintain this balance?


 * -a) 1.644E-01 A
 * -b) 1.808E-01 A
 * +c) 1.989E-01 A
 * -d) 2.188E-01 A
 * -e) 2.406E-01 A