Quizbank/University Physics Semester 2/T5

University Physics Semester 2/T5 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-T5.pdf

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

T5 A0
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 4.69 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (8.9 i + 4.27 j  + 7.52 k) x 104 m/s?


 * a) 5.296E-14 N
 * b) 5.826E-14 N
 * c) 6.408E-14 N
 * d) 7.049E-14 N
 * e) 7.754E-14 N

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) Three wires sit at the corners of a square of length 0.774 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 (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.270E-05 T
 * b) Bx= 7.997E-05 T
 * c) Bx= 8.797E-05 T
 * d) Bx= 9.677E-05 T
 * e) Bx= 1.064E-04 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 2.533E-05 T
 * b) 2.787E-05 T
 * c) 3.065E-05 T
 * d) 3.372E-05 T
 * e) 3.709E-05 T

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) A very long and thin solenoid has 1016 turns and is 142 meters long. The wire carrys a current of 9.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 27 meters from the center and stops 84 meters from the center?


 * a) 3.05E+03 A
 * b) 3.35E+03 A
 * c) 3.67E+03 A
 * d) 4.03E+03 A
 * e) 4.41E+03 A

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * a) 2.28E-01 A/m
 * b) 2.50E-01 A/m
 * c) 2.74E-01 A/m
 * d) 3.00E-01 A/m
 * e) 3.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * a) 1.89E+01 amps
 * b) 2.08E+01 amps
 * c) 2.28E+01 amps
 * d) 2.49E+01 amps
 * e) 2.74E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * a) 1.73E+01 amps
 * b) 1.89E+01 amps
 * c) 2.07E+01 amps
 * d) 2.28E+01 amps
 * e) 2.49E+01 amps

T5 A1
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.2m from a wire carrying a current of 4.8A?


 * a) 9.35E-02 A/m
 * b) 1.02E-01 A/m
 * c) 1.12E-01 A/m
 * d) 1.23E-01 A/m
 * e) 1.35E-01 A/m

2) Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.487E-05 T
 * b) Bx= 8.236E-05 T
 * c) Bx= 9.060E-05 T
 * d) Bx= 9.966E-05 T
 * e) Bx= 1.096E-04 T

3) 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

4) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * a) 2.97E+03 A
 * b) 3.26E+03 A
 * c) 3.57E+03 A
 * d) 3.92E+03 A
 * e) 4.30E+03 A

5) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.83 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (6.16 i + 2.1 j  + 1.74 k) x 104 m/s?


 * a) 4.783E-14 N
 * b) 5.262E-14 N
 * c) 5.788E-14 N
 * d) 6.367E-14 N
 * e) 7.003E-14 N

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 37A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * a) 8.44E+00 amps
 * b) 9.25E+00 amps
 * c) 1.01E+01 amps
 * d) 1.11E+01 amps
 * e) 1.22E+01 amps

7) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * a) 1.73E+01 amps
 * b) 1.89E+01 amps
 * c) 2.07E+01 amps
 * d) 2.28E+01 amps
 * e) 2.49E+01 amps

9) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

10) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 2.533E-05 T
 * b) 2.787E-05 T
 * c) 3.065E-05 T
 * d) 3.372E-05 T
 * e) 3.709E-05 T

T5 A2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * a) 7.96E-02 A/m
 * b) 8.73E-02 A/m
 * c) 9.57E-02 A/m
 * d) 1.05E-01 A/m
 * e) 1.15E-01 A/m

2) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

3) The silver ribbon shown are a=3.89 cm, b=3.43 cm, and c= 1.21 cm. The current carries a current of 77 A and it lies in a uniform magnetic field of 2.16 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.322E-06 V
 * b) 1.454E-06 V
 * c) 1.600E-06 V
 * d) 1.759E-06 V
 * e) 1.935E-06 V

4) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.78 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.43 i + 8.8 j  + 4.16 k) x 104 m/s?


 * a) 1.064E-13 N
 * b) 1.171E-13 N
 * c) 1.288E-13 N
 * d) 1.417E-13 N
 * e) 1.558E-13 N

5) 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

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.1, 8.1) to the point (8.1, 8.1).


 * a) 2.01E+01 amps
 * b) 2.20E+01 amps
 * c) 2.41E+01 amps
 * d) 2.64E+01 amps
 * e) 2.90E+01 amps

8) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 78A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.6) to the point (4.6,0).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.14E+01 amps
 * e) 2.34E+01 amps

10) A very long and thin solenoid has 2006 turns and is 118 meters long. The wire carrys a current of 9.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 30 meters from the center and stops 78 meters from the center?


 * a) 4.78E+03 A
 * b) 5.24E+03 A
 * c) 5.75E+03 A
 * d) 6.30E+03 A
 * e) 6.91E+03 A

T5 B0
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 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

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=2.38 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

4) 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

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.9m from a wire carrying a current of 6.8A?


 * a) 1.14E-01 A/m
 * b) 1.25E-01 A/m
 * c) 1.37E-01 A/m
 * d) 1.50E-01 A/m
 * e) 1.65E-01 A/m

8) What is the sum of 0.8 apples plus 18 apples?


 * a) 1.56E+01 apples
 * b) 1.71E+01 apples
 * c) 1.88E+01 apples
 * d) 2.06E+01 apples
 * e) 2.26E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.6) to (+ &infin; ,9.6).


 * a) 3.16E+01 amps
 * b) 3.47E+01 amps
 * c) 3.80E+01 amps
 * d) 4.17E+01 amps
 * e) 4.57E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * a) 1.73E+01 amps
 * b) 1.89E+01 amps
 * c) 2.07E+01 amps
 * d) 2.28E+01 amps
 * e) 2.49E+01 amps

T5 B1
1) What is the sum of 6.6 apples plus 33 apples?


 * a) 3.61E+01 apples
 * b) 3.96E+01 apples
 * c) 4.34E+01 apples
 * d) 4.76E+01 apples
 * e) 5.22E+01 apples

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=2.38 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

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,6.9) to (+ &infin; ,6.9).


 * a) 2.54E+01 amps
 * b) 2.79E+01 amps
 * c) 3.06E+01 amps
 * d) 3.35E+01 amps
 * e) 3.67E+01 amps

4) 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

5) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * b) 1.413E+00 Tesla
 * c) 1.554E+00 Tesla
 * d) 1.710E+00 Tesla
 * e) 1.881E+00 Tesla

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * a) 1.21E+01 amps
 * b) 1.33E+01 amps
 * c) 1.46E+01 amps
 * d) 1.60E+01 amps
 * e) 1.75E+01 amps

7) A 62 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 0.351 T. What current is required to maintain this balance?


 * a) 3.999E-01 A
 * b) 4.398E-01 A
 * c) 4.838E-01 A
 * d) 5.322E-01 A
 * e) 5.854E-01 A

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * a) 7.96E-02 A/m
 * b) 8.73E-02 A/m
 * c) 9.57E-02 A/m
 * d) 1.05E-01 A/m
 * e) 1.15E-01 A/m

T5 B2
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=2.72 kA, I2=2.17 kA, and I3=3.21 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 3.905E-03 T-m
 * b) 4.295E-03 T-m
 * c) 4.725E-03 T-m
 * d) 5.197E-03 T-m
 * e) 5.717E-03 T-m

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * a) 7.96E-02 A/m
 * b) 8.73E-02 A/m
 * c) 9.57E-02 A/m
 * d) 1.05E-01 A/m
 * e) 1.15E-01 A/m

3) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * b) 1.413E+00 Tesla
 * c) 1.554E+00 Tesla
 * d) 1.710E+00 Tesla
 * e) 1.881E+00 Tesla

4) The silver ribbon shown are a=4.65 cm, b=3.43 cm, and c= 1.15 cm. The current carries a current of 279 A and it lies in a uniform magnetic field of 3.48 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 6.100E-06 V
 * b) 6.710E-06 V
 * c) 7.381E-06 V
 * d) 8.120E-06 V
 * e) 8.931E-06 V

5) 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

6) What is the sum of 0.2 apples plus 57 apples?


 * a) 5.72E+01 apples
 * b) 6.27E+01 apples
 * c) 6.88E+01 apples
 * d) 7.54E+01 apples
 * e) 8.27E+01 apples

7) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.7, 5.7) to the point (5.7, 5.7).


 * a) 1.54E+01 amps
 * b) 1.69E+01 amps
 * c) 1.85E+01 amps
 * d) 2.03E+01 amps
 * e) 2.22E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 69A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * a) 2.87E+01 amps
 * b) 3.15E+01 amps
 * c) 3.45E+01 amps
 * d) 3.78E+01 amps
 * e) 4.15E+01 amps

T5 C0
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 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) 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) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

8) A very long and thin solenoid has 2662 turns and is 182 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * a) 1.54E-04 Tesla
 * b) 1.69E-04 Tesla
 * c) 1.85E-04 Tesla
 * d) 2.03E-04 Tesla
 * e) 2.23E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * a) 2.32E+01 amps
 * b) 2.54E+01 amps
 * c) 2.79E+01 amps
 * d) 3.06E+01 amps
 * e) 3.35E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * a) 1.89E+01 amps
 * b) 2.08E+01 amps
 * c) 2.28E+01 amps
 * d) 2.49E+01 amps
 * e) 2.74E+01 amps

T5 C1
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 very long and thin solenoid has 1259 turns and is 154 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?


 * a) 9.25E-05 Tesla
 * b) 1.01E-04 Tesla
 * c) 1.11E-04 Tesla
 * d) 1.22E-04 Tesla
 * e) 1.34E-04 Tesla

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * a) 1.28E-01 A/m
 * b) 1.40E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.68E-01 A/m
 * e) 1.85E-01 A/m

4) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 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) 3.498E+00 Tesla
 * b) 3.848E+00 Tesla
 * c) 4.233E+00 Tesla
 * d) 4.656E+00 Tesla
 * e) 5.122E+00 Tesla

5) 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

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,0).


 * a) 2.28E+01 amps
 * b) 2.49E+01 amps
 * c) 2.74E+01 amps
 * d) 3.00E+01 amps
 * e) 3.29E+01 amps

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * a) 3.53E+01 amps
 * b) 3.87E+01 amps
 * c) 4.24E+01 amps
 * d) 4.65E+01 amps
 * e) 5.10E+01 amps

9) 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

10) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

T5 C2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * a) 3.37E+01 amps
 * b) 3.70E+01 amps
 * c) 4.06E+01 amps
 * d) 4.45E+01 amps
 * e) 4.88E+01 amps

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

4) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * a) 3.863E-02 T
 * b) 4.249E-02 T
 * c) 4.674E-02 T
 * d) 5.141E-02 T
 * e) 5.655E-02 T

5) 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

6) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * b) 2.092E+00 Tesla
 * c) 2.301E+00 Tesla
 * d) 2.532E+00 Tesla
 * e) 2.785E+00 Tesla

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

8) 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

9) A very long and thin solenoid has 2662 turns and is 182 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * a) 1.54E-04 Tesla
 * b) 1.69E-04 Tesla
 * c) 1.85E-04 Tesla
 * d) 2.03E-04 Tesla
 * e) 2.23E-04 Tesla

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 78A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.6) to the point (4.6,0).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.14E+01 amps
 * e) 2.34E+01 amps

T5 D0
1) 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

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0263 T . It emerges after being deflected by 65&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 8.137E-07 s
 * b) 8.951E-07 s
 * c) 9.846E-07 s
 * d) 1.083E-06 s
 * e) 1.191E-06 s

3) Two loops of wire carry the same current of 29 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.76 m while the other has a radius of 1.12 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 0.544 m from the first (smaller) loopif the disance between the loops is 1.56 m?


 * a) 1.950E-02 T
 * b) 2.145E-02 T
 * c) 2.360E-02 T
 * d) 2.596E-02 T
 * e) 2.855E-02 T

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) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) A very long and thin solenoid has 1409 turns and is 170 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 37 meters from the center and stops 100 meters from the center?


 * a) 2.94E+03 A
 * b) 3.22E+03 A
 * c) 3.53E+03 A
 * d) 3.87E+03 A
 * e) 4.25E+03 A

8) A very long and thin solenoid has 1992 turns and is 162 meters long. The wire carrys a current of 8.7A. What is the magnetic field in the center?


 * a) 1.02E-04 Tesla
 * b) 1.12E-04 Tesla
 * c) 1.23E-04 Tesla
 * d) 1.34E-04 Tesla
 * e) 1.47E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.1, 6.1) to the point (6.1, 6.1).


 * a) 1.50E+01 amps
 * b) 1.65E+01 amps
 * c) 1.81E+01 amps
 * d) 1.98E+01 amps
 * e) 2.18E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 37A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * a) 8.44E+00 amps
 * b) 9.25E+00 amps
 * c) 1.01E+01 amps
 * d) 1.11E+01 amps
 * e) 1.22E+01 amps

T5 D1
1) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

2) 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

3) 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

4) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.1) to the point (7.1,0).


 * a) 2.30E+01 amps
 * b) 2.52E+01 amps
 * c) 2.77E+01 amps
 * d) 3.03E+01 amps
 * e) 3.32E+01 amps

6) 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

7) A very long and thin solenoid has 1397 turns and is 154 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 31 meters from the center and stops 93 meters from the center?


 * a) 3.76E+03 A
 * b) 4.12E+03 A
 * c) 4.52E+03 A
 * d) 4.95E+03 A
 * e) 5.43E+03 A

8) 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

9) A very long and thin solenoid has 2066 turns and is 156 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?


 * a) 8.75E-05 Tesla
 * b) 9.59E-05 Tesla
 * c) 1.05E-04 Tesla
 * d) 1.15E-04 Tesla
 * e) 1.26E-04 Tesla

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * a) 1.21E+01 amps
 * b) 1.33E+01 amps
 * c) 1.46E+01 amps
 * d) 1.60E+01 amps
 * e) 1.75E+01 amps

T5 D2
1) Three wires sit at the corners of a square of length 0.466 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 (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 1.335E-04 T
 * b) Bx= 1.468E-04 T
 * c) Bx= 1.615E-04 T
 * d) Bx= 1.777E-04 T
 * e) Bx= 1.954E-04 T

2) A very long and thin solenoid has 1992 turns and is 162 meters long. The wire carrys a current of 8.7A. What is the magnetic field in the center?


 * a) 1.02E-04 Tesla
 * b) 1.12E-04 Tesla
 * c) 1.23E-04 Tesla
 * d) 1.34E-04 Tesla
 * e) 1.47E-04 Tesla

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.28E+01 amps
 * b) 1.40E+01 amps
 * c) 1.54E+01 amps
 * d) 1.69E+01 amps
 * e) 1.85E+01 amps

4) A very long and thin solenoid has 1397 turns and is 154 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 31 meters from the center and stops 93 meters from the center?


 * a) 3.76E+03 A
 * b) 4.12E+03 A
 * c) 4.52E+03 A
 * d) 4.95E+03 A
 * e) 5.43E+03 A

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 99A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.2) to the point (6.2,0).


 * a) 2.48E+01 amps
 * b) 2.71E+01 amps
 * c) 2.98E+01 amps
 * d) 3.26E+01 amps
 * e) 3.58E+01 amps

7) Two loops of wire carry the same current of 44 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.678 m while the other has a radius of 1.14 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 0.508 m from the first (smaller) loopif the disance between the loops is 1.16 m?


 * a) 3.342E-02 T
 * b) 3.676E-02 T
 * c) 4.044E-02 T
 * d) 4.448E-02 T
 * e) 4.893E-02 T

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

9) 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

10) 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

T5 E0
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 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

3) 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

4) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * a) 2.28E-01 A/m
 * b) 2.50E-01 A/m
 * c) 2.74E-01 A/m
 * d) 3.00E-01 A/m
 * e) 3.29E-01 A/m

8) A very long and thin solenoid has 1016 turns and is 136 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?


 * a) 5.41E-05 Tesla
 * b) 5.93E-05 Tesla
 * c) 6.51E-05 Tesla
 * d) 7.13E-05 Tesla
 * e) 7.82E-05 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * a) 1.89E+01 amps
 * b) 2.08E+01 amps
 * c) 2.28E+01 amps
 * d) 2.49E+01 amps
 * e) 2.74E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.13E+01 amps
 * e) 2.34E+01 amps

T5 E1
1) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * b) 1.413E+00 Tesla
 * c) 1.554E+00 Tesla
 * d) 1.710E+00 Tesla
 * e) 1.881E+00 Tesla

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.2m from a wire carrying a current of 4.8A?


 * a) 9.35E-02 A/m
 * b) 1.02E-01 A/m
 * c) 1.12E-01 A/m
 * d) 1.23E-01 A/m
 * e) 1.35E-01 A/m

3) 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

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 electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?


 * a) 1.60E-04 Tesla
 * b) 1.75E-04 Tesla
 * c) 1.92E-04 Tesla
 * d) 2.11E-04 Tesla
 * e) 2.31E-04 Tesla

7) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 1.21 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.75 i + 9.06 j  + 3.5 k) x 104 m/s?


 * a) 2.899E-14 N
 * b) 3.189E-14 N
 * c) 3.508E-14 N
 * d) 3.859E-14 N
 * e) 4.245E-14 N

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * a) 1.63E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.14E+01 amps
 * e) 2.35E+01 amps

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.13E+01 amps
 * e) 2.34E+01 amps

T5 E2
1) 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

2) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.4) to the point (6.4,0).


 * a) 2.10E+01 amps
 * b) 2.30E+01 amps
 * c) 2.52E+01 amps
 * d) 2.77E+01 amps
 * e) 3.03E+01 amps

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

5) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 8.8m from a wire carrying a current of 8.6A?


 * a) 1.56E-01 A/m
 * b) 1.71E-01 A/m
 * c) 1.87E-01 A/m
 * d) 2.05E-01 A/m
 * e) 2.25E-01 A/m

6) 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

7) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.22 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.85 i + 1.28 j  + 8.49 k) x 104 m/s?


 * a) 2.222E-14 N
 * b) 2.444E-14 N
 * c) 2.688E-14 N
 * d) 2.957E-14 N
 * e) 3.253E-14 N

8) A very long and thin solenoid has 2979 turns and is 170 meters long. The wire carrys a current of 8.1A. What is the magnetic field in the center?


 * a) 1.78E-04 Tesla
 * b) 1.96E-04 Tesla
 * c) 2.14E-04 Tesla
 * d) 2.35E-04 Tesla
 * e) 2.58E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 77A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.8, 9.8) to the point (9.8, 9.8).


 * a) 1.60E+01 amps
 * b) 1.76E+01 amps
 * c) 1.93E+01 amps
 * d) 2.11E+01 amps
 * e) 2.31E+01 amps

10) Three wires sit at the corners of a square of length 0.796 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 (2.48 A, 1.4 A, 1.47 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 4.506E-05 T
 * b) Bx= 4.957E-05 T
 * c) Bx= 5.452E-05 T
 * d) Bx= 5.997E-05 T
 * e) Bx= 6.597E-05 T

T5 F0
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 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

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 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.487E-05 T
 * b) Bx= 8.236E-05 T
 * c) Bx= 9.060E-05 T
 * d) Bx= 9.966E-05 T
 * e) Bx= 1.096E-04 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 cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.1588,1.5958) if a current of 5A flows through a wire that runs along the z axis?


 * a) 1.41E-01 A/m
 * b) 1.54E-01 A/m
 * c) 1.69E-01 A/m
 * d) 1.86E-01 A/m
 * e) 2.03E-01 A/m

8) A very long and thin solenoid has 1965 turns and is 136 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 88 meters from the center?


 * a) 2.75E+03 A
 * b) 3.01E+03 A
 * c) 3.30E+03 A
 * d) 3.62E+03 A
 * e) 3.97E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).


 * a) 9.34E+00 amps
 * b) 1.02E+01 amps
 * c) 1.12E+01 amps
 * d) 1.23E+01 amps
 * e) 1.35E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * a) 6.25E+00 amps
 * b) 6.85E+00 amps
 * c) 7.51E+00 amps
 * d) 8.24E+00 amps
 * e) 9.03E+00 amps

T5 F1
1) 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

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 3.41 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

3) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * a) 3.88E+00 amps
 * b) 4.25E+00 amps
 * c) 4.66E+00 amps
 * d) 5.11E+00 amps
 * e) 5.60E+00 amps

6) 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

7) A very long and thin solenoid has 2850 turns and is 164 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 108 meters from the center?


 * a) 5.16E+03 A
 * b) 5.66E+03 A
 * c) 6.20E+03 A
 * d) 6.80E+03 A
 * e) 7.46E+03 A

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.3) to the point (9.3,0).


 * a) 2.18E+01 amps
 * b) 2.38E+01 amps
 * c) 2.61E+01 amps
 * d) 2.87E+01 amps
 * e) 3.14E+01 amps

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?


 * a) 1.75E-01 A/m
 * b) 1.92E-01 A/m
 * c) 2.11E-01 A/m
 * d) 2.31E-01 A/m
 * e) 2.53E-01 A/m

10) Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.487E-05 T
 * b) Bx= 8.236E-05 T
 * c) Bx= 9.060E-05 T
 * d) Bx= 9.966E-05 T
 * e) Bx= 1.096E-04 T

T5 F2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

2) 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

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

4) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * a) 3.84E+03 A
 * b) 4.21E+03 A
 * c) 4.62E+03 A
 * d) 5.06E+03 A
 * e) 5.55E+03 A

5) 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.4) to the point (6.4,0).


 * a) 2.10E+01 amps
 * b) 2.30E+01 amps
 * c) 2.52E+01 amps
 * d) 2.77E+01 amps
 * e) 3.03E+01 amps

7) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 1.21 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.75 i + 9.06 j  + 3.5 k) x 104 m/s?


 * a) 2.899E-14 N
 * b) 3.189E-14 N
 * c) 3.508E-14 N
 * d) 3.859E-14 N
 * e) 4.245E-14 N

8) 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

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * a) 7.68E+00 amps
 * b) 8.42E+00 amps
 * c) 9.23E+00 amps
 * d) 1.01E+01 amps
 * e) 1.11E+01 amps

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

T5 G0
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 0.232 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

2) 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

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) 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

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.6m from a wire carrying a current of 9.8A?


 * a) 2.57E-01 A/m
 * b) 2.82E-01 A/m
 * c) 3.09E-01 A/m
 * d) 3.39E-01 A/m
 * e) 3.72E-01 A/m

8) What is the sum of 6.6 apples plus 33 apples?


 * a) 3.61E+01 apples
 * b) 3.96E+01 apples
 * c) 4.34E+01 apples
 * d) 4.76E+01 apples
 * e) 5.22E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * a) 1.21E+01 amps
 * b) 1.33E+01 amps
 * c) 1.46E+01 amps
 * d) 1.60E+01 amps
 * e) 1.75E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * a) 6.25E+00 amps
 * b) 6.85E+00 amps
 * c) 7.51E+00 amps
 * d) 8.24E+00 amps
 * e) 9.03E+00 amps

T5 G1
1) 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

2) What is the sum of 0.2 apples plus 57 apples?


 * a) 5.72E+01 apples
 * b) 6.27E+01 apples
 * c) 6.88E+01 apples
 * d) 7.54E+01 apples
 * e) 8.27E+01 apples

3) 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

4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 65A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 4.9, 4.9) to the point (4.9, 4.9).


 * a) 1.23E+01 amps
 * b) 1.35E+01 amps
 * c) 1.48E+01 amps
 * d) 1.63E+01 amps
 * e) 1.78E+01 amps

7) A wire carries a current of 266 A in a circular arc with radius 2.21 cm swept through 73 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) 5.034E+00 Tesla
 * b) 5.538E+00 Tesla
 * c) 6.091E+00 Tesla
 * d) 6.701E+00 Tesla
 * e) 7.371E+00 Tesla

8) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?


 * a) 2.588E-10 N/m
 * b) 2.847E-10 N/m
 * c) 3.131E-10 N/m
 * d) 3.444E-10 N/m
 * e) 3.789E-10 N/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 9.77E+00 amps
 * b) 1.07E+01 amps
 * c) 1.18E+01 amps
 * d) 1.29E+01 amps
 * e) 1.41E+01 amps

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * a) 2.28E-01 A/m
 * b) 2.50E-01 A/m
 * c) 2.74E-01 A/m
 * d) 3.00E-01 A/m
 * e) 3.29E-01 A/m

T5 G2
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 0.157 m and a magneticfield of 0.512 T. What is their maximum kinetic energy?


 * a) 2.574E-01 MeV
 * b) 2.831E-01 MeV
 * c) 3.114E-01 MeV
 * d) 3.425E-01 MeV
 * e) 3.768E-01 MeV

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.55E+01 amps
 * b) 1.70E+01 amps
 * c) 1.86E+01 amps
 * d) 2.04E+01 amps
 * e) 2.24E+01 amps

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,8.4).


 * a) 5.47E+00 amps
 * b) 6.00E+00 amps
 * c) 6.58E+00 amps
 * d) 7.21E+00 amps
 * e) 7.91E+00 amps

4) 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

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) 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

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 7.9A?


 * a) 2.73E-01 A/m
 * b) 2.99E-01 A/m
 * c) 3.28E-01 A/m
 * d) 3.60E-01 A/m
 * e) 3.95E-01 A/m

8) A wire carries a current of 353 A in a circular arc with radius 2.44 cm swept through 86 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) 5.891E+00 Tesla
 * b) 6.481E+00 Tesla
 * c) 7.129E+00 Tesla
 * d) 7.841E+00 Tesla
 * e) 8.626E+00 Tesla

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

10) What is the sum of 7.2 apples plus 9 apples?


 * a) 1.62E+01 apples
 * b) 1.78E+01 apples
 * c) 1.95E+01 apples
 * d) 2.14E+01 apples
 * e) 2.34E+01 apples

T5 H0
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) 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

3) Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.397E-05 T
 * b) Bx= 7.037E-05 T
 * c) Bx= 7.740E-05 T
 * d) Bx= 8.514E-05 T
 * e) Bx= 9.366E-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) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.6m from a wire carrying a current of 9.8A?


 * a) 2.57E-01 A/m
 * b) 2.82E-01 A/m
 * c) 3.09E-01 A/m
 * d) 3.39E-01 A/m
 * e) 3.72E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.8, 5.8) to the point (5.8, 5.8).


 * a) 1.78E+01 amps
 * b) 1.95E+01 amps
 * c) 2.14E+01 amps
 * d) 2.35E+01 amps
 * e) 2.58E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 39A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.5) to the point (8.5,8.5).


 * a) 4.88E+00 amps
 * b) 5.35E+00 amps
 * c) 5.86E+00 amps
 * d) 6.43E+00 amps
 * e) 7.05E+00 amps

T5 H1
1) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

2) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 63A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.3, 9.3) to the point (9.3, 9.3).


 * a) 1.19E+01 amps
 * b) 1.31E+01 amps
 * c) 1.44E+01 amps
 * d) 1.58E+01 amps
 * e) 1.73E+01 amps

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.2097,1.9209) if a current of 4.7A flows through a wire that runs along the z axis?


 * a) 8.34E-02 A/m
 * b) 9.14E-02 A/m
 * c) 1.00E-01 A/m
 * d) 1.10E-01 A/m
 * e) 1.21E-01 A/m

5) Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.397E-05 T
 * b) Bx= 7.037E-05 T
 * c) Bx= 7.740E-05 T
 * d) Bx= 8.514E-05 T
 * e) Bx= 9.366E-05 T

6) 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

7) 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

8) 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 5.46 mT and 1.710E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 3.132E+05 m/s
 * b) 3.445E+05 m/s
 * c) 3.790E+05 m/s
 * d) 4.169E+05 m/s
 * e) 4.585E+05 m/s

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 5.4m from a wire carrying a current of 5A?


 * a) 1.34E-01 A/m
 * b) 1.47E-01 A/m
 * c) 1.62E-01 A/m
 * d) 1.77E-01 A/m
 * e) 1.94E-01 A/m

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * a) 7.44E+00 amps
 * b) 8.15E+00 amps
 * c) 8.94E+00 amps
 * d) 9.80E+00 amps
 * e) 1.08E+01 amps

T5 H2
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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.7m from a wire carrying a current of 4.8A?


 * a) 9.92E-02 A/m
 * b) 1.09E-01 A/m
 * c) 1.19E-01 A/m
 * d) 1.31E-01 A/m
 * e) 1.43E-01 A/m

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.28E+01 amps
 * b) 1.40E+01 amps
 * c) 1.54E+01 amps
 * d) 1.69E+01 amps
 * e) 1.85E+01 amps

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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * a) 1.23E-01 A/m
 * b) 1.34E-01 A/m
 * c) 1.47E-01 A/m
 * d) 1.62E-01 A/m
 * e) 1.77E-01 A/m

7) 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

8) 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

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 8.72E+00 amps
 * b) 9.57E+00 amps
 * c) 1.05E+01 amps
 * d) 1.15E+01 amps
 * e) 1.26E+01 amps

T5 I0
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) The silver ribbon shown are a=3.89 cm, b=3.43 cm, and c= 1.21 cm. The current carries a current of 77 A and it lies in a uniform magnetic field of 2.16 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 1.322E-06 V
 * b) 1.454E-06 V
 * c) 1.600E-06 V
 * d) 1.759E-06 V
 * e) 1.935E-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=2.55 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

4) Three wires sit at the corners of a square of length 0.823 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 (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 6.718E-05 T
 * b) By= 7.390E-05 T
 * c) By= 8.129E-05 T
 * d) By= 8.942E-05 T
 * e) By= 9.836E-05 T

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * a) 5.31E+01 amps per meter
 * b) 5.73E+01 amps per meter
 * c) 6.19E+01 amps per meter
 * d) 6.68E+01 amps per meter
 * e) 7.21E+01 amps per meter

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.1m from a wire carrying a current of 5.8A?


 * a) 1.38E-01 A/m
 * b) 1.51E-01 A/m
 * c) 1.66E-01 A/m
 * d) 1.82E-01 A/m
 * e) 1.99E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * a) 1.73E+01 amps
 * b) 1.89E+01 amps
 * c) 2.07E+01 amps
 * d) 2.28E+01 amps
 * e) 2.49E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 9.77E+00 amps
 * b) 1.07E+01 amps
 * c) 1.18E+01 amps
 * d) 1.29E+01 amps
 * e) 1.41E+01 amps

T5 I1
1) The silver ribbon shown are a=3.96 cm, b=3.35 cm, and c= 1.07 cm. The current carries a current of 295 A and it lies in a uniform magnetic field of 3.4 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * a) 9.015E-06 V
 * b) 9.916E-06 V
 * c) 1.091E-05 V
 * d) 1.200E-05 V
 * e) 1.320E-05 V

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=2.48 kA, I2=1.47 kA, and I3=2.6 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.420E-03 T-m
 * b) 1.562E-03 T-m
 * c) 1.718E-03 T-m
 * d) 1.890E-03 T-m
 * e) 2.079E-03 T-m

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 38A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,6.7).


 * a) 4.33E+00 amps
 * b) 4.75E+00 amps
 * c) 5.21E+00 amps
 * d) 5.71E+00 amps
 * e) 6.26E+00 amps

4) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

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 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 2.656E+05 m/s
 * b) 2.922E+05 m/s
 * c) 3.214E+05 m/s
 * d) 3.535E+05 m/s
 * e) 3.889E+05 m/s

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.28E+01 amps
 * b) 1.40E+01 amps
 * c) 1.54E+01 amps
 * d) 1.69E+01 amps
 * e) 1.85E+01 amps

8) What is the sum of 7.2 apples plus 9 apples?


 * a) 1.62E+01 apples
 * b) 1.78E+01 apples
 * c) 1.95E+01 apples
 * d) 2.14E+01 apples
 * e) 2.34E+01 apples

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 9.9m from a wire carrying a current of 6.9A?


 * a) 1.11E-01 A/m
 * b) 1.22E-01 A/m
 * c) 1.33E-01 A/m
 * d) 1.46E-01 A/m
 * e) 1.60E-01 A/m

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

T5 I2
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.55E+01 amps
 * b) 1.70E+01 amps
 * c) 1.86E+01 amps
 * d) 2.04E+01 amps
 * e) 2.24E+01 amps

2) What is the sum of 0.8 apples plus 18 apples?


 * a) 1.56E+01 apples
 * b) 1.71E+01 apples
 * c) 1.88E+01 apples
 * d) 2.06E+01 apples
 * e) 2.26E+01 apples

3) Three wires sit at the corners of a square of length 0.834 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 (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 7.518E-05 T
 * b) By= 8.270E-05 T
 * c) By= 9.097E-05 T
 * d) By= 1.001E-04 T
 * e) By= 1.101E-04 T

4) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

5) 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

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.1m from a wire carrying a current of 5.8A?


 * a) 1.38E-01 A/m
 * b) 1.51E-01 A/m
 * c) 1.66E-01 A/m
 * d) 1.82E-01 A/m
 * e) 1.99E-01 A/m

8) 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 5.46 mT and 1.710E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 3.132E+05 m/s
 * b) 3.445E+05 m/s
 * c) 3.790E+05 m/s
 * d) 4.169E+05 m/s
 * e) 4.585E+05 m/s

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.6) to the point (6.6,6.6).


 * a) 9.15E+00 amps
 * b) 1.00E+01 amps
 * c) 1.10E+01 amps
 * d) 1.21E+01 amps
 * e) 1.32E+01 amps

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=2.44 kA, I2=1.1 kA, and I3=1.99 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.017E-03 T-m
 * b) 1.118E-03 T-m
 * c) 1.230E-03 T-m
 * d) 1.353E-03 T-m
 * e) 1.489E-03 T-m

T5 J0
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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 5.554E+05 m/s
 * b) 6.110E+05 m/s
 * c) 6.720E+05 m/s
 * d) 7.393E+05 m/s
 * e) 8.132E+05 m/s

2) 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

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 $$a=$$ 0.51 m and $$B_{max}=\,$$ 0.649 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.376 m that is centered on the axis with its plane perpendicular to the axis?


 * a) 9.388E+05 A
 * b) 1.033E+06 A
 * c) 1.136E+06 A
 * d) 1.249E+06 A
 * e) 1.374E+06 A

4) 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

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 9.6A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 9.8m.


 * a) 4.26E+01 m
 * b) 4.67E+01 m
 * c) 5.12E+01 m
 * d) 5.62E+01 m
 * e) 6.16E+01 m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * a) 7.96E-02 A/m
 * b) 8.73E-02 A/m
 * c) 9.57E-02 A/m
 * d) 1.05E-01 A/m
 * e) 1.15E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.6) to the point (8.6,8.6).


 * a) 4.50E+00 amps
 * b) 4.93E+00 amps
 * c) 5.41E+00 amps
 * d) 5.93E+00 amps
 * e) 6.50E+00 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 96A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 2.00E+01 amps
 * b) 2.19E+01 amps
 * c) 2.40E+01 amps
 * d) 2.63E+01 amps
 * e) 2.89E+01 amps

T5 J1
1) 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

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * a) 2.28E-01 A/m
 * b) 2.50E-01 A/m
 * c) 2.74E-01 A/m
 * d) 3.00E-01 A/m
 * e) 3.29E-01 A/m

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 $$a=$$ 0.547 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

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,8.4).


 * a) 5.47E+00 amps
 * b) 6.00E+00 amps
 * c) 6.58E+00 amps
 * d) 7.21E+00 amps
 * e) 7.91E+00 amps

5) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 5.8A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 4.4m.


 * a) 2.30E+01 m
 * b) 2.52E+01 m
 * c) 2.76E+01 m
 * d) 3.03E+01 m
 * e) 3.32E+01 m

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 4.66 mT and 2.860E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 5.072E+05 m/s
 * b) 5.579E+05 m/s
 * c) 6.137E+05 m/s
 * d) 6.751E+05 m/s
 * e) 7.426E+05 m/s

7) 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

8) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.7, 5.7) to the point (5.7, 5.7).


 * a) 1.54E+01 amps
 * b) 1.69E+01 amps
 * c) 1.85E+01 amps
 * d) 2.03E+01 amps
 * e) 2.22E+01 amps

T5 J2
1) 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

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 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

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.13E+01 amps
 * e) 2.34E+01 amps

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * a) 2.28E-01 A/m
 * b) 2.50E-01 A/m
 * c) 2.74E-01 A/m
 * d) 3.00E-01 A/m
 * e) 3.29E-01 A/m

7) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 6.9A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 9.9m.


 * a) 6.22E+01 m
 * b) 6.82E+01 m
 * c) 7.48E+01 m
 * d) 8.20E+01 m
 * e) 8.99E+01 m

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) 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

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * a) 7.44E+00 amps
 * b) 8.15E+00 amps
 * c) 8.94E+00 amps
 * d) 9.80E+00 amps
 * e) 1.08E+01 amps

T5 K0
1) A 57 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 0.447 T. What current is required to maintain this balance?


 * a) 2.225E-01 A
 * b) 2.448E-01 A
 * c) 2.692E-01 A
 * d) 2.962E-01 A
 * e) 3.258E-01 A

2) 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

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=2.5 kA, I2=1.53 kA, and I3=2.34 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.018E-03 T-m
 * b) 1.120E-03 T-m
 * c) 1.232E-03 T-m
 * d) 1.355E-03 T-m
 * e) 1.490E-03 T-m

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.593E+03
 * b) $$\chi \text{ (chi) }=$$ 1.753E+03
 * c) $$\chi \text{ (chi) }=$$ 1.928E+03
 * d) $$\chi \text{ (chi) }=$$ 2.121E+03
 * e) $$\chi \text{ (chi) }=$$ 2.333E+03

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) What is the sum of 0.8 apples plus 18 apples?


 * a) 1.56E+01 apples
 * b) 1.71E+01 apples
 * c) 1.88E+01 apples
 * d) 2.06E+01 apples
 * e) 2.26E+01 apples

8) A very long and thin solenoid has 2219 turns and is 134 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * a) 2.41E+03 A
 * b) 2.64E+03 A
 * c) 2.89E+03 A
 * d) 3.17E+03 A
 * e) 3.48E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7, 7) to the point (7, 7).


 * a) 9.67E+00 amps
 * b) 1.06E+01 amps
 * c) 1.16E+01 amps
 * d) 1.28E+01 amps
 * e) 1.40E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * a) 3.37E+01 amps
 * b) 3.70E+01 amps
 * c) 4.06E+01 amps
 * d) 4.45E+01 amps
 * e) 4.88E+01 amps

T5 K1
1) A 82 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 0.459 T. What current is required to maintain this balance?


 * a) 1.956E-01 A
 * b) 2.152E-01 A
 * c) 2.367E-01 A
 * d) 2.604E-01 A
 * e) 2.864E-01 A

2) 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

3) A circular current loop of radius 3.04 cm carries a current of 1.94 mA. What is the magnitude of the torque if the dipole is oriented at 50 &deg; to a uniform magnetic fied of 0.193 T?


 * a) 6.257E-07 N m
 * b) 6.882E-07 N m
 * c) 7.570E-07 N m
 * d) 8.327E-07 N m
 * e) 9.160E-07 N m

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7.4, 7.4) to the point (7.4, 7.4).


 * a) 1.69E+01 amps
 * b) 1.85E+01 amps
 * c) 2.03E+01 amps
 * d) 2.22E+01 amps
 * e) 2.44E+01 amps

5) What is the sum of 3.4 apples plus 62 apples?


 * a) 4.96E+01 apples
 * b) 5.44E+01 apples
 * c) 5.96E+01 apples
 * d) 6.54E+01 apples
 * e) 7.17E+01 apples

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 66A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.5) to (+ &infin; ,5.5).


 * a) 3.01E+01 amps
 * b) 3.30E+01 amps
 * c) 3.62E+01 amps
 * d) 3.97E+01 amps
 * e) 4.35E+01 amps

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=2.84 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

9) A very long and thin solenoid has 2850 turns and is 164 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 108 meters from the center?


 * a) 5.16E+03 A
 * b) 5.66E+03 A
 * c) 6.20E+03 A
 * d) 6.80E+03 A
 * e) 7.46E+03 A

10) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

T5 K2
1) 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

2) A very long and thin solenoid has 1016 turns and is 142 meters long. The wire carrys a current of 9.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 27 meters from the center and stops 84 meters from the center?


 * a) 3.05E+03 A
 * b) 3.35E+03 A
 * c) 3.67E+03 A
 * d) 4.03E+03 A
 * e) 4.41E+03 A

3) 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 265 mA, the net magnetic field is measured to be 1.11 T. What is the magnetic susceptibility for this case?


 * a) $$\chi \text{ (chi) }=$$ 1.376E+03
 * b) $$\chi \text{ (chi) }=$$ 1.514E+03
 * c) $$\chi \text{ (chi) }=$$ 1.666E+03
 * d) $$\chi \text{ (chi) }=$$ 1.832E+03
 * e) $$\chi \text{ (chi) }=$$ 2.015E+03

4) A torus is centered around the x-y plane, with major radius, a = 3.24 m, and  minor radius, r = 1.35m.  A wire carrying 4.9A is uniformly wrapped with 731 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.81m from the outermost edge of the torus?


 * a) 1.11E+02 amps per meter
 * b) 1.20E+02 amps per meter
 * c) 1.30E+02 amps per meter
 * d) 1.40E+02 amps per meter
 * e) 1.51E+02 amps per meter

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=2.55 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 77A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.8, 9.8) to the point (9.8, 9.8).


 * a) 1.60E+01 amps
 * b) 1.76E+01 amps
 * c) 1.93E+01 amps
 * d) 2.11E+01 amps
 * e) 2.31E+01 amps

7) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * a) 3.37E+01 amps
 * b) 3.70E+01 amps
 * c) 4.06E+01 amps
 * d) 4.45E+01 amps
 * e) 4.88E+01 amps

9) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

10) 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

T5 L0
1) 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

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) 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

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (7.9293,2.4528) if a current of 7.3A flows through a wire that runs along the z axis?


 * a) 1.11E-01 A/m
 * b) 1.22E-01 A/m
 * c) 1.34E-01 A/m
 * d) 1.47E-01 A/m
 * e) 1.61E-01 A/m

8) A very long and thin solenoid has 1946 turns and is 144 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?


 * a) 1.06E-04 Tesla
 * b) 1.16E-04 Tesla
 * c) 1.27E-04 Tesla
 * d) 1.39E-04 Tesla
 * e) 1.53E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * a) 7.44E+00 amps
 * b) 8.15E+00 amps
 * c) 8.94E+00 amps
 * d) 9.80E+00 amps
 * e) 1.08E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * a) 3.53E+01 amps
 * b) 3.87E+01 amps
 * c) 4.24E+01 amps
 * d) 4.65E+01 amps
 * e) 5.10E+01 amps

T5 L1
1) Three wires sit at the corners of a square of length 0.785 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 (2.23 A, 1.52 A, 1.86 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 4.559E-05 T
 * b) Bx= 5.015E-05 T
 * c) Bx= 5.517E-05 T
 * d) Bx= 6.068E-05 T
 * e) Bx= 6.675E-05 T

2) 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

3) A very long and thin solenoid has 1259 turns and is 154 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?


 * a) 9.25E-05 Tesla
 * b) 1.01E-04 Tesla
 * c) 1.11E-04 Tesla
 * d) 1.22E-04 Tesla
 * e) 1.34E-04 Tesla

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * a) 3.53E+01 amps
 * b) 3.87E+01 amps
 * c) 4.24E+01 amps
 * d) 4.65E+01 amps
 * e) 5.10E+01 amps

5) 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

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 46A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * a) 5.24E+00 amps
 * b) 5.75E+00 amps
 * c) 6.30E+00 amps
 * d) 6.91E+00 amps
 * e) 7.58E+00 amps

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.0898,3.6432) if a current of 4.9A flows through a wire that runs along the z axis?


 * a) 6.39E-02 A/m
 * b) 7.01E-02 A/m
 * c) 7.68E-02 A/m
 * d) 8.43E-02 A/m
 * e) 9.24E-02 A/m

T5 L2
1) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?


 * a) 7.623E-03 T
 * b) 8.385E-03 T
 * c) 9.223E-03 T
 * d) 1.015E-02 T
 * e) 1.116E-02 T

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * a) 7.44E+00 amps
 * b) 8.15E+00 amps
 * c) 8.94E+00 amps
 * d) 9.80E+00 amps
 * e) 1.08E+01 amps

3) 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

4) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.0898,3.6432) if a current of 7.9A flows through a wire that runs along the z axis?


 * a) 1.36E-01 A/m
 * b) 1.49E-01 A/m
 * c) 1.63E-01 A/m
 * d) 1.79E-01 A/m
 * e) 1.96E-01 A/m

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,6.9) to (+ &infin; ,6.9).


 * a) 2.54E+01 amps
 * b) 2.79E+01 amps
 * c) 3.06E+01 amps
 * d) 3.35E+01 amps
 * e) 3.67E+01 amps

9) A very long and thin solenoid has 2662 turns and is 182 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * a) 1.54E-04 Tesla
 * b) 1.69E-04 Tesla
 * c) 1.85E-04 Tesla
 * d) 2.03E-04 Tesla
 * e) 2.23E-04 Tesla

10) 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

T5 M0
1) 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

2) 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

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) 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

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 7.9A?


 * a) 2.73E-01 A/m
 * b) 2.99E-01 A/m
 * c) 3.28E-01 A/m
 * d) 3.60E-01 A/m
 * e) 3.95E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.2097,1.9209) if a current of 4.7A flows through a wire that runs along the z axis?


 * a) 8.34E-02 A/m
 * b) 9.14E-02 A/m
 * c) 1.00E-01 A/m
 * d) 1.10E-01 A/m
 * e) 1.21E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * a) 1.89E+01 amps
 * b) 2.08E+01 amps
 * c) 2.28E+01 amps
 * d) 2.49E+01 amps
 * e) 2.74E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.55E+01 amps
 * b) 1.70E+01 amps
 * c) 1.86E+01 amps
 * d) 2.04E+01 amps
 * e) 2.24E+01 amps

T5 M1
1) 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

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 4.9A?


 * a) 1.28E-01 A/m
 * b) 1.41E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.69E-01 A/m
 * e) 1.86E-01 A/m

3) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.8, 6.8) to the point (6.8, 6.8).


 * a) 1.06E+01 amps
 * b) 1.16E+01 amps
 * c) 1.28E+01 amps
 * d) 1.40E+01 amps
 * e) 1.53E+01 amps

5) 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

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.3) to the point (9.3,0).


 * a) 2.18E+01 amps
 * b) 2.38E+01 amps
 * c) 2.61E+01 amps
 * d) 2.87E+01 amps
 * e) 3.14E+01 amps

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

9) A wire carries a current of 109 A in a circular arc with radius 1.26 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) 2.908E+00 Tesla
 * b) 3.199E+00 Tesla
 * c) 3.519E+00 Tesla
 * d) 3.871E+00 Tesla
 * e) 4.258E+00 Tesla

10) 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

T5 M2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * a) 2.28E-01 A/m
 * b) 2.50E-01 A/m
 * c) 2.74E-01 A/m
 * d) 3.00E-01 A/m
 * e) 3.29E-01 A/m

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * a) 1.55E+01 amps
 * b) 1.70E+01 amps
 * c) 1.86E+01 amps
 * d) 2.04E+01 amps
 * e) 2.24E+01 amps

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

4) 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

5) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 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) 3.498E+00 Tesla
 * b) 3.848E+00 Tesla
 * c) 4.233E+00 Tesla
 * d) 4.656E+00 Tesla
 * e) 5.122E+00 Tesla

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.1) to the point (7.1,0).


 * a) 2.30E+01 amps
 * b) 2.52E+01 amps
 * c) 2.77E+01 amps
 * d) 3.03E+01 amps
 * e) 3.32E+01 amps

7) 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

8) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

9) 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

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

T5 N0
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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 5.554E+05 m/s
 * b) 6.110E+05 m/s
 * c) 6.720E+05 m/s
 * d) 7.393E+05 m/s
 * e) 8.132E+05 m/s

2) 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

3) Three wires sit at the corners of a square of length 0.547 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 (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 6.118E-05 T
 * b) By= 6.730E-05 T
 * c) By= 7.403E-05 T
 * d) By= 8.144E-05 T
 * e) By= 8.958E-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 $$a=$$ 0.432 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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.2104,5.6854) if a current of 5.8A flows through a wire that runs along the z axis?


 * a) 4.16E-02 A/m
 * b) 4.56E-02 A/m
 * c) 5.00E-02 A/m
 * d) 5.48E-02 A/m
 * e) 6.01E-02 A/m

8) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * a) 5.31E+01 amps per meter
 * b) 5.73E+01 amps per meter
 * c) 6.19E+01 amps per meter
 * d) 6.68E+01 amps per meter
 * e) 7.21E+01 amps per meter

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9) to (+ &infin; ,9).


 * a) 3.08E+01 amps
 * b) 3.37E+01 amps
 * c) 3.70E+01 amps
 * d) 4.06E+01 amps
 * e) 4.45E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * a) 6.25E+00 amps
 * b) 6.85E+00 amps
 * c) 7.51E+00 amps
 * d) 8.24E+00 amps
 * e) 9.03E+00 amps

T5 N1
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 5.49 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

2) Three wires sit at the corners of a square of length 0.547 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 (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 6.118E-05 T
 * b) By= 6.730E-05 T
 * c) By= 7.403E-05 T
 * d) By= 8.144E-05 T
 * e) By= 8.958E-05 T

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * a) 3.88E+00 amps
 * b) 4.25E+00 amps
 * c) 4.66E+00 amps
 * d) 5.11E+00 amps
 * e) 5.60E+00 amps

4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

5) 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

6) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.3551,4.3477) if a current of 4.8A flows through a wire that runs along the z axis?


 * a) 8.19E-02 A/m
 * b) 8.98E-02 A/m
 * c) 9.84E-02 A/m
 * d) 1.08E-01 A/m
 * e) 1.18E-01 A/m

7) 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

8) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 69A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * a) 2.87E+01 amps
 * b) 3.15E+01 amps
 * c) 3.45E+01 amps
 * d) 3.78E+01 amps
 * e) 4.15E+01 amps

10) What is the sum of 7.2 apples plus 9 apples?


 * a) 1.62E+01 apples
 * b) 1.78E+01 apples
 * c) 1.95E+01 apples
 * d) 2.14E+01 apples
 * e) 2.34E+01 apples

T5 N2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

2) Three wires sit at the corners of a square of length 0.591 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 (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?


 * a) By= 1.191E-04 T
 * b) By= 1.310E-04 T
 * c) By= 1.441E-04 T
 * d) By= 1.585E-04 T
 * e) By= 1.744E-04 T

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 42A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.2) to the point (4.2,4.2).


 * a) 3.98E+00 amps
 * b) 4.37E+00 amps
 * c) 4.79E+00 amps
 * d) 5.25E+00 amps
 * e) 5.76E+00 amps

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * a) 3.53E+01 amps
 * b) 3.87E+01 amps
 * c) 4.24E+01 amps
 * d) 4.65E+01 amps
 * e) 5.10E+01 amps

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) 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

7) 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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 5.554E+05 m/s
 * b) 6.110E+05 m/s
 * c) 6.720E+05 m/s
 * d) 7.393E+05 m/s
 * e) 8.132E+05 m/s

8) What is the sum of 3.4 apples plus 62 apples?


 * a) 4.96E+01 apples
 * b) 5.44E+01 apples
 * c) 5.96E+01 apples
 * d) 6.54E+01 apples
 * e) 7.17E+01 apples

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * a) 1.23E-01 A/m
 * b) 1.34E-01 A/m
 * c) 1.47E-01 A/m
 * d) 1.62E-01 A/m
 * e) 1.77E-01 A/m

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

T5 O0
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 0.378 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

2) 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

3) Two parallel wires each carry a 6.53 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.82 cm, 1.17 cm), while the other is located at (4.07 cm, 5.5 cm). What is the force per unit length between the wires?


 * a) 1.788E-10 N/m
 * b) 1.966E-10 N/m
 * c) 2.163E-10 N/m
 * d) 2.379E-10 N/m
 * e) 2.617E-10 N/m

4) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * a) 5.31E+01 amps per meter
 * b) 5.73E+01 amps per meter
 * c) 6.19E+01 amps per meter
 * d) 6.68E+01 amps per meter
 * e) 7.21E+01 amps per meter

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).


 * a) 9.34E+00 amps
 * b) 1.02E+01 amps
 * c) 1.12E+01 amps
 * d) 1.23E+01 amps
 * e) 1.35E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.13E+01 amps
 * e) 2.34E+01 amps

T5 O1
1) 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

2) 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

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * a) 1.28E-01 A/m
 * b) 1.40E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.68E-01 A/m
 * e) 1.85E-01 A/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 0.449 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 55A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.7) to the point (8.7,0).


 * a) 1.38E+01 amps
 * b) 1.51E+01 amps
 * c) 1.65E+01 amps
 * d) 1.81E+01 amps
 * e) 1.99E+01 amps

7) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * a) 5.31E+01 amps per meter
 * b) 5.73E+01 amps per meter
 * c) 6.19E+01 amps per meter
 * d) 6.68E+01 amps per meter
 * e) 7.21E+01 amps per meter

8) Two parallel wires each carry a 9.59 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.97 cm, 1.4 cm), while the other is located at (4.02 cm, 5.19 cm). What is the force per unit length between the wires?


 * a) 4.412E-10 N/m
 * b) 4.853E-10 N/m
 * c) 5.338E-10 N/m
 * d) 5.872E-10 N/m
 * e) 6.459E-10 N/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.13E+01 amps
 * e) 2.34E+01 amps

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

T5 O2
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 82A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.3, 9.3) to the point (9.3, 9.3).


 * a) 2.05E+01 amps
 * b) 2.25E+01 amps
 * c) 2.46E+01 amps
 * d) 2.70E+01 amps
 * e) 2.96E+01 amps

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 0.449 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

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.4963,2.0095) if a current of 6.5A flows through a wire that runs along the z axis?


 * a) 1.33E-01 A/m
 * b) 1.45E-01 A/m
 * c) 1.59E-01 A/m
 * d) 1.75E-01 A/m
 * e) 1.92E-01 A/m

4) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

5) 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * a) 1.63E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.14E+01 amps
 * e) 2.35E+01 amps

7) 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

8) What is the sum of 3.4 apples plus 62 apples?


 * a) 4.96E+01 apples
 * b) 5.44E+01 apples
 * c) 5.96E+01 apples
 * d) 6.54E+01 apples
 * e) 7.17E+01 apples

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

10) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?


 * a) 1.973E-10 N/m
 * b) 2.170E-10 N/m
 * c) 2.387E-10 N/m
 * d) 2.625E-10 N/m
 * e) 2.888E-10 N/m

T5 P0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.061 T . It emerges after being deflected by 75&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 4.453E-07 s
 * b) 4.898E-07 s
 * c) 5.388E-07 s
 * d) 5.927E-07 s
 * e) 6.519E-07 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 3.34 mT and 7.430E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 1.671E+06 m/s
 * b) 1.838E+06 m/s
 * c) 2.022E+06 m/s
 * d) 2.225E+06 m/s
 * e) 2.447E+06 m/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=2.46 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) A solenoid has 4.900E+04 turns wound around a cylinder of diameter 1.74 cm and length 19 m. The current through the coils is 0.432 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;4.18 cm to z=+1.77 cm


 * a) 6.884E-05 T-m
 * b) 7.573E-05 T-m
 * c) 8.330E-05 T-m
 * d) 9.163E-05 T-m
 * e) 1.008E-04 T-m

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?


 * a) 1.06E-01 A/m
 * b) 1.16E-01 A/m
 * c) 1.28E-01 A/m
 * d) 1.40E-01 A/m
 * e) 1.54E-01 A/m

8) What is the sum of 0.8 apples plus 18 apples?


 * a) 1.56E+01 apples
 * b) 1.71E+01 apples
 * c) 1.88E+01 apples
 * d) 2.06E+01 apples
 * e) 2.26E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 49A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.8) to the point (9.8,9.8).


 * a) 6.13E+00 amps
 * b) 6.72E+00 amps
 * c) 7.36E+00 amps
 * d) 8.07E+00 amps
 * e) 8.85E+00 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 65A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 4.9, 4.9) to the point (4.9, 4.9).


 * a) 1.23E+01 amps
 * b) 1.35E+01 amps
 * c) 1.48E+01 amps
 * d) 1.63E+01 amps
 * e) 1.78E+01 amps

T5 P1
1) 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

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=2.42 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

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.1539,7.7549) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 5.23E-02 A/m
 * b) 5.74E-02 A/m
 * c) 6.29E-02 A/m
 * d) 6.90E-02 A/m
 * e) 7.56E-02 A/m

4) What is the sum of 0.2 apples plus 57 apples?


 * a) 5.72E+01 apples
 * b) 6.27E+01 apples
 * c) 6.88E+01 apples
 * d) 7.54E+01 apples
 * e) 8.27E+01 apples

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 33A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.6, 6.6) to the point (6.6, 6.6).


 * a) 5.71E+00 amps
 * b) 6.26E+00 amps
 * c) 6.86E+00 amps
 * d) 7.52E+00 amps
 * e) 8.25E+00 amps

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 38A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,6.7).


 * a) 4.33E+00 amps
 * b) 4.75E+00 amps
 * c) 5.21E+00 amps
 * d) 5.71E+00 amps
 * e) 6.26E+00 amps

7) 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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 8.971E+05 m/s
 * b) 9.868E+05 m/s
 * c) 1.085E+06 m/s
 * d) 1.194E+06 m/s
 * e) 1.313E+06 m/s

8) 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

9) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

10) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

T5 P2
1) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

2) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

3) 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

4) What is the sum of 7.2 apples plus 9 apples?


 * a) 1.62E+01 apples
 * b) 1.78E+01 apples
 * c) 1.95E+01 apples
 * d) 2.14E+01 apples
 * e) 2.34E+01 apples

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=2.84 kA, I2=3.3 kA, and I3=5.85 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 5.598E-03 T-m
 * b) 6.158E-03 T-m
 * c) 6.773E-03 T-m
 * d) 7.451E-03 T-m
 * e) 8.196E-03 T-m

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 3.34 mT and 7.430E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 1.671E+06 m/s
 * b) 1.838E+06 m/s
 * c) 2.022E+06 m/s
 * d) 2.225E+06 m/s
 * e) 2.447E+06 m/s

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.2) to the point (7.2,7.2).


 * a) 7.38E+00 amps
 * b) 8.09E+00 amps
 * c) 8.87E+00 amps
 * d) 9.72E+00 amps
 * e) 1.07E+01 amps

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7.4, 7.4) to the point (7.4, 7.4).


 * a) 1.69E+01 amps
 * b) 1.85E+01 amps
 * c) 2.03E+01 amps
 * d) 2.22E+01 amps
 * e) 2.44E+01 amps

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?


 * a) 1.06E-01 A/m
 * b) 1.16E-01 A/m
 * c) 1.28E-01 A/m
 * d) 1.40E-01 A/m
 * e) 1.54E-01 A/m

T5 Q0
1) 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

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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 8.971E+05 m/s
 * b) 9.868E+05 m/s
 * c) 1.085E+06 m/s
 * d) 1.194E+06 m/s
 * e) 1.313E+06 m/s

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) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?


 * a) 7.623E-03 T
 * b) 8.385E-03 T
 * c) 9.223E-03 T
 * d) 1.015E-02 T
 * e) 1.116E-02 T

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.2097,1.9209) if a current of 4.7A flows through a wire that runs along the z axis?


 * a) 8.34E-02 A/m
 * b) 9.14E-02 A/m
 * c) 1.00E-01 A/m
 * d) 1.10E-01 A/m
 * e) 1.21E-01 A/m

8) A very long and thin solenoid has 2472 turns and is 144 meters long. The wire carrys a current of 8.4A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 87 meters from the center?


 * a) 3.17E+03 A
 * b) 3.48E+03 A
 * c) 3.81E+03 A
 * d) 4.18E+03 A
 * e) 4.59E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * a) 3.25E+01 amps
 * b) 3.57E+01 amps
 * c) 3.91E+01 amps
 * d) 4.29E+01 amps
 * e) 4.70E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.1) to the point (4.1,0).


 * a) 1.28E+01 amps
 * b) 1.40E+01 amps
 * c) 1.54E+01 amps
 * d) 1.69E+01 amps
 * e) 1.85E+01 amps

T5 Q1
1) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * b) 2.092E+00 Tesla
 * c) 2.301E+00 Tesla
 * d) 2.532E+00 Tesla
 * e) 2.785E+00 Tesla

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * a) 1.28E-01 A/m
 * b) 1.40E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.68E-01 A/m
 * e) 1.85E-01 A/m

3) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,6.9) to (+ &infin; ,6.9).


 * a) 2.54E+01 amps
 * b) 2.79E+01 amps
 * c) 3.06E+01 amps
 * d) 3.35E+01 amps
 * e) 3.67E+01 amps

5) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * a) 4.908E+00 N/m
 * b) 5.399E+00 N/m
 * c) 5.939E+00 N/m
 * d) 6.533E+00 N/m
 * e) 7.186E+00 N/m

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 1.85 mT and 5.080E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 2.746E+06 m/s
 * b) 3.021E+06 m/s
 * c) 3.323E+06 m/s
 * d) 3.655E+06 m/s
 * e) 4.020E+06 m/s

7) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 85A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.8) to the point (9.8,0).


 * a) 1.77E+01 amps
 * b) 1.94E+01 amps
 * c) 2.13E+01 amps
 * d) 2.33E+01 amps
 * e) 2.55E+01 amps

9) 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

10) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * a) 3.84E+03 A
 * b) 4.21E+03 A
 * c) 4.62E+03 A
 * d) 5.06E+03 A
 * e) 5.55E+03 A

T5 Q2
1) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * a) 3.863E-02 T
 * b) 4.249E-02 T
 * c) 4.674E-02 T
 * d) 5.141E-02 T
 * e) 5.655E-02 T

2) 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

3) 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 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 2.656E+05 m/s
 * b) 2.922E+05 m/s
 * c) 3.214E+05 m/s
 * d) 3.535E+05 m/s
 * e) 3.889E+05 m/s

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 99A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.2) to the point (6.2,0).


 * a) 2.48E+01 amps
 * b) 2.71E+01 amps
 * c) 2.98E+01 amps
 * d) 3.26E+01 amps
 * e) 3.58E+01 amps

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 44A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5) to (+ &infin; ,5).


 * a) 1.67E+01 amps
 * b) 1.83E+01 amps
 * c) 2.01E+01 amps
 * d) 2.20E+01 amps
 * e) 2.41E+01 amps

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * a) 1.23E-01 A/m
 * b) 1.34E-01 A/m
 * c) 1.47E-01 A/m
 * d) 1.62E-01 A/m
 * e) 1.77E-01 A/m

8) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * a) 2.97E+03 A
 * b) 3.26E+03 A
 * c) 3.57E+03 A
 * d) 3.92E+03 A
 * e) 4.30E+03 A

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

10) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * a) 4.908E+00 N/m
 * b) 5.399E+00 N/m
 * c) 5.939E+00 N/m
 * d) 6.533E+00 N/m
 * e) 7.186E+00 N/m

T5 R0
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 long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * a) 4.908E+00 N/m
 * b) 5.399E+00 N/m
 * c) 5.939E+00 N/m
 * d) 6.533E+00 N/m
 * e) 7.186E+00 N/m

3) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?


 * a) 7.623E-03 T
 * b) 8.385E-03 T
 * c) 9.223E-03 T
 * d) 1.015E-02 T
 * e) 1.116E-02 T

4) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

8) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 7.9A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 4.2m.


 * a) 1.83E+01 m
 * b) 2.00E+01 m
 * c) 2.19E+01 m
 * d) 2.41E+01 m
 * e) 2.64E+01 m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.8, 5.8) to the point (5.8, 5.8).


 * a) 1.78E+01 amps
 * b) 1.95E+01 amps
 * c) 2.14E+01 amps
 * d) 2.35E+01 amps
 * e) 2.58E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * a) 3.16E+01 amps
 * b) 3.47E+01 amps
 * c) 3.80E+01 amps
 * d) 4.17E+01 amps
 * e) 4.57E+01 amps

T5 R1
1) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * a) 1.62E+01 amps
 * b) 1.78E+01 amps
 * c) 1.95E+01 amps
 * d) 2.13E+01 amps
 * e) 2.34E+01 amps

3) 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

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.3) to (+ &infin; ,8.3).


 * a) 1.50E+01 amps
 * b) 1.64E+01 amps
 * c) 1.80E+01 amps
 * d) 1.97E+01 amps
 * e) 2.16E+01 amps

5) 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

6) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.848 m while the other has a radius of 1.42 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 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?


 * a) 7.952E-03 T
 * b) 8.747E-03 T
 * c) 9.622E-03 T
 * d) 1.058E-02 T
 * e) 1.164E-02 T

7) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

8) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 6.5A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 6.8m.


 * a) 4.27E+01 m
 * b) 4.68E+01 m
 * c) 5.14E+01 m
 * d) 5.63E+01 m
 * e) 6.18E+01 m

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?


 * a) 1.75E-01 A/m
 * b) 1.92E-01 A/m
 * c) 2.11E-01 A/m
 * d) 2.31E-01 A/m
 * e) 2.53E-01 A/m

10) 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

T5 R2
1) 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

2) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * a) 3.863E-02 T
 * b) 4.249E-02 T
 * c) 4.674E-02 T
 * d) 5.141E-02 T
 * e) 5.655E-02 T

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.7803,5.3849) if a current of 6.8A flows through a wire that runs along the z axis?


 * a) 6.93E-02 A/m
 * b) 7.60E-02 A/m
 * c) 8.34E-02 A/m
 * d) 9.14E-02 A/m
 * e) 1.00E-01 A/m

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) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * a) 3.25E+01 amps
 * b) 3.57E+01 amps
 * c) 3.91E+01 amps
 * d) 4.29E+01 amps
 * e) 4.70E+01 amps

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.1, 6.1) to the point (6.1, 6.1).


 * a) 1.50E+01 amps
 * b) 1.65E+01 amps
 * c) 1.81E+01 amps
 * d) 1.98E+01 amps
 * e) 2.18E+01 amps

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

10) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 9.6A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 9.8m.


 * a) 4.26E+01 m
 * b) 4.67E+01 m
 * c) 5.12E+01 m
 * d) 5.62E+01 m
 * e) 6.16E+01 m

T5 S0
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 4.36 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (8.25 i + 7.71 j  + 2.91 k) x 104 m/s?


 * a) 8.890E-14 N
 * b) 9.779E-14 N
 * c) 1.076E-13 N
 * d) 1.183E-13 N
 * e) 1.302E-13 N

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 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * a) 3.863E-02 T
 * b) 4.249E-02 T
 * c) 4.674E-02 T
 * d) 5.141E-02 T
 * e) 5.655E-02 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 $$a=$$ 0.353 m and $$B_{max}=\,$$ 0.697 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) 5.479E+05 A
 * b) 6.027E+05 A
 * c) 6.630E+05 A
 * d) 7.293E+05 A
 * e) 8.022E+05 A

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

7) What is the sum of 0.8 apples plus 18 apples?


 * a) 1.56E+01 apples
 * b) 1.71E+01 apples
 * c) 1.88E+01 apples
 * d) 2.06E+01 apples
 * e) 2.26E+01 apples

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?


 * a) 8.90E-02 A/m
 * b) 9.76E-02 A/m
 * c) 1.07E-01 A/m
 * d) 1.17E-01 A/m
 * e) 1.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 8.72E+00 amps
 * b) 9.57E+00 amps
 * c) 1.05E+01 amps
 * d) 1.15E+01 amps
 * e) 1.26E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * a) 1.21E+01 amps
 * b) 1.33E+01 amps
 * c) 1.46E+01 amps
 * d) 1.60E+01 amps
 * e) 1.75E+01 amps

T5 S1
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * a) 7.68E+00 amps
 * b) 8.42E+00 amps
 * c) 9.23E+00 amps
 * d) 1.01E+01 amps
 * e) 1.11E+01 amps

2) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

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 5.75 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.81 i + 2.05 j  + 4.49 k) x 104 m/s?


 * a) 2.576E-14 N
 * b) 2.834E-14 N
 * c) 3.117E-14 N
 * d) 3.429E-14 N
 * e) 3.772E-14 N

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.4963,2.0095) if a current of 6.5A flows through a wire that runs along the z axis?


 * a) 1.33E-01 A/m
 * b) 1.45E-01 A/m
 * c) 1.59E-01 A/m
 * d) 1.75E-01 A/m
 * e) 1.92E-01 A/m

5) What is the sum of 3.4 apples plus 62 apples?


 * a) 4.96E+01 apples
 * b) 5.44E+01 apples
 * c) 5.96E+01 apples
 * d) 6.54E+01 apples
 * e) 7.17E+01 apples

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7, 7) to the point (7, 7).


 * a) 9.67E+00 amps
 * b) 1.06E+01 amps
 * c) 1.16E+01 amps
 * d) 1.28E+01 amps
 * e) 1.40E+01 amps

7) 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

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 $$a=$$ 0.547 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

9) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * a) 3.863E-02 T
 * b) 4.249E-02 T
 * c) 4.674E-02 T
 * d) 5.141E-02 T
 * e) 5.655E-02 T

10) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

T5 S2
1) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7.4, 7.4) to the point (7.4, 7.4).


 * a) 1.69E+01 amps
 * b) 1.85E+01 amps
 * c) 2.03E+01 amps
 * d) 2.22E+01 amps
 * e) 2.44E+01 amps

3) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

4) What is the sum of 0.2 apples plus 57 apples?


 * a) 5.72E+01 apples
 * b) 6.27E+01 apples
 * c) 6.88E+01 apples
 * d) 7.54E+01 apples
 * e) 8.27E+01 apples

5) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.848 m while the other has a radius of 1.42 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 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?


 * a) 7.952E-03 T
 * b) 8.747E-03 T
 * c) 9.622E-03 T
 * d) 1.058E-02 T
 * e) 1.164E-02 T

6) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.22 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.85 i + 1.28 j  + 8.49 k) x 104 m/s?


 * a) 2.222E-14 N
 * b) 2.444E-14 N
 * c) 2.688E-14 N
 * d) 2.957E-14 N
 * e) 3.253E-14 N

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 58A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.5) to the point (8.5,8.5).


 * a) 6.03E+00 amps
 * b) 6.61E+00 amps
 * c) 7.25E+00 amps
 * d) 7.95E+00 amps
 * e) 8.72E+00 amps

9) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.783 T magnetic field is directed 77&deg; away from the wire?


 * a) 3.648E+00 N/m
 * b) 4.012E+00 N/m
 * c) 4.414E+00 N/m
 * d) 4.855E+00 N/m
 * e) 5.341E+00 N/m

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

T5 T0
1) A 97 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 0.753 T. What current is required to maintain this balance?


 * a) 7.056E-02 A
 * b) 7.762E-02 A
 * c) 8.538E-02 A
 * d) 9.392E-02 A
 * e) 1.033E-01 A

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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 8.971E+05 m/s
 * b) 9.868E+05 m/s
 * c) 1.085E+06 m/s
 * d) 1.194E+06 m/s
 * e) 1.313E+06 m/s

3) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?


 * a) 1.434E-10 N/m
 * b) 1.578E-10 N/m
 * c) 1.736E-10 N/m
 * d) 1.909E-10 N/m
 * e) 2.100E-10 N/m

4) 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

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) A very long and thin solenoid has 2543 turns and is 166 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * a) 1.34E-04 Tesla
 * b) 1.47E-04 Tesla
 * c) 1.62E-04 Tesla
 * d) 1.77E-04 Tesla
 * e) 1.94E-04 Tesla

8) A very long and thin solenoid has 1292 turns and is 122 meters long. The wire carrys a current of 8.4A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 39 meters from the center and stops 75 meters from the center?


 * a) 1.63E+03 A
 * b) 1.78E+03 A
 * c) 1.96E+03 A
 * d) 2.15E+03 A
 * e) 2.35E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * a) 7.44E+00 amps
 * b) 8.15E+00 amps
 * c) 8.94E+00 amps
 * d) 9.80E+00 amps
 * e) 1.08E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * a) 1.55E+01 amps
 * b) 1.70E+01 amps
 * c) 1.86E+01 amps
 * d) 2.04E+01 amps
 * e) 2.24E+01 amps

T5 T1
1) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 3.324E-05 T
 * b) 3.657E-05 T
 * c) 4.022E-05 T
 * d) 4.424E-05 T
 * e) 4.867E-05 T

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * a) 2.32E+01 amps
 * b) 2.54E+01 amps
 * c) 2.79E+01 amps
 * d) 3.06E+01 amps
 * e) 3.35E+01 amps

3) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

4) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

5) 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

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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 8.971E+05 m/s
 * b) 9.868E+05 m/s
 * c) 1.085E+06 m/s
 * d) 1.194E+06 m/s
 * e) 1.313E+06 m/s

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 8.72E+00 amps
 * b) 9.57E+00 amps
 * c) 1.05E+01 amps
 * d) 1.15E+01 amps
 * e) 1.26E+01 amps

8) A very long and thin solenoid has 1982 turns and is 154 meters long. The wire carrys a current of 9.1A. What is the magnetic field in the center?


 * a) 1.12E-04 Tesla
 * b) 1.22E-04 Tesla
 * c) 1.34E-04 Tesla
 * d) 1.47E-04 Tesla
 * e) 1.61E-04 Tesla

9) A very long and thin solenoid has 1259 turns and is 156 meters long. The wire carrys a current of 8.9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 35 meters from the center and stops 90 meters from the center?


 * a) 2.82E+03 A
 * b) 3.09E+03 A
 * c) 3.39E+03 A
 * d) 3.71E+03 A
 * e) 4.07E+03 A

10) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?


 * a) 2.588E-10 N/m
 * b) 2.847E-10 N/m
 * c) 3.131E-10 N/m
 * d) 3.444E-10 N/m
 * e) 3.789E-10 N/m

T5 T2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

2) A 82 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 0.459 T. What current is required to maintain this balance?


 * a) 1.956E-01 A
 * b) 2.152E-01 A
 * c) 2.367E-01 A
 * d) 2.604E-01 A
 * e) 2.864E-01 A

3) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * a) 3.84E+03 A
 * b) 4.21E+03 A
 * c) 4.62E+03 A
 * d) 5.06E+03 A
 * e) 5.55E+03 A

4) 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 4.66 mT and 2.860E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * a) 5.072E+05 m/s
 * b) 5.579E+05 m/s
 * c) 6.137E+05 m/s
 * d) 6.751E+05 m/s
 * e) 7.426E+05 m/s

5) A very long and thin solenoid has 2175 turns and is 134 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?


 * a) 1.29E-04 Tesla
 * b) 1.41E-04 Tesla
 * c) 1.55E-04 Tesla
 * d) 1.70E-04 Tesla
 * e) 1.86E-04 Tesla

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 8.72E+00 amps
 * b) 9.57E+00 amps
 * c) 1.05E+01 amps
 * d) 1.15E+01 amps
 * e) 1.26E+01 amps

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 85A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8) to (+ &infin; ,8).


 * a) 2.94E+01 amps
 * b) 3.22E+01 amps
 * c) 3.53E+01 amps
 * d) 3.88E+01 amps
 * e) 4.25E+01 amps

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

10) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?


 * a) 1.720E-05 T
 * b) 1.892E-05 T
 * c) 2.081E-05 T
 * d) 2.289E-05 T
 * e) 2.518E-05 T

T5 U0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0482 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 4.629E-07 s
 * b) 5.092E-07 s
 * c) 5.601E-07 s
 * d) 6.161E-07 s
 * e) 6.777E-07 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 0.157 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

3) Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 6.397E-05 T
 * b) Bx= 7.037E-05 T
 * c) Bx= 7.740E-05 T
 * d) Bx= 8.514E-05 T
 * e) Bx= 9.366E-05 T

4) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?


 * a) 2.634E-11 N/m
 * b) 2.897E-11 N/m
 * c) 3.187E-11 N/m
 * d) 3.506E-11 N/m
 * e) 3.856E-11 N/m

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 5.8A?


 * a) 1.91E-01 A/m
 * b) 2.10E-01 A/m
 * c) 2.30E-01 A/m
 * d) 2.52E-01 A/m
 * e) 2.77E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * a) 1.28E-01 A/m
 * b) 1.40E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.68E-01 A/m
 * e) 1.85E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.2) to the point (7.2,7.2).


 * a) 7.38E+00 amps
 * b) 8.09E+00 amps
 * c) 8.87E+00 amps
 * d) 9.72E+00 amps
 * e) 1.07E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).


 * a) 9.34E+00 amps
 * b) 1.02E+01 amps
 * c) 1.12E+01 amps
 * d) 1.23E+01 amps
 * e) 1.35E+01 amps

T5 U1
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?


 * a) 1.75E-01 A/m
 * b) 1.92E-01 A/m
 * c) 2.11E-01 A/m
 * d) 2.31E-01 A/m
 * e) 2.53E-01 A/m

2) 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

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 55A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.7) to the point (8.7,0).


 * a) 1.38E+01 amps
 * b) 1.51E+01 amps
 * c) 1.65E+01 amps
 * d) 1.81E+01 amps
 * e) 1.99E+01 amps

4) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0482 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * a) 4.629E-07 s
 * b) 5.092E-07 s
 * c) 5.601E-07 s
 * d) 6.161E-07 s
 * e) 6.777E-07 s

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 42A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.2) to the point (4.2,4.2).


 * a) 3.98E+00 amps
 * b) 4.37E+00 amps
 * c) 4.79E+00 amps
 * d) 5.25E+00 amps
 * e) 5.76E+00 amps

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 0.388 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

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.9m from a wire carrying a current of 6.8A?


 * a) 1.14E-01 A/m
 * b) 1.25E-01 A/m
 * c) 1.37E-01 A/m
 * d) 1.50E-01 A/m
 * e) 1.65E-01 A/m

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

T5 U2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 9.77E+00 amps
 * b) 1.07E+01 amps
 * c) 1.18E+01 amps
 * d) 1.29E+01 amps
 * e) 1.41E+01 amps

3) Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * a) Bx= 7.487E-05 T
 * b) Bx= 8.236E-05 T
 * c) Bx= 9.060E-05 T
 * d) Bx= 9.966E-05 T
 * e) Bx= 1.096E-04 T

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 8.2m from a wire carrying a current of 7.2A?


 * a) 9.67E-02 A/m
 * b) 1.06E-01 A/m
 * c) 1.16E-01 A/m
 * d) 1.27E-01 A/m
 * e) 1.40E-01 A/m

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 0.118 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

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

8) 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

9) 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

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.4) to the point (6.4,0).


 * a) 2.10E+01 amps
 * b) 2.30E+01 amps
 * c) 2.52E+01 amps
 * d) 2.77E+01 amps
 * e) 3.03E+01 amps

T5 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) 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) 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) 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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.6m from a wire carrying a current of 9.8A?


 * a) 2.57E-01 A/m
 * b) 2.82E-01 A/m
 * c) 3.09E-01 A/m
 * d) 3.39E-01 A/m
 * e) 3.72E-01 A/m

8) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * a) 2.97E+03 A
 * b) 3.26E+03 A
 * c) 3.57E+03 A
 * d) 3.92E+03 A
 * e) 4.30E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.1) to the point (4.1,0).


 * a) 1.28E+01 amps
 * b) 1.40E+01 amps
 * c) 1.54E+01 amps
 * d) 1.69E+01 amps
 * e) 1.85E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 38A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,6.7).


 * a) 4.33E+00 amps
 * b) 4.75E+00 amps
 * c) 5.21E+00 amps
 * d) 5.71E+00 amps
 * e) 6.26E+00 amps

T5 V1
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=2.31 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

2) 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

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 46A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * a) 5.24E+00 amps
 * b) 5.75E+00 amps
 * c) 6.30E+00 amps
 * d) 6.91E+00 amps
 * e) 7.58E+00 amps

4) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * a) 4.908E+00 N/m
 * b) 5.399E+00 N/m
 * c) 5.939E+00 N/m
 * d) 6.533E+00 N/m
 * e) 7.186E+00 N/m

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 0.157 m and a magneticfield of 0.512 T. What is their maximum kinetic energy?


 * a) 2.574E-01 MeV
 * b) 2.831E-01 MeV
 * c) 3.114E-01 MeV
 * d) 3.425E-01 MeV
 * e) 3.768E-01 MeV

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 5.8A?


 * a) 1.91E-01 A/m
 * b) 2.10E-01 A/m
 * c) 2.30E-01 A/m
 * d) 2.52E-01 A/m
 * e) 2.77E-01 A/m

8) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

9) A very long and thin solenoid has 1397 turns and is 154 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 31 meters from the center and stops 93 meters from the center?


 * a) 3.76E+03 A
 * b) 4.12E+03 A
 * c) 4.52E+03 A
 * d) 4.95E+03 A
 * e) 5.43E+03 A

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.1) to the point (4.1,0).


 * a) 1.28E+01 amps
 * b) 1.40E+01 amps
 * c) 1.54E+01 amps
 * d) 1.69E+01 amps
 * e) 1.85E+01 amps

T5 V2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 40A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.6) to the point (6.6,0).


 * a) 1.00E+01 amps
 * b) 1.10E+01 amps
 * c) 1.20E+01 amps
 * d) 1.32E+01 amps
 * e) 1.45E+01 amps

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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.2m from a wire carrying a current of 4.8A?


 * a) 9.35E-02 A/m
 * b) 1.02E-01 A/m
 * c) 1.12E-01 A/m
 * d) 1.23E-01 A/m
 * e) 1.35E-01 A/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=2.89 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

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 9.77E+00 amps
 * b) 1.07E+01 amps
 * c) 1.18E+01 amps
 * d) 1.29E+01 amps
 * e) 1.41E+01 amps

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 0.388 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

9) A very long and thin solenoid has 1847 turns and is 162 meters long. The wire carrys a current of 8.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 42 meters from the center and stops 103 meters from the center?


 * a) 2.68E+03 A
 * b) 2.93E+03 A
 * c) 3.22E+03 A
 * d) 3.53E+03 A
 * e) 3.87E+03 A

10) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

T5 W0
1) 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

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 wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * b) 2.092E+00 Tesla
 * c) 2.301E+00 Tesla
 * d) 2.532E+00 Tesla
 * e) 2.785E+00 Tesla

4) 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

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.1m from a wire carrying a current of 6.7A?


 * a) 2.60E-01 A/m
 * b) 2.85E-01 A/m
 * c) 3.13E-01 A/m
 * d) 3.43E-01 A/m
 * e) 3.76E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * a) 7.68E+00 amps
 * b) 8.42E+00 amps
 * c) 9.23E+00 amps
 * d) 1.01E+01 amps
 * e) 1.11E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.7) to (+ &infin; ,8.7).


 * a) 4.01E+01 amps
 * b) 4.40E+01 amps
 * c) 4.82E+01 amps
 * d) 5.29E+01 amps
 * e) 5.80E+01 amps

T5 W1
1) A circular current loop of radius 1.56 cm carries a current of 2.57 mA. What is the magnitude of the torque if the dipole is oriented at 38 &deg; to a uniform magnetic fied of 0.79 T?


 * a) 7.898E-07 N m
 * b) 8.688E-07 N m
 * c) 9.557E-07 N m
 * d) 1.051E-06 N m
 * e) 1.156E-06 N m

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

3) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * b) 2.092E+00 Tesla
 * c) 2.301E+00 Tesla
 * d) 2.532E+00 Tesla
 * e) 2.785E+00 Tesla

4) 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

5) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.7m from a wire carrying a current of 4.8A?


 * a) 9.92E-02 A/m
 * b) 1.09E-01 A/m
 * c) 1.19E-01 A/m
 * d) 1.31E-01 A/m
 * e) 1.43E-01 A/m

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * a) 7.44E+00 amps
 * b) 8.15E+00 amps
 * c) 8.94E+00 amps
 * d) 9.80E+00 amps
 * e) 1.08E+01 amps

8) 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

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.6) to (+ &infin; ,9.6).


 * a) 3.16E+01 amps
 * b) 3.47E+01 amps
 * c) 3.80E+01 amps
 * d) 4.17E+01 amps
 * e) 4.57E+01 amps

T5 W2
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * a) 3.88E+00 amps
 * b) 4.25E+00 amps
 * c) 4.66E+00 amps
 * d) 5.11E+00 amps
 * e) 5.60E+00 amps

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 44A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5) to (+ &infin; ,5).


 * a) 1.67E+01 amps
 * b) 1.83E+01 amps
 * c) 2.01E+01 amps
 * d) 2.20E+01 amps
 * e) 2.41E+01 amps

3) 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

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * a) 1.28E-01 A/m
 * b) 1.40E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.68E-01 A/m
 * e) 1.85E-01 A/m

5) 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

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

9) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * b) 2.092E+00 Tesla
 * c) 2.301E+00 Tesla
 * d) 2.532E+00 Tesla
 * e) 2.785E+00 Tesla

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 4.9A?


 * a) 1.28E-01 A/m
 * b) 1.41E-01 A/m
 * c) 1.54E-01 A/m
 * d) 1.69E-01 A/m
 * e) 1.86E-01 A/m

T5 X0
1) 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

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) 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

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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

7) A very long and thin solenoid has 2762 turns and is 142 meters long. The wire carrys a current of 9.7A. What is the magnetic field in the center?


 * a) 2.37E-04 Tesla
 * b) 2.60E-04 Tesla
 * c) 2.85E-04 Tesla
 * d) 3.13E-04 Tesla
 * e) 3.43E-04 Tesla

8) A very long and thin solenoid has 2850 turns and is 164 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 108 meters from the center?


 * a) 5.16E+03 A
 * b) 5.66E+03 A
 * c) 6.20E+03 A
 * d) 6.80E+03 A
 * e) 7.46E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.3) to (+ &infin; ,8.3).


 * a) 1.50E+01 amps
 * b) 1.64E+01 amps
 * c) 1.80E+01 amps
 * d) 1.97E+01 amps
 * e) 2.16E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * a) 8.72E+00 amps
 * b) 9.57E+00 amps
 * c) 1.05E+01 amps
 * d) 1.15E+01 amps
 * e) 1.26E+01 amps

T5 X1
1) A very long and thin solenoid has 1292 turns and is 122 meters long. The wire carrys a current of 8.4A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 39 meters from the center and stops 75 meters from the center?


 * a) 1.63E+03 A
 * b) 1.78E+03 A
 * c) 1.96E+03 A
 * d) 2.15E+03 A
 * e) 2.35E+03 A

2) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

3) A 82 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 0.459 T. What current is required to maintain this balance?


 * a) 1.956E-01 A
 * b) 2.152E-01 A
 * c) 2.367E-01 A
 * d) 2.604E-01 A
 * e) 2.864E-01 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=2.85 kA, I2=1.8 kA, and I3=4.89 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 3.530E-03 T-m
 * b) 3.883E-03 T-m
 * c) 4.271E-03 T-m
 * d) 4.698E-03 T-m
 * e) 5.168E-03 T-m

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * a) 3.16E+01 amps
 * b) 3.47E+01 amps
 * c) 3.80E+01 amps
 * d) 4.17E+01 amps
 * e) 4.57E+01 amps

7) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?


 * a) 1.434E-10 N/m
 * b) 1.578E-10 N/m
 * c) 1.736E-10 N/m
 * d) 1.909E-10 N/m
 * e) 2.100E-10 N/m

8) A very long and thin solenoid has 2543 turns and is 166 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * a) 1.34E-04 Tesla
 * b) 1.47E-04 Tesla
 * c) 1.62E-04 Tesla
 * d) 1.77E-04 Tesla
 * e) 1.94E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * a) 6.25E+00 amps
 * b) 6.85E+00 amps
 * c) 7.51E+00 amps
 * d) 8.24E+00 amps
 * e) 9.03E+00 amps

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

T5 X2
1) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?


 * a) 1.60E-04 Tesla
 * b) 1.75E-04 Tesla
 * c) 1.92E-04 Tesla
 * d) 2.11E-04 Tesla
 * e) 2.31E-04 Tesla

2) A very long and thin solenoid has 1880 turns and is 166 meters long. The wire carrys a current of 9.2A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 48 meters from the center and stops 102 meters from the center?


 * a) 3.65E+03 A
 * b) 4.00E+03 A
 * c) 4.38E+03 A
 * d) 4.81E+03 A
 * e) 5.27E+03 A

3) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

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=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.724E-03 T-m
 * b) 1.896E-03 T-m
 * c) 2.086E-03 T-m
 * d) 2.295E-03 T-m
 * e) 2.524E-03 T-m

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?


 * a) 1.434E-10 N/m
 * b) 1.578E-10 N/m
 * c) 1.736E-10 N/m
 * d) 1.909E-10 N/m
 * e) 2.100E-10 N/m

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * a) 3.53E+01 amps
 * b) 3.87E+01 amps
 * c) 4.24E+01 amps
 * d) 4.65E+01 amps
 * e) 5.10E+01 amps

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * a) 3.88E+00 amps
 * b) 4.25E+00 amps
 * c) 4.66E+00 amps
 * d) 5.11E+00 amps
 * e) 5.60E+00 amps

10) 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

T5 Y0
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) 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) 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=2.49 kA, I2=0.996 kA, and I3=2.61 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.385E-03 T-m
 * b) 1.524E-03 T-m
 * c) 1.676E-03 T-m
 * d) 1.844E-03 T-m
 * e) 2.028E-03 T-m

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * a) 1.23E-01 A/m
 * b) 1.34E-01 A/m
 * c) 1.47E-01 A/m
 * d) 1.62E-01 A/m
 * e) 1.77E-01 A/m

8) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * a) 2.97E+03 A
 * b) 3.26E+03 A
 * c) 3.57E+03 A
 * d) 3.92E+03 A
 * e) 4.30E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * a) 1.73E+01 amps
 * b) 1.89E+01 amps
 * c) 2.07E+01 amps
 * d) 2.28E+01 amps
 * e) 2.49E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 43A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * a) 1.63E+01 amps
 * b) 1.79E+01 amps
 * c) 1.96E+01 amps
 * d) 2.15E+01 amps
 * e) 2.36E+01 amps

T5 Y1
1) A very long and thin solenoid has 2994 turns and is 180 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 101 meters from the center?


 * a) 6.63E+03 A
 * b) 7.27E+03 A
 * c) 7.97E+03 A
 * d) 8.74E+03 A
 * e) 9.58E+03 A

2) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.1, 8.1) to the point (8.1, 8.1).


 * a) 2.01E+01 amps
 * b) 2.20E+01 amps
 * c) 2.41E+01 amps
 * d) 2.64E+01 amps
 * e) 2.90E+01 amps

4) A wire carries a current of 280 A in a circular arc with radius 2.48 cm swept through 46 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) 2.032E+00 Tesla
 * b) 2.236E+00 Tesla
 * c) 2.459E+00 Tesla
 * d) 2.705E+00 Tesla
 * e) 2.976E+00 Tesla

5) 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * a) 3.37E+01 amps
 * b) 3.70E+01 amps
 * c) 4.06E+01 amps
 * d) 4.45E+01 amps
 * e) 4.88E+01 amps

7) 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

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=2.55 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

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (1.5944,4.101) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 6.86E-02 A/m
 * b) 7.52E-02 A/m
 * c) 8.25E-02 A/m
 * d) 9.04E-02 A/m
 * e) 9.92E-02 A/m

T5 Y2
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) H is defined by, B=&mu;0H, where B is magnetic field. A current of 85A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8) to (+ &infin; ,8).


 * a) 2.94E+01 amps
 * b) 3.22E+01 amps
 * c) 3.53E+01 amps
 * d) 3.88E+01 amps
 * e) 4.25E+01 amps

3) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 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=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * a) 1.133E-03 T-m
 * b) 1.246E-03 T-m
 * c) 1.371E-03 T-m
 * d) 1.508E-03 T-m
 * e) 1.659E-03 T-m

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

6) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * a) 3.84E+03 A
 * b) 4.21E+03 A
 * c) 4.62E+03 A
 * d) 5.06E+03 A
 * e) 5.55E+03 A

7) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * b) 1.413E+00 Tesla
 * c) 1.554E+00 Tesla
 * d) 1.710E+00 Tesla
 * e) 1.881E+00 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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (1.5944,4.101) if a current of 6.9A flows through a wire that runs along the z axis?


 * a) 6.86E-02 A/m
 * b) 7.52E-02 A/m
 * c) 8.25E-02 A/m
 * d) 9.04E-02 A/m
 * e) 9.92E-02 A/m

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.1, 6.1) to the point (6.1, 6.1).


 * a) 1.50E+01 amps
 * b) 1.65E+01 amps
 * c) 1.81E+01 amps
 * d) 1.98E+01 amps
 * e) 2.18E+01 amps

T5 Z0
1) 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

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 3.78 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.43 i + 8.8 j  + 4.16 k) x 104 m/s?


 * a) 1.064E-13 N
 * b) 1.171E-13 N
 * c) 1.288E-13 N
 * d) 1.417E-13 N
 * e) 1.558E-13 N

3) Two parallel wires each carry a 9.68 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.55 cm, 1.79 cm), while the other is located at (3.16 cm, 4.78 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) 5.684E-10 N/m

4) Two loops of wire carry the same current of 88 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.655 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 0.531 m from the first (smaller) loopif the disance between the loops is 1.72 m?


 * a) 4.162E-02 T
 * b) 4.578E-02 T
 * c) 5.036E-02 T
 * d) 5.540E-02 T
 * e) 6.094E-02 T

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

7) A very long and thin solenoid has 1259 turns and is 156 meters long. The wire carrys a current of 8.9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 35 meters from the center and stops 90 meters from the center?


 * a) 2.82E+03 A
 * b) 3.09E+03 A
 * c) 3.39E+03 A
 * d) 3.71E+03 A
 * e) 4.07E+03 A

8) What is the sum of 0.2 apples plus 57 apples?


 * a) 5.72E+01 apples
 * b) 6.27E+01 apples
 * c) 6.88E+01 apples
 * d) 7.54E+01 apples
 * e) 8.27E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.6) to the point (8.6,8.6).


 * a) 4.50E+00 amps
 * b) 4.93E+00 amps
 * c) 5.41E+00 amps
 * d) 5.93E+00 amps
 * e) 6.50E+00 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 63A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.3, 9.3) to the point (9.3, 9.3).


 * a) 1.19E+01 amps
 * b) 1.31E+01 amps
 * c) 1.44E+01 amps
 * d) 1.58E+01 amps
 * e) 1.73E+01 amps

T5 Z1
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) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

3) 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

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 very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * a) 2.97E+03 A
 * b) 3.26E+03 A
 * c) 3.57E+03 A
 * d) 3.92E+03 A
 * e) 4.30E+03 A

6) A torus is centered around the x-y plane, with major radius, a = 3.24 m, and  minor radius, r = 1.35m.  A wire carrying 4.9A is uniformly wrapped with 731 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.81m from the outermost edge of the torus?


 * a) 1.11E+02 amps per meter
 * b) 1.20E+02 amps per meter
 * c) 1.30E+02 amps per meter
 * d) 1.40E+02 amps per meter
 * e) 1.51E+02 amps per meter

7) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?


 * a) 1.973E-10 N/m
 * b) 2.170E-10 N/m
 * c) 2.387E-10 N/m
 * d) 2.625E-10 N/m
 * e) 2.888E-10 N/m

8) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7, 7) to the point (7, 7).


 * a) 9.67E+00 amps
 * b) 1.06E+01 amps
 * c) 1.16E+01 amps
 * d) 1.28E+01 amps
 * e) 1.40E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.2) to the point (7.2,7.2).


 * a) 7.38E+00 amps
 * b) 8.09E+00 amps
 * c) 8.87E+00 amps
 * d) 9.72E+00 amps
 * e) 1.07E+01 amps

T5 Z2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

2) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?


 * a) 5.926E-11 N/m
 * b) 6.518E-11 N/m
 * c) 7.170E-11 N/m
 * d) 7.887E-11 N/m
 * e) 8.676E-11 N/m

3) A very long and thin solenoid has 1409 turns and is 170 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 37 meters from the center and stops 100 meters from the center?


 * a) 2.94E+03 A
 * b) 3.22E+03 A
 * c) 3.53E+03 A
 * d) 3.87E+03 A
 * e) 4.25E+03 A

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,8.4).


 * a) 5.47E+00 amps
 * b) 6.00E+00 amps
 * c) 6.58E+00 amps
 * d) 7.21E+00 amps
 * e) 7.91E+00 amps

6) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * a) 5.31E+01 amps per meter
 * b) 5.73E+01 amps per meter
 * c) 6.19E+01 amps per meter
 * d) 6.68E+01 amps per meter
 * e) 7.21E+01 amps per meter

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * a) 1.21E+01 amps
 * b) 1.33E+01 amps
 * c) 1.46E+01 amps
 * d) 1.60E+01 amps
 * e) 1.75E+01 amps

8) A 11 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 0.809 T. What current is required to maintain this balance?


 * a) 1.432E+00 A
 * b) 1.575E+00 A
 * c) 1.732E+00 A
 * d) 1.905E+00 A
 * e) 2.096E+00 A

9) 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

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 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


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Key: A0
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 4.69 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (8.9 i + 4.27 j  + 7.52 k) x 104 m/s?


 * -a) 5.296E-14 N
 * -b) 5.826E-14 N
 * +c) 6.408E-14 N
 * -d) 7.049E-14 N
 * -e) 7.754E-14 N

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) Three wires sit at the corners of a square of length 0.774 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 (1.57 A, 2.03 A, 2.08 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 7.270E-05 T
 * +b) Bx= 7.997E-05 T
 * -c) Bx= 8.797E-05 T
 * -d) Bx= 9.677E-05 T
 * -e) Bx= 1.064E-04 T

4) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?


 * +a) 2.533E-05 T
 * -b) 2.787E-05 T
 * -c) 3.065E-05 T
 * -d) 3.372E-05 T
 * -e) 3.709E-05 T

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) A very long and thin solenoid has 1016 turns and is 142 meters long. The wire carrys a current of 9.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 27 meters from the center and stops 84 meters from the center?


 * +a) 3.05E+03 A
 * -b) 3.35E+03 A
 * -c) 3.67E+03 A
 * -d) 4.03E+03 A
 * -e) 4.41E+03 A

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * -a) 2.28E-01 A/m
 * +b) 2.50E-01 A/m
 * -c) 2.74E-01 A/m
 * -d) 3.00E-01 A/m
 * -e) 3.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * -a) 1.89E+01 amps
 * +b) 2.08E+01 amps
 * -c) 2.28E+01 amps
 * -d) 2.49E+01 amps
 * -e) 2.74E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * -a) 1.73E+01 amps
 * -b) 1.89E+01 amps
 * -c) 2.07E+01 amps
 * +d) 2.28E+01 amps
 * -e) 2.49E+01 amps

Key: A1
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.2m from a wire carrying a current of 4.8A?


 * -a) 9.35E-02 A/m
 * -b) 1.02E-01 A/m
 * -c) 1.12E-01 A/m
 * +d) 1.23E-01 A/m
 * -e) 1.35E-01 A/m

2) Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * +a) Bx= 7.487E-05 T
 * -b) Bx= 8.236E-05 T
 * -c) Bx= 9.060E-05 T
 * -d) Bx= 9.966E-05 T
 * -e) Bx= 1.096E-04 T

3) 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

4) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * -a) 2.97E+03 A
 * -b) 3.26E+03 A
 * +c) 3.57E+03 A
 * -d) 3.92E+03 A
 * -e) 4.30E+03 A

5) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.83 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (6.16 i + 2.1 j  + 1.74 k) x 104 m/s?


 * -a) 4.783E-14 N
 * +b) 5.262E-14 N
 * -c) 5.788E-14 N
 * -d) 6.367E-14 N
 * -e) 7.003E-14 N

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 37A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * -a) 8.44E+00 amps
 * +b) 9.25E+00 amps
 * -c) 1.01E+01 amps
 * -d) 1.11E+01 amps
 * -e) 1.22E+01 amps

7) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * -a) 1.73E+01 amps
 * -b) 1.89E+01 amps
 * -c) 2.07E+01 amps
 * +d) 2.28E+01 amps
 * -e) 2.49E+01 amps

9) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

10) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.14 mm from the center of a wire of radius 3 mm if the current is 1A?


 * +a) 2.533E-05 T
 * -b) 2.787E-05 T
 * -c) 3.065E-05 T
 * -d) 3.372E-05 T
 * -e) 3.709E-05 T

Key: A2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * -a) 7.96E-02 A/m
 * -b) 8.73E-02 A/m
 * -c) 9.57E-02 A/m
 * -d) 1.05E-01 A/m
 * +e) 1.15E-01 A/m

2) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

3) The silver ribbon shown are a=3.89 cm, b=3.43 cm, and c= 1.21 cm. The current carries a current of 77 A and it lies in a uniform magnetic field of 2.16 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.322E-06 V
 * +b) 1.454E-06 V
 * -c) 1.600E-06 V
 * -d) 1.759E-06 V
 * -e) 1.935E-06 V

4) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 3.78 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.43 i + 8.8 j  + 4.16 k) x 104 m/s?


 * +a) 1.064E-13 N
 * -b) 1.171E-13 N
 * -c) 1.288E-13 N
 * -d) 1.417E-13 N
 * -e) 1.558E-13 N

5) 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

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.1, 8.1) to the point (8.1, 8.1).


 * -a) 2.01E+01 amps
 * +b) 2.20E+01 amps
 * -c) 2.41E+01 amps
 * -d) 2.64E+01 amps
 * -e) 2.90E+01 amps

8) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 78A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.6) to the point (4.6,0).


 * -a) 1.62E+01 amps
 * -b) 1.78E+01 amps
 * +c) 1.95E+01 amps
 * -d) 2.14E+01 amps
 * -e) 2.34E+01 amps

10) A very long and thin solenoid has 2006 turns and is 118 meters long. The wire carrys a current of 9.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 30 meters from the center and stops 78 meters from the center?


 * +a) 4.78E+03 A
 * -b) 5.24E+03 A
 * -c) 5.75E+03 A
 * -d) 6.30E+03 A
 * -e) 6.91E+03 A

Key: B0
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 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

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=2.38 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

4) 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

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.9m from a wire carrying a current of 6.8A?


 * -a) 1.14E-01 A/m
 * -b) 1.25E-01 A/m
 * +c) 1.37E-01 A/m
 * -d) 1.50E-01 A/m
 * -e) 1.65E-01 A/m

8) What is the sum of 0.8 apples plus 18 apples?


 * -a) 1.56E+01 apples
 * -b) 1.71E+01 apples
 * +c) 1.88E+01 apples
 * -d) 2.06E+01 apples
 * -e) 2.26E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.6) to (+ &infin; ,9.6).


 * -a) 3.16E+01 amps
 * -b) 3.47E+01 amps
 * +c) 3.80E+01 amps
 * -d) 4.17E+01 amps
 * -e) 4.57E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * -a) 1.73E+01 amps
 * -b) 1.89E+01 amps
 * -c) 2.07E+01 amps
 * +d) 2.28E+01 amps
 * -e) 2.49E+01 amps

Key: B1
1) What is the sum of 6.6 apples plus 33 apples?


 * -a) 3.61E+01 apples
 * +b) 3.96E+01 apples
 * -c) 4.34E+01 apples
 * -d) 4.76E+01 apples
 * -e) 5.22E+01 apples

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=2.38 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

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,6.9) to (+ &infin; ,6.9).


 * -a) 2.54E+01 amps
 * -b) 2.79E+01 amps
 * -c) 3.06E+01 amps
 * +d) 3.35E+01 amps
 * -e) 3.67E+01 amps

4) 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

5) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * +b) 1.413E+00 Tesla
 * -c) 1.554E+00 Tesla
 * -d) 1.710E+00 Tesla
 * -e) 1.881E+00 Tesla

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * -a) 1.21E+01 amps
 * -b) 1.33E+01 amps
 * -c) 1.46E+01 amps
 * -d) 1.60E+01 amps
 * +e) 1.75E+01 amps

7) A 62 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 0.351 T. What current is required to maintain this balance?


 * -a) 3.999E-01 A
 * -b) 4.398E-01 A
 * -c) 4.838E-01 A
 * -d) 5.322E-01 A
 * +e) 5.854E-01 A

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * -a) 7.96E-02 A/m
 * -b) 8.73E-02 A/m
 * -c) 9.57E-02 A/m
 * -d) 1.05E-01 A/m
 * +e) 1.15E-01 A/m

Key: B2
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=2.72 kA, I2=2.17 kA, and I3=3.21 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 3.905E-03 T-m
 * -b) 4.295E-03 T-m
 * +c) 4.725E-03 T-m
 * -d) 5.197E-03 T-m
 * -e) 5.717E-03 T-m

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * -a) 7.96E-02 A/m
 * -b) 8.73E-02 A/m
 * -c) 9.57E-02 A/m
 * -d) 1.05E-01 A/m
 * +e) 1.15E-01 A/m

3) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * +b) 1.413E+00 Tesla
 * -c) 1.554E+00 Tesla
 * -d) 1.710E+00 Tesla
 * -e) 1.881E+00 Tesla

4) The silver ribbon shown are a=4.65 cm, b=3.43 cm, and c= 1.15 cm. The current carries a current of 279 A and it lies in a uniform magnetic field of 3.48 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 6.100E-06 V
 * -b) 6.710E-06 V
 * -c) 7.381E-06 V
 * -d) 8.120E-06 V
 * +e) 8.931E-06 V

5) 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

6) What is the sum of 0.2 apples plus 57 apples?


 * +a) 5.72E+01 apples
 * -b) 6.27E+01 apples
 * -c) 6.88E+01 apples
 * -d) 7.54E+01 apples
 * -e) 8.27E+01 apples

7) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.7, 5.7) to the point (5.7, 5.7).


 * -a) 1.54E+01 amps
 * -b) 1.69E+01 amps
 * +c) 1.85E+01 amps
 * -d) 2.03E+01 amps
 * -e) 2.22E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 69A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * -a) 2.87E+01 amps
 * -b) 3.15E+01 amps
 * +c) 3.45E+01 amps
 * -d) 3.78E+01 amps
 * -e) 4.15E+01 amps

Key: C0
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 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) 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) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * +c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * -e) 1.29E-01 A/m

8) A very long and thin solenoid has 2662 turns and is 182 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * -a) 1.54E-04 Tesla
 * +b) 1.69E-04 Tesla
 * -c) 1.85E-04 Tesla
 * -d) 2.03E-04 Tesla
 * -e) 2.23E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * -a) 2.32E+01 amps
 * -b) 2.54E+01 amps
 * -c) 2.79E+01 amps
 * -d) 3.06E+01 amps
 * +e) 3.35E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * -a) 1.89E+01 amps
 * +b) 2.08E+01 amps
 * -c) 2.28E+01 amps
 * -d) 2.49E+01 amps
 * -e) 2.74E+01 amps

Key: C1
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 very long and thin solenoid has 1259 turns and is 154 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?


 * +a) 9.25E-05 Tesla
 * -b) 1.01E-04 Tesla
 * -c) 1.11E-04 Tesla
 * -d) 1.22E-04 Tesla
 * -e) 1.34E-04 Tesla

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * -a) 1.28E-01 A/m
 * -b) 1.40E-01 A/m
 * -c) 1.54E-01 A/m
 * +d) 1.68E-01 A/m
 * -e) 1.85E-01 A/m

4) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 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) 3.498E+00 Tesla
 * -b) 3.848E+00 Tesla
 * -c) 4.233E+00 Tesla
 * -d) 4.656E+00 Tesla
 * -e) 5.122E+00 Tesla

5) 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

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,0).


 * +a) 2.28E+01 amps
 * -b) 2.49E+01 amps
 * -c) 2.74E+01 amps
 * -d) 3.00E+01 amps
 * -e) 3.29E+01 amps

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * -a) 3.53E+01 amps
 * -b) 3.87E+01 amps
 * -c) 4.24E+01 amps
 * +d) 4.65E+01 amps
 * -e) 5.10E+01 amps

9) 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

10) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

Key: C2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * -a) 3.37E+01 amps
 * +b) 3.70E+01 amps
 * -c) 4.06E+01 amps
 * -d) 4.45E+01 amps
 * -e) 4.88E+01 amps

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

4) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * -a) 3.863E-02 T
 * +b) 4.249E-02 T
 * -c) 4.674E-02 T
 * -d) 5.141E-02 T
 * -e) 5.655E-02 T

5) 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

6) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * -b) 2.092E+00 Tesla
 * -c) 2.301E+00 Tesla
 * +d) 2.532E+00 Tesla
 * -e) 2.785E+00 Tesla

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * -a) 1.13E-01 A/m
 * -b) 1.24E-01 A/m
 * -c) 1.36E-01 A/m
 * +d) 1.49E-01 A/m
 * -e) 1.63E-01 A/m

8) 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

9) A very long and thin solenoid has 2662 turns and is 182 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * -a) 1.54E-04 Tesla
 * +b) 1.69E-04 Tesla
 * -c) 1.85E-04 Tesla
 * -d) 2.03E-04 Tesla
 * -e) 2.23E-04 Tesla

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 78A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.6) to the point (4.6,0).


 * -a) 1.62E+01 amps
 * -b) 1.78E+01 amps
 * +c) 1.95E+01 amps
 * -d) 2.14E+01 amps
 * -e) 2.34E+01 amps

Key: D0
1) 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

2) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0263 T . It emerges after being deflected by 65&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 8.137E-07 s
 * +b) 8.951E-07 s
 * -c) 9.846E-07 s
 * -d) 1.083E-06 s
 * -e) 1.191E-06 s

3) Two loops of wire carry the same current of 29 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.76 m while the other has a radius of 1.12 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 0.544 m from the first (smaller) loopif the disance between the loops is 1.56 m?


 * +a) 1.950E-02 T
 * -b) 2.145E-02 T
 * -c) 2.360E-02 T
 * -d) 2.596E-02 T
 * -e) 2.855E-02 T

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) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) A very long and thin solenoid has 1409 turns and is 170 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 37 meters from the center and stops 100 meters from the center?


 * -a) 2.94E+03 A
 * +b) 3.22E+03 A
 * -c) 3.53E+03 A
 * -d) 3.87E+03 A
 * -e) 4.25E+03 A

8) A very long and thin solenoid has 1992 turns and is 162 meters long. The wire carrys a current of 8.7A. What is the magnetic field in the center?


 * -a) 1.02E-04 Tesla
 * -b) 1.12E-04 Tesla
 * -c) 1.23E-04 Tesla
 * +d) 1.34E-04 Tesla
 * -e) 1.47E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.1, 6.1) to the point (6.1, 6.1).


 * -a) 1.50E+01 amps
 * -b) 1.65E+01 amps
 * -c) 1.81E+01 amps
 * -d) 1.98E+01 amps
 * +e) 2.18E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 37A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * -a) 8.44E+00 amps
 * +b) 9.25E+00 amps
 * -c) 1.01E+01 amps
 * -d) 1.11E+01 amps
 * -e) 1.22E+01 amps

Key: D1
1) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

2) 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

3) 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

4) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.1) to the point (7.1,0).


 * +a) 2.30E+01 amps
 * -b) 2.52E+01 amps
 * -c) 2.77E+01 amps
 * -d) 3.03E+01 amps
 * -e) 3.32E+01 amps

6) 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

7) A very long and thin solenoid has 1397 turns and is 154 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 31 meters from the center and stops 93 meters from the center?


 * +a) 3.76E+03 A
 * -b) 4.12E+03 A
 * -c) 4.52E+03 A
 * -d) 4.95E+03 A
 * -e) 5.43E+03 A

8) 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

9) A very long and thin solenoid has 2066 turns and is 156 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?


 * -a) 8.75E-05 Tesla
 * -b) 9.59E-05 Tesla
 * -c) 1.05E-04 Tesla
 * -d) 1.15E-04 Tesla
 * +e) 1.26E-04 Tesla

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * -a) 1.21E+01 amps
 * -b) 1.33E+01 amps
 * -c) 1.46E+01 amps
 * -d) 1.60E+01 amps
 * +e) 1.75E+01 amps

Key: D2
1) Three wires sit at the corners of a square of length 0.466 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 (1.4 A, 2.42 A, 1.9 A), respectively. What is the x-component of the magnetic field at point P?


 * +a) Bx= 1.335E-04 T
 * -b) Bx= 1.468E-04 T
 * -c) Bx= 1.615E-04 T
 * -d) Bx= 1.777E-04 T
 * -e) Bx= 1.954E-04 T

2) A very long and thin solenoid has 1992 turns and is 162 meters long. The wire carrys a current of 8.7A. What is the magnetic field in the center?


 * -a) 1.02E-04 Tesla
 * -b) 1.12E-04 Tesla
 * -c) 1.23E-04 Tesla
 * +d) 1.34E-04 Tesla
 * -e) 1.47E-04 Tesla

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.28E+01 amps
 * -b) 1.40E+01 amps
 * -c) 1.54E+01 amps
 * -d) 1.69E+01 amps
 * +e) 1.85E+01 amps

4) A very long and thin solenoid has 1397 turns and is 154 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 31 meters from the center and stops 93 meters from the center?


 * +a) 3.76E+03 A
 * -b) 4.12E+03 A
 * -c) 4.52E+03 A
 * -d) 4.95E+03 A
 * -e) 5.43E+03 A

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 99A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.2) to the point (6.2,0).


 * +a) 2.48E+01 amps
 * -b) 2.71E+01 amps
 * -c) 2.98E+01 amps
 * -d) 3.26E+01 amps
 * -e) 3.58E+01 amps

7) Two loops of wire carry the same current of 44 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.678 m while the other has a radius of 1.14 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 0.508 m from the first (smaller) loopif the disance between the loops is 1.16 m?


 * -a) 3.342E-02 T
 * +b) 3.676E-02 T
 * -c) 4.044E-02 T
 * -d) 4.448E-02 T
 * -e) 4.893E-02 T

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

9) 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

10) 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

Key: E0
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 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

3) 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

4) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * -a) 2.28E-01 A/m
 * +b) 2.50E-01 A/m
 * -c) 2.74E-01 A/m
 * -d) 3.00E-01 A/m
 * -e) 3.29E-01 A/m

8) A very long and thin solenoid has 1016 turns and is 136 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?


 * -a) 5.41E-05 Tesla
 * -b) 5.93E-05 Tesla
 * -c) 6.51E-05 Tesla
 * +d) 7.13E-05 Tesla
 * -e) 7.82E-05 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * -a) 1.89E+01 amps
 * +b) 2.08E+01 amps
 * -c) 2.28E+01 amps
 * -d) 2.49E+01 amps
 * -e) 2.74E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * -a) 1.62E+01 amps
 * +b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.13E+01 amps
 * -e) 2.34E+01 amps

Key: E1
1) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * +b) 1.413E+00 Tesla
 * -c) 1.554E+00 Tesla
 * -d) 1.710E+00 Tesla
 * -e) 1.881E+00 Tesla

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.2m from a wire carrying a current of 4.8A?


 * -a) 9.35E-02 A/m
 * -b) 1.02E-01 A/m
 * -c) 1.12E-01 A/m
 * +d) 1.23E-01 A/m
 * -e) 1.35E-01 A/m

3) 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

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 electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?


 * +a) 1.60E-04 Tesla
 * -b) 1.75E-04 Tesla
 * -c) 1.92E-04 Tesla
 * -d) 2.11E-04 Tesla
 * -e) 2.31E-04 Tesla

7) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 1.21 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.75 i + 9.06 j  + 3.5 k) x 104 m/s?


 * -a) 2.899E-14 N
 * -b) 3.189E-14 N
 * +c) 3.508E-14 N
 * -d) 3.859E-14 N
 * -e) 4.245E-14 N

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * -a) 1.63E+01 amps
 * -b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.14E+01 amps
 * +e) 2.35E+01 amps

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * -a) 1.62E+01 amps
 * +b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.13E+01 amps
 * -e) 2.34E+01 amps

Key: E2
1) 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

2) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.4) to the point (6.4,0).


 * -a) 2.10E+01 amps
 * +b) 2.30E+01 amps
 * -c) 2.52E+01 amps
 * -d) 2.77E+01 amps
 * -e) 3.03E+01 amps

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

5) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 8.8m from a wire carrying a current of 8.6A?


 * +a) 1.56E-01 A/m
 * -b) 1.71E-01 A/m
 * -c) 1.87E-01 A/m
 * -d) 2.05E-01 A/m
 * -e) 2.25E-01 A/m

6) 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

7) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.22 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.85 i + 1.28 j  + 8.49 k) x 104 m/s?


 * -a) 2.222E-14 N
 * -b) 2.444E-14 N
 * -c) 2.688E-14 N
 * +d) 2.957E-14 N
 * -e) 3.253E-14 N

8) A very long and thin solenoid has 2979 turns and is 170 meters long. The wire carrys a current of 8.1A. What is the magnetic field in the center?


 * +a) 1.78E-04 Tesla
 * -b) 1.96E-04 Tesla
 * -c) 2.14E-04 Tesla
 * -d) 2.35E-04 Tesla
 * -e) 2.58E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 77A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.8, 9.8) to the point (9.8, 9.8).


 * -a) 1.60E+01 amps
 * -b) 1.76E+01 amps
 * +c) 1.93E+01 amps
 * -d) 2.11E+01 amps
 * -e) 2.31E+01 amps

10) Three wires sit at the corners of a square of length 0.796 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 (2.48 A, 1.4 A, 1.47 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 4.506E-05 T
 * -b) Bx= 4.957E-05 T
 * +c) Bx= 5.452E-05 T
 * -d) Bx= 5.997E-05 T
 * -e) Bx= 6.597E-05 T

Key: F0
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 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

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 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * +a) Bx= 7.487E-05 T
 * -b) Bx= 8.236E-05 T
 * -c) Bx= 9.060E-05 T
 * -d) Bx= 9.966E-05 T
 * -e) Bx= 1.096E-04 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 cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.1588,1.5958) if a current of 5A flows through a wire that runs along the z axis?


 * +a) 1.41E-01 A/m
 * -b) 1.54E-01 A/m
 * -c) 1.69E-01 A/m
 * -d) 1.86E-01 A/m
 * -e) 2.03E-01 A/m

8) A very long and thin solenoid has 1965 turns and is 136 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 88 meters from the center?


 * +a) 2.75E+03 A
 * -b) 3.01E+03 A
 * -c) 3.30E+03 A
 * -d) 3.62E+03 A
 * -e) 3.97E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).


 * -a) 9.34E+00 amps
 * -b) 1.02E+01 amps
 * -c) 1.12E+01 amps
 * -d) 1.23E+01 amps
 * +e) 1.35E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * +a) 6.25E+00 amps
 * -b) 6.85E+00 amps
 * -c) 7.51E+00 amps
 * -d) 8.24E+00 amps
 * -e) 9.03E+00 amps

Key: F1
1) 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

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 3.41 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

3) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * +a) 3.88E+00 amps
 * -b) 4.25E+00 amps
 * -c) 4.66E+00 amps
 * -d) 5.11E+00 amps
 * -e) 5.60E+00 amps

6) 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

7) A very long and thin solenoid has 2850 turns and is 164 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 108 meters from the center?


 * -a) 5.16E+03 A
 * +b) 5.66E+03 A
 * -c) 6.20E+03 A
 * -d) 6.80E+03 A
 * -e) 7.46E+03 A

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.3) to the point (9.3,0).


 * +a) 2.18E+01 amps
 * -b) 2.38E+01 amps
 * -c) 2.61E+01 amps
 * -d) 2.87E+01 amps
 * -e) 3.14E+01 amps

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?


 * -a) 1.75E-01 A/m
 * -b) 1.92E-01 A/m
 * +c) 2.11E-01 A/m
 * -d) 2.31E-01 A/m
 * -e) 2.53E-01 A/m

10) Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * +a) Bx= 7.487E-05 T
 * -b) Bx= 8.236E-05 T
 * -c) Bx= 9.060E-05 T
 * -d) Bx= 9.966E-05 T
 * -e) Bx= 1.096E-04 T

Key: F2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * +c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * -e) 1.29E-01 A/m

2) 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

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

4) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * -a) 3.84E+03 A
 * -b) 4.21E+03 A
 * -c) 4.62E+03 A
 * +d) 5.06E+03 A
 * -e) 5.55E+03 A

5) 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.4) to the point (6.4,0).


 * -a) 2.10E+01 amps
 * +b) 2.30E+01 amps
 * -c) 2.52E+01 amps
 * -d) 2.77E+01 amps
 * -e) 3.03E+01 amps

7) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 1.21 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.75 i + 9.06 j  + 3.5 k) x 104 m/s?


 * -a) 2.899E-14 N
 * -b) 3.189E-14 N
 * +c) 3.508E-14 N
 * -d) 3.859E-14 N
 * -e) 4.245E-14 N

8) 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

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * -a) 7.68E+00 amps
 * -b) 8.42E+00 amps
 * -c) 9.23E+00 amps
 * +d) 1.01E+01 amps
 * -e) 1.11E+01 amps

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

Key: G0
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 0.232 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

2) 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

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) 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

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.6m from a wire carrying a current of 9.8A?


 * -a) 2.57E-01 A/m
 * -b) 2.82E-01 A/m
 * -c) 3.09E-01 A/m
 * +d) 3.39E-01 A/m
 * -e) 3.72E-01 A/m

8) What is the sum of 6.6 apples plus 33 apples?


 * -a) 3.61E+01 apples
 * +b) 3.96E+01 apples
 * -c) 4.34E+01 apples
 * -d) 4.76E+01 apples
 * -e) 5.22E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * -a) 1.21E+01 amps
 * -b) 1.33E+01 amps
 * -c) 1.46E+01 amps
 * -d) 1.60E+01 amps
 * +e) 1.75E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * +a) 6.25E+00 amps
 * -b) 6.85E+00 amps
 * -c) 7.51E+00 amps
 * -d) 8.24E+00 amps
 * -e) 9.03E+00 amps

Key: G1
1) 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

2) What is the sum of 0.2 apples plus 57 apples?


 * +a) 5.72E+01 apples
 * -b) 6.27E+01 apples
 * -c) 6.88E+01 apples
 * -d) 7.54E+01 apples
 * -e) 8.27E+01 apples

3) 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

4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 65A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 4.9, 4.9) to the point (4.9, 4.9).


 * -a) 1.23E+01 amps
 * -b) 1.35E+01 amps
 * -c) 1.48E+01 amps
 * +d) 1.63E+01 amps
 * -e) 1.78E+01 amps

7) A wire carries a current of 266 A in a circular arc with radius 2.21 cm swept through 73 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) 5.034E+00 Tesla
 * -b) 5.538E+00 Tesla
 * -c) 6.091E+00 Tesla
 * -d) 6.701E+00 Tesla
 * -e) 7.371E+00 Tesla

8) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?


 * -a) 2.588E-10 N/m
 * +b) 2.847E-10 N/m
 * -c) 3.131E-10 N/m
 * -d) 3.444E-10 N/m
 * -e) 3.789E-10 N/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 9.77E+00 amps
 * -b) 1.07E+01 amps
 * +c) 1.18E+01 amps
 * -d) 1.29E+01 amps
 * -e) 1.41E+01 amps

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * -a) 2.28E-01 A/m
 * +b) 2.50E-01 A/m
 * -c) 2.74E-01 A/m
 * -d) 3.00E-01 A/m
 * -e) 3.29E-01 A/m

Key: G2
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 0.157 m and a magneticfield of 0.512 T. What is their maximum kinetic energy?


 * -a) 2.574E-01 MeV
 * -b) 2.831E-01 MeV
 * +c) 3.114E-01 MeV
 * -d) 3.425E-01 MeV
 * -e) 3.768E-01 MeV

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.55E+01 amps
 * +b) 1.70E+01 amps
 * -c) 1.86E+01 amps
 * -d) 2.04E+01 amps
 * -e) 2.24E+01 amps

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,8.4).


 * -a) 5.47E+00 amps
 * +b) 6.00E+00 amps
 * -c) 6.58E+00 amps
 * -d) 7.21E+00 amps
 * -e) 7.91E+00 amps

4) 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

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) 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

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 7.9A?


 * -a) 2.73E-01 A/m
 * +b) 2.99E-01 A/m
 * -c) 3.28E-01 A/m
 * -d) 3.60E-01 A/m
 * -e) 3.95E-01 A/m

8) A wire carries a current of 353 A in a circular arc with radius 2.44 cm swept through 86 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) 5.891E+00 Tesla
 * -b) 6.481E+00 Tesla
 * +c) 7.129E+00 Tesla
 * -d) 7.841E+00 Tesla
 * -e) 8.626E+00 Tesla

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

10) What is the sum of 7.2 apples plus 9 apples?


 * +a) 1.62E+01 apples
 * -b) 1.78E+01 apples
 * -c) 1.95E+01 apples
 * -d) 2.14E+01 apples
 * -e) 2.34E+01 apples

Key: H0
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) 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

3) Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.397E-05 T
 * +b) Bx= 7.037E-05 T
 * -c) Bx= 7.740E-05 T
 * -d) Bx= 8.514E-05 T
 * -e) Bx= 9.366E-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) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.6m from a wire carrying a current of 9.8A?


 * -a) 2.57E-01 A/m
 * -b) 2.82E-01 A/m
 * -c) 3.09E-01 A/m
 * +d) 3.39E-01 A/m
 * -e) 3.72E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * +c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * -e) 1.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.8, 5.8) to the point (5.8, 5.8).


 * -a) 1.78E+01 amps
 * -b) 1.95E+01 amps
 * -c) 2.14E+01 amps
 * +d) 2.35E+01 amps
 * -e) 2.58E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 39A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.5) to the point (8.5,8.5).


 * +a) 4.88E+00 amps
 * -b) 5.35E+00 amps
 * -c) 5.86E+00 amps
 * -d) 6.43E+00 amps
 * -e) 7.05E+00 amps

Key: H1
1) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

2) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 63A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.3, 9.3) to the point (9.3, 9.3).


 * -a) 1.19E+01 amps
 * -b) 1.31E+01 amps
 * -c) 1.44E+01 amps
 * +d) 1.58E+01 amps
 * -e) 1.73E+01 amps

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.2097,1.9209) if a current of 4.7A flows through a wire that runs along the z axis?


 * -a) 8.34E-02 A/m
 * -b) 9.14E-02 A/m
 * -c) 1.00E-01 A/m
 * +d) 1.10E-01 A/m
 * -e) 1.21E-01 A/m

5) Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.397E-05 T
 * +b) Bx= 7.037E-05 T
 * -c) Bx= 7.740E-05 T
 * -d) Bx= 8.514E-05 T
 * -e) Bx= 9.366E-05 T

6) 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

7) 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

8) 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 5.46 mT and 1.710E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 3.132E+05 m/s
 * -b) 3.445E+05 m/s
 * -c) 3.790E+05 m/s
 * -d) 4.169E+05 m/s
 * -e) 4.585E+05 m/s

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 5.4m from a wire carrying a current of 5A?


 * -a) 1.34E-01 A/m
 * +b) 1.47E-01 A/m
 * -c) 1.62E-01 A/m
 * -d) 1.77E-01 A/m
 * -e) 1.94E-01 A/m

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * -a) 7.44E+00 amps
 * -b) 8.15E+00 amps
 * -c) 8.94E+00 amps
 * -d) 9.80E+00 amps
 * +e) 1.08E+01 amps

Key: H2
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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.7m from a wire carrying a current of 4.8A?


 * +a) 9.92E-02 A/m
 * -b) 1.09E-01 A/m
 * -c) 1.19E-01 A/m
 * -d) 1.31E-01 A/m
 * -e) 1.43E-01 A/m

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.28E+01 amps
 * -b) 1.40E+01 amps
 * -c) 1.54E+01 amps
 * -d) 1.69E+01 amps
 * +e) 1.85E+01 amps

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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * -a) 1.23E-01 A/m
 * -b) 1.34E-01 A/m
 * -c) 1.47E-01 A/m
 * +d) 1.62E-01 A/m
 * -e) 1.77E-01 A/m

7) 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

8) 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

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 8.72E+00 amps
 * -b) 9.57E+00 amps
 * -c) 1.05E+01 amps
 * +d) 1.15E+01 amps
 * -e) 1.26E+01 amps

Key: I0
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) The silver ribbon shown are a=3.89 cm, b=3.43 cm, and c= 1.21 cm. The current carries a current of 77 A and it lies in a uniform magnetic field of 2.16 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 1.322E-06 V
 * +b) 1.454E-06 V
 * -c) 1.600E-06 V
 * -d) 1.759E-06 V
 * -e) 1.935E-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=2.55 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

4) Three wires sit at the corners of a square of length 0.823 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 (2.41 A, 1.87 A, 2.21 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 6.718E-05 T
 * -b) By= 7.390E-05 T
 * +c) By= 8.129E-05 T
 * -d) By= 8.942E-05 T
 * -e) By= 9.836E-05 T

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * -a) 5.31E+01 amps per meter
 * -b) 5.73E+01 amps per meter
 * -c) 6.19E+01 amps per meter
 * -d) 6.68E+01 amps per meter
 * +e) 7.21E+01 amps per meter

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.1m from a wire carrying a current of 5.8A?


 * -a) 1.38E-01 A/m
 * +b) 1.51E-01 A/m
 * -c) 1.66E-01 A/m
 * -d) 1.82E-01 A/m
 * -e) 1.99E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * -a) 1.73E+01 amps
 * -b) 1.89E+01 amps
 * -c) 2.07E+01 amps
 * +d) 2.28E+01 amps
 * -e) 2.49E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 9.77E+00 amps
 * -b) 1.07E+01 amps
 * +c) 1.18E+01 amps
 * -d) 1.29E+01 amps
 * -e) 1.41E+01 amps

Key: I1
1) The silver ribbon shown are a=3.96 cm, b=3.35 cm, and c= 1.07 cm. The current carries a current of 295 A and it lies in a uniform magnetic field of 3.4 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.


 * -a) 9.015E-06 V
 * +b) 9.916E-06 V
 * -c) 1.091E-05 V
 * -d) 1.200E-05 V
 * -e) 1.320E-05 V

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=2.48 kA, I2=1.47 kA, and I3=2.6 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 1.420E-03 T-m
 * -b) 1.562E-03 T-m
 * -c) 1.718E-03 T-m
 * -d) 1.890E-03 T-m
 * -e) 2.079E-03 T-m

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 38A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,6.7).


 * -a) 4.33E+00 amps
 * +b) 4.75E+00 amps
 * -c) 5.21E+00 amps
 * -d) 5.71E+00 amps
 * -e) 6.26E+00 amps

4) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

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 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 2.656E+05 m/s
 * -b) 2.922E+05 m/s
 * +c) 3.214E+05 m/s
 * -d) 3.535E+05 m/s
 * -e) 3.889E+05 m/s

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.28E+01 amps
 * -b) 1.40E+01 amps
 * -c) 1.54E+01 amps
 * -d) 1.69E+01 amps
 * +e) 1.85E+01 amps

8) What is the sum of 7.2 apples plus 9 apples?


 * +a) 1.62E+01 apples
 * -b) 1.78E+01 apples
 * -c) 1.95E+01 apples
 * -d) 2.14E+01 apples
 * -e) 2.34E+01 apples

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 9.9m from a wire carrying a current of 6.9A?


 * +a) 1.11E-01 A/m
 * -b) 1.22E-01 A/m
 * -c) 1.33E-01 A/m
 * -d) 1.46E-01 A/m
 * -e) 1.60E-01 A/m

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

Key: I2
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.55E+01 amps
 * +b) 1.70E+01 amps
 * -c) 1.86E+01 amps
 * -d) 2.04E+01 amps
 * -e) 2.24E+01 amps

2) What is the sum of 0.8 apples plus 18 apples?


 * -a) 1.56E+01 apples
 * -b) 1.71E+01 apples
 * +c) 1.88E+01 apples
 * -d) 2.06E+01 apples
 * -e) 2.26E+01 apples

3) Three wires sit at the corners of a square of length 0.834 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 (2.26 A, 1.75 A, 2.47 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 7.518E-05 T
 * -b) By= 8.270E-05 T
 * -c) By= 9.097E-05 T
 * -d) By= 1.001E-04 T
 * -e) By= 1.101E-04 T

4) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

5) 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

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.1m from a wire carrying a current of 5.8A?


 * -a) 1.38E-01 A/m
 * +b) 1.51E-01 A/m
 * -c) 1.66E-01 A/m
 * -d) 1.82E-01 A/m
 * -e) 1.99E-01 A/m

8) 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 5.46 mT and 1.710E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 3.132E+05 m/s
 * -b) 3.445E+05 m/s
 * -c) 3.790E+05 m/s
 * -d) 4.169E+05 m/s
 * -e) 4.585E+05 m/s

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.6) to the point (6.6,6.6).


 * -a) 9.15E+00 amps
 * -b) 1.00E+01 amps
 * +c) 1.10E+01 amps
 * -d) 1.21E+01 amps
 * -e) 1.32E+01 amps

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=2.44 kA, I2=1.1 kA, and I3=1.99 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.017E-03 T-m
 * +b) 1.118E-03 T-m
 * -c) 1.230E-03 T-m
 * -d) 1.353E-03 T-m
 * -e) 1.489E-03 T-m

Key: J0
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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 5.554E+05 m/s
 * -b) 6.110E+05 m/s
 * -c) 6.720E+05 m/s
 * -d) 7.393E+05 m/s
 * -e) 8.132E+05 m/s

2) 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

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 $$a=$$ 0.51 m and $$B_{max}=\,$$ 0.649 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.376 m that is centered on the axis with its plane perpendicular to the axis?


 * -a) 9.388E+05 A
 * -b) 1.033E+06 A
 * +c) 1.136E+06 A
 * -d) 1.249E+06 A
 * -e) 1.374E+06 A

4) 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

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 9.6A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 9.8m.


 * -a) 4.26E+01 m
 * -b) 4.67E+01 m
 * -c) 5.12E+01 m
 * -d) 5.62E+01 m
 * +e) 6.16E+01 m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.5m from a wire carrying a current of 4.7A?


 * -a) 7.96E-02 A/m
 * -b) 8.73E-02 A/m
 * -c) 9.57E-02 A/m
 * -d) 1.05E-01 A/m
 * +e) 1.15E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.6) to the point (8.6,8.6).


 * +a) 4.50E+00 amps
 * -b) 4.93E+00 amps
 * -c) 5.41E+00 amps
 * -d) 5.93E+00 amps
 * -e) 6.50E+00 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 96A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 2.00E+01 amps
 * -b) 2.19E+01 amps
 * +c) 2.40E+01 amps
 * -d) 2.63E+01 amps
 * -e) 2.89E+01 amps

Key: J1
1) 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

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * -a) 2.28E-01 A/m
 * +b) 2.50E-01 A/m
 * -c) 2.74E-01 A/m
 * -d) 3.00E-01 A/m
 * -e) 3.29E-01 A/m

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 $$a=$$ 0.547 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

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,8.4).


 * -a) 5.47E+00 amps
 * +b) 6.00E+00 amps
 * -c) 6.58E+00 amps
 * -d) 7.21E+00 amps
 * -e) 7.91E+00 amps

5) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 5.8A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 4.4m.


 * -a) 2.30E+01 m
 * -b) 2.52E+01 m
 * +c) 2.76E+01 m
 * -d) 3.03E+01 m
 * -e) 3.32E+01 m

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 4.66 mT and 2.860E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 5.072E+05 m/s
 * -b) 5.579E+05 m/s
 * +c) 6.137E+05 m/s
 * -d) 6.751E+05 m/s
 * -e) 7.426E+05 m/s

7) 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

8) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.7, 5.7) to the point (5.7, 5.7).


 * -a) 1.54E+01 amps
 * -b) 1.69E+01 amps
 * +c) 1.85E+01 amps
 * -d) 2.03E+01 amps
 * -e) 2.22E+01 amps

Key: J2
1) 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

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 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

3) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * -a) 1.62E+01 amps
 * +b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.13E+01 amps
 * -e) 2.34E+01 amps

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * -a) 2.28E-01 A/m
 * +b) 2.50E-01 A/m
 * -c) 2.74E-01 A/m
 * -d) 3.00E-01 A/m
 * -e) 3.29E-01 A/m

7) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 6.9A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 9.9m.


 * +a) 6.22E+01 m
 * -b) 6.82E+01 m
 * -c) 7.48E+01 m
 * -d) 8.20E+01 m
 * -e) 8.99E+01 m

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) 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

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * -a) 7.44E+00 amps
 * -b) 8.15E+00 amps
 * -c) 8.94E+00 amps
 * -d) 9.80E+00 amps
 * +e) 1.08E+01 amps

Key: K0
1) A 57 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 0.447 T. What current is required to maintain this balance?


 * -a) 2.225E-01 A
 * -b) 2.448E-01 A
 * +c) 2.692E-01 A
 * -d) 2.962E-01 A
 * -e) 3.258E-01 A

2) 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

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=2.5 kA, I2=1.53 kA, and I3=2.34 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * +a) 1.018E-03 T-m
 * -b) 1.120E-03 T-m
 * -c) 1.232E-03 T-m
 * -d) 1.355E-03 T-m
 * -e) 1.490E-03 T-m

4) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 17 turns per centimeter and the current applied to the solenoid is 331 mA, the net magnetic field is measured to be 1.24 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 1.593E+03
 * +b) $$\chi \text{ (chi) }=$$ 1.753E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.928E+03
 * -d) $$\chi \text{ (chi) }=$$ 2.121E+03
 * -e) $$\chi \text{ (chi) }=$$ 2.333E+03

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) What is the sum of 0.8 apples plus 18 apples?


 * -a) 1.56E+01 apples
 * -b) 1.71E+01 apples
 * +c) 1.88E+01 apples
 * -d) 2.06E+01 apples
 * -e) 2.26E+01 apples

8) A very long and thin solenoid has 2219 turns and is 134 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * -a) 2.41E+03 A
 * -b) 2.64E+03 A
 * +c) 2.89E+03 A
 * -d) 3.17E+03 A
 * -e) 3.48E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7, 7) to the point (7, 7).


 * -a) 9.67E+00 amps
 * -b) 1.06E+01 amps
 * -c) 1.16E+01 amps
 * +d) 1.28E+01 amps
 * -e) 1.40E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * -a) 3.37E+01 amps
 * +b) 3.70E+01 amps
 * -c) 4.06E+01 amps
 * -d) 4.45E+01 amps
 * -e) 4.88E+01 amps

Key: K1
1) A 82 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 0.459 T. What current is required to maintain this balance?


 * -a) 1.956E-01 A
 * -b) 2.152E-01 A
 * -c) 2.367E-01 A
 * -d) 2.604E-01 A
 * +e) 2.864E-01 A

2) 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

3) A circular current loop of radius 3.04 cm carries a current of 1.94 mA. What is the magnitude of the torque if the dipole is oriented at 50 &deg; to a uniform magnetic fied of 0.193 T?


 * -a) 6.257E-07 N m
 * -b) 6.882E-07 N m
 * -c) 7.570E-07 N m
 * +d) 8.327E-07 N m
 * -e) 9.160E-07 N m

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7.4, 7.4) to the point (7.4, 7.4).


 * -a) 1.69E+01 amps
 * +b) 1.85E+01 amps
 * -c) 2.03E+01 amps
 * -d) 2.22E+01 amps
 * -e) 2.44E+01 amps

5) What is the sum of 3.4 apples plus 62 apples?


 * -a) 4.96E+01 apples
 * -b) 5.44E+01 apples
 * -c) 5.96E+01 apples
 * +d) 6.54E+01 apples
 * -e) 7.17E+01 apples

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 66A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.5) to (+ &infin; ,5.5).


 * -a) 3.01E+01 amps
 * +b) 3.30E+01 amps
 * -c) 3.62E+01 amps
 * -d) 3.97E+01 amps
 * -e) 4.35E+01 amps

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=2.84 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

9) A very long and thin solenoid has 2850 turns and is 164 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 108 meters from the center?


 * -a) 5.16E+03 A
 * +b) 5.66E+03 A
 * -c) 6.20E+03 A
 * -d) 6.80E+03 A
 * -e) 7.46E+03 A

10) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

Key: K2
1) 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

2) A very long and thin solenoid has 1016 turns and is 142 meters long. The wire carrys a current of 9.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 27 meters from the center and stops 84 meters from the center?


 * +a) 3.05E+03 A
 * -b) 3.35E+03 A
 * -c) 3.67E+03 A
 * -d) 4.03E+03 A
 * -e) 4.41E+03 A

3) 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 265 mA, the net magnetic field is measured to be 1.11 T. What is the magnetic susceptibility for this case?


 * -a) $$\chi \text{ (chi) }=$$ 1.376E+03
 * +b) $$\chi \text{ (chi) }=$$ 1.514E+03
 * -c) $$\chi \text{ (chi) }=$$ 1.666E+03
 * -d) $$\chi \text{ (chi) }=$$ 1.832E+03
 * -e) $$\chi \text{ (chi) }=$$ 2.015E+03

4) A torus is centered around the x-y plane, with major radius, a = 3.24 m, and  minor radius, r = 1.35m.  A wire carrying 4.9A is uniformly wrapped with 731 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.81m from the outermost edge of the torus?


 * +a) 1.11E+02 amps per meter
 * -b) 1.20E+02 amps per meter
 * -c) 1.30E+02 amps per meter
 * -d) 1.40E+02 amps per meter
 * -e) 1.51E+02 amps per meter

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=2.55 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 77A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.8, 9.8) to the point (9.8, 9.8).


 * -a) 1.60E+01 amps
 * -b) 1.76E+01 amps
 * +c) 1.93E+01 amps
 * -d) 2.11E+01 amps
 * -e) 2.31E+01 amps

7) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * -a) 3.37E+01 amps
 * +b) 3.70E+01 amps
 * -c) 4.06E+01 amps
 * -d) 4.45E+01 amps
 * -e) 4.88E+01 amps

9) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

10) 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: L0
1) 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

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) 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

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (7.9293,2.4528) if a current of 7.3A flows through a wire that runs along the z axis?


 * -a) 1.11E-01 A/m
 * -b) 1.22E-01 A/m
 * +c) 1.34E-01 A/m
 * -d) 1.47E-01 A/m
 * -e) 1.61E-01 A/m

8) A very long and thin solenoid has 1946 turns and is 144 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?


 * -a) 1.06E-04 Tesla
 * -b) 1.16E-04 Tesla
 * -c) 1.27E-04 Tesla
 * -d) 1.39E-04 Tesla
 * +e) 1.53E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * -a) 7.44E+00 amps
 * -b) 8.15E+00 amps
 * -c) 8.94E+00 amps
 * -d) 9.80E+00 amps
 * +e) 1.08E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * -a) 3.53E+01 amps
 * -b) 3.87E+01 amps
 * -c) 4.24E+01 amps
 * +d) 4.65E+01 amps
 * -e) 5.10E+01 amps

Key: L1
1) Three wires sit at the corners of a square of length 0.785 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 (2.23 A, 1.52 A, 1.86 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 4.559E-05 T
 * -b) Bx= 5.015E-05 T
 * -c) Bx= 5.517E-05 T
 * -d) Bx= 6.068E-05 T
 * +e) Bx= 6.675E-05 T

2) 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

3) A very long and thin solenoid has 1259 turns and is 154 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?


 * +a) 9.25E-05 Tesla
 * -b) 1.01E-04 Tesla
 * -c) 1.11E-04 Tesla
 * -d) 1.22E-04 Tesla
 * -e) 1.34E-04 Tesla

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * -a) 3.53E+01 amps
 * -b) 3.87E+01 amps
 * -c) 4.24E+01 amps
 * +d) 4.65E+01 amps
 * -e) 5.10E+01 amps

5) 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

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 46A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * -a) 5.24E+00 amps
 * +b) 5.75E+00 amps
 * -c) 6.30E+00 amps
 * -d) 6.91E+00 amps
 * -e) 7.58E+00 amps

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.0898,3.6432) if a current of 4.9A flows through a wire that runs along the z axis?


 * -a) 6.39E-02 A/m
 * -b) 7.01E-02 A/m
 * -c) 7.68E-02 A/m
 * -d) 8.43E-02 A/m
 * +e) 9.24E-02 A/m

Key: L2
1) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?


 * +a) 7.623E-03 T
 * -b) 8.385E-03 T
 * -c) 9.223E-03 T
 * -d) 1.015E-02 T
 * -e) 1.116E-02 T

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * -a) 7.44E+00 amps
 * -b) 8.15E+00 amps
 * -c) 8.94E+00 amps
 * -d) 9.80E+00 amps
 * +e) 1.08E+01 amps

3) 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

4) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.0898,3.6432) if a current of 7.9A flows through a wire that runs along the z axis?


 * -a) 1.36E-01 A/m
 * +b) 1.49E-01 A/m
 * -c) 1.63E-01 A/m
 * -d) 1.79E-01 A/m
 * -e) 1.96E-01 A/m

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,6.9) to (+ &infin; ,6.9).


 * -a) 2.54E+01 amps
 * -b) 2.79E+01 amps
 * -c) 3.06E+01 amps
 * +d) 3.35E+01 amps
 * -e) 3.67E+01 amps

9) A very long and thin solenoid has 2662 turns and is 182 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * -a) 1.54E-04 Tesla
 * +b) 1.69E-04 Tesla
 * -c) 1.85E-04 Tesla
 * -d) 2.03E-04 Tesla
 * -e) 2.23E-04 Tesla

10) 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

Key: M0
1) 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

2) 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

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) 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

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 7.9A?


 * -a) 2.73E-01 A/m
 * +b) 2.99E-01 A/m
 * -c) 3.28E-01 A/m
 * -d) 3.60E-01 A/m
 * -e) 3.95E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.2097,1.9209) if a current of 4.7A flows through a wire that runs along the z axis?


 * -a) 8.34E-02 A/m
 * -b) 9.14E-02 A/m
 * -c) 1.00E-01 A/m
 * +d) 1.10E-01 A/m
 * -e) 1.21E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 83A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.4) to the point (7.4,0).


 * -a) 1.89E+01 amps
 * +b) 2.08E+01 amps
 * -c) 2.28E+01 amps
 * -d) 2.49E+01 amps
 * -e) 2.74E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.55E+01 amps
 * +b) 1.70E+01 amps
 * -c) 1.86E+01 amps
 * -d) 2.04E+01 amps
 * -e) 2.24E+01 amps

Key: M1
1) 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

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 4.9A?


 * -a) 1.28E-01 A/m
 * -b) 1.41E-01 A/m
 * -c) 1.54E-01 A/m
 * -d) 1.69E-01 A/m
 * +e) 1.86E-01 A/m

3) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.8, 6.8) to the point (6.8, 6.8).


 * -a) 1.06E+01 amps
 * -b) 1.16E+01 amps
 * +c) 1.28E+01 amps
 * -d) 1.40E+01 amps
 * -e) 1.53E+01 amps

5) 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

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.3) to the point (9.3,0).


 * +a) 2.18E+01 amps
 * -b) 2.38E+01 amps
 * -c) 2.61E+01 amps
 * -d) 2.87E+01 amps
 * -e) 3.14E+01 amps

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * -a) 1.13E-01 A/m
 * -b) 1.24E-01 A/m
 * -c) 1.36E-01 A/m
 * +d) 1.49E-01 A/m
 * -e) 1.63E-01 A/m

9) A wire carries a current of 109 A in a circular arc with radius 1.26 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) 2.908E+00 Tesla
 * -b) 3.199E+00 Tesla
 * +c) 3.519E+00 Tesla
 * -d) 3.871E+00 Tesla
 * -e) 4.258E+00 Tesla

10) 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: M2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 6.9A?


 * -a) 2.28E-01 A/m
 * +b) 2.50E-01 A/m
 * -c) 2.74E-01 A/m
 * -d) 3.00E-01 A/m
 * -e) 3.29E-01 A/m

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).


 * -a) 1.55E+01 amps
 * +b) 1.70E+01 amps
 * -c) 1.86E+01 amps
 * -d) 2.04E+01 amps
 * -e) 2.24E+01 amps

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (9.3623,2.8961) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * +c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * -e) 1.29E-01 A/m

4) 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

5) A wire carries a current of 250 A in a circular arc with radius 2.17 cm swept through 53 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) 3.498E+00 Tesla
 * -b) 3.848E+00 Tesla
 * -c) 4.233E+00 Tesla
 * -d) 4.656E+00 Tesla
 * -e) 5.122E+00 Tesla

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.1) to the point (7.1,0).


 * +a) 2.30E+01 amps
 * -b) 2.52E+01 amps
 * -c) 2.77E+01 amps
 * -d) 3.03E+01 amps
 * -e) 3.32E+01 amps

7) 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

8) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

9) 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

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

Key: N0
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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 5.554E+05 m/s
 * -b) 6.110E+05 m/s
 * -c) 6.720E+05 m/s
 * -d) 7.393E+05 m/s
 * -e) 8.132E+05 m/s

2) 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

3) Three wires sit at the corners of a square of length 0.547 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 (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 6.118E-05 T
 * -b) By= 6.730E-05 T
 * -c) By= 7.403E-05 T
 * -d) By= 8.144E-05 T
 * +e) By= 8.958E-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 $$a=$$ 0.432 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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.2104,5.6854) if a current of 5.8A flows through a wire that runs along the z axis?


 * -a) 4.16E-02 A/m
 * -b) 4.56E-02 A/m
 * -c) 5.00E-02 A/m
 * +d) 5.48E-02 A/m
 * -e) 6.01E-02 A/m

8) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * -a) 5.31E+01 amps per meter
 * -b) 5.73E+01 amps per meter
 * -c) 6.19E+01 amps per meter
 * -d) 6.68E+01 amps per meter
 * +e) 7.21E+01 amps per meter

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9) to (+ &infin; ,9).


 * -a) 3.08E+01 amps
 * -b) 3.37E+01 amps
 * +c) 3.70E+01 amps
 * -d) 4.06E+01 amps
 * -e) 4.45E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * +a) 6.25E+00 amps
 * -b) 6.85E+00 amps
 * -c) 7.51E+00 amps
 * -d) 8.24E+00 amps
 * -e) 9.03E+00 amps

Key: N1
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 5.49 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

2) Three wires sit at the corners of a square of length 0.547 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 (1.78 A, 1.34 A, 1.64 A), respectively. What is the y-component of the magnetic field at point P?


 * -a) By= 6.118E-05 T
 * -b) By= 6.730E-05 T
 * -c) By= 7.403E-05 T
 * -d) By= 8.144E-05 T
 * +e) By= 8.958E-05 T

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * +a) 3.88E+00 amps
 * -b) 4.25E+00 amps
 * -c) 4.66E+00 amps
 * -d) 5.11E+00 amps
 * -e) 5.60E+00 amps

4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

5) 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

6) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.3551,4.3477) if a current of 4.8A flows through a wire that runs along the z axis?


 * +a) 8.19E-02 A/m
 * -b) 8.98E-02 A/m
 * -c) 9.84E-02 A/m
 * -d) 1.08E-01 A/m
 * -e) 1.18E-01 A/m

7) 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

8) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 69A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * -a) 2.87E+01 amps
 * -b) 3.15E+01 amps
 * +c) 3.45E+01 amps
 * -d) 3.78E+01 amps
 * -e) 4.15E+01 amps

10) What is the sum of 7.2 apples plus 9 apples?


 * +a) 1.62E+01 apples
 * -b) 1.78E+01 apples
 * -c) 1.95E+01 apples
 * -d) 2.14E+01 apples
 * -e) 2.34E+01 apples

Key: N2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

2) Three wires sit at the corners of a square of length 0.591 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 (2.47 A, 2.1 A, 2.24 A), respectively. What is the y-component of the magnetic field at point P?


 * +a) By= 1.191E-04 T
 * -b) By= 1.310E-04 T
 * -c) By= 1.441E-04 T
 * -d) By= 1.585E-04 T
 * -e) By= 1.744E-04 T

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 42A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.2) to the point (4.2,4.2).


 * -a) 3.98E+00 amps
 * -b) 4.37E+00 amps
 * -c) 4.79E+00 amps
 * +d) 5.25E+00 amps
 * -e) 5.76E+00 amps

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * -a) 3.53E+01 amps
 * -b) 3.87E+01 amps
 * -c) 4.24E+01 amps
 * +d) 4.65E+01 amps
 * -e) 5.10E+01 amps

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) 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

7) 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 7.67 mT and 4.260E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 5.554E+05 m/s
 * -b) 6.110E+05 m/s
 * -c) 6.720E+05 m/s
 * -d) 7.393E+05 m/s
 * -e) 8.132E+05 m/s

8) What is the sum of 3.4 apples plus 62 apples?


 * -a) 4.96E+01 apples
 * -b) 5.44E+01 apples
 * -c) 5.96E+01 apples
 * +d) 6.54E+01 apples
 * -e) 7.17E+01 apples

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * -a) 1.23E-01 A/m
 * -b) 1.34E-01 A/m
 * -c) 1.47E-01 A/m
 * +d) 1.62E-01 A/m
 * -e) 1.77E-01 A/m

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

Key: O0
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 0.378 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

2) 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

3) Two parallel wires each carry a 6.53 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.82 cm, 1.17 cm), while the other is located at (4.07 cm, 5.5 cm). What is the force per unit length between the wires?


 * -a) 1.788E-10 N/m
 * +b) 1.966E-10 N/m
 * -c) 2.163E-10 N/m
 * -d) 2.379E-10 N/m
 * -e) 2.617E-10 N/m

4) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * -a) 5.31E+01 amps per meter
 * -b) 5.73E+01 amps per meter
 * -c) 6.19E+01 amps per meter
 * -d) 6.68E+01 amps per meter
 * +e) 7.21E+01 amps per meter

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * -c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * +e) 1.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).


 * -a) 9.34E+00 amps
 * -b) 1.02E+01 amps
 * -c) 1.12E+01 amps
 * -d) 1.23E+01 amps
 * +e) 1.35E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * -a) 1.62E+01 amps
 * +b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.13E+01 amps
 * -e) 2.34E+01 amps

Key: O1
1) 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

2) 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

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * -a) 1.28E-01 A/m
 * -b) 1.40E-01 A/m
 * -c) 1.54E-01 A/m
 * +d) 1.68E-01 A/m
 * -e) 1.85E-01 A/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 0.449 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 55A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.7) to the point (8.7,0).


 * +a) 1.38E+01 amps
 * -b) 1.51E+01 amps
 * -c) 1.65E+01 amps
 * -d) 1.81E+01 amps
 * -e) 1.99E+01 amps

7) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * -a) 5.31E+01 amps per meter
 * -b) 5.73E+01 amps per meter
 * -c) 6.19E+01 amps per meter
 * -d) 6.68E+01 amps per meter
 * +e) 7.21E+01 amps per meter

8) Two parallel wires each carry a 9.59 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.97 cm, 1.4 cm), while the other is located at (4.02 cm, 5.19 cm). What is the force per unit length between the wires?


 * -a) 4.412E-10 N/m
 * +b) 4.853E-10 N/m
 * -c) 5.338E-10 N/m
 * -d) 5.872E-10 N/m
 * -e) 6.459E-10 N/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * -a) 1.62E+01 amps
 * +b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.13E+01 amps
 * -e) 2.34E+01 amps

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

Key: O2
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 82A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.3, 9.3) to the point (9.3, 9.3).


 * +a) 2.05E+01 amps
 * -b) 2.25E+01 amps
 * -c) 2.46E+01 amps
 * -d) 2.70E+01 amps
 * -e) 2.96E+01 amps

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 0.449 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

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.4963,2.0095) if a current of 6.5A flows through a wire that runs along the z axis?


 * -a) 1.33E-01 A/m
 * +b) 1.45E-01 A/m
 * -c) 1.59E-01 A/m
 * -d) 1.75E-01 A/m
 * -e) 1.92E-01 A/m

4) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

5) 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,0).


 * -a) 1.63E+01 amps
 * -b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.14E+01 amps
 * +e) 2.35E+01 amps

7) 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

8) What is the sum of 3.4 apples plus 62 apples?


 * -a) 4.96E+01 apples
 * -b) 5.44E+01 apples
 * -c) 5.96E+01 apples
 * +d) 6.54E+01 apples
 * -e) 7.17E+01 apples

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

10) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?


 * -a) 1.973E-10 N/m
 * -b) 2.170E-10 N/m
 * -c) 2.387E-10 N/m
 * -d) 2.625E-10 N/m
 * +e) 2.888E-10 N/m

Key: P0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.061 T . It emerges after being deflected by 75&deg; from its original direction. How much time did it spend in that magnetic field?


 * +a) 4.453E-07 s
 * -b) 4.898E-07 s
 * -c) 5.388E-07 s
 * -d) 5.927E-07 s
 * -e) 6.519E-07 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 3.34 mT and 7.430E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 1.671E+06 m/s
 * -b) 1.838E+06 m/s
 * -c) 2.022E+06 m/s
 * +d) 2.225E+06 m/s
 * -e) 2.447E+06 m/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=2.46 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) A solenoid has 4.900E+04 turns wound around a cylinder of diameter 1.74 cm and length 19 m. The current through the coils is 0.432 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;4.18 cm to z=+1.77 cm


 * -a) 6.884E-05 T-m
 * -b) 7.573E-05 T-m
 * +c) 8.330E-05 T-m
 * -d) 9.163E-05 T-m
 * -e) 1.008E-04 T-m

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?


 * -a) 1.06E-01 A/m
 * -b) 1.16E-01 A/m
 * -c) 1.28E-01 A/m
 * -d) 1.40E-01 A/m
 * +e) 1.54E-01 A/m

8) What is the sum of 0.8 apples plus 18 apples?


 * -a) 1.56E+01 apples
 * -b) 1.71E+01 apples
 * +c) 1.88E+01 apples
 * -d) 2.06E+01 apples
 * -e) 2.26E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 49A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.8) to the point (9.8,9.8).


 * +a) 6.13E+00 amps
 * -b) 6.72E+00 amps
 * -c) 7.36E+00 amps
 * -d) 8.07E+00 amps
 * -e) 8.85E+00 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 65A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 4.9, 4.9) to the point (4.9, 4.9).


 * -a) 1.23E+01 amps
 * -b) 1.35E+01 amps
 * -c) 1.48E+01 amps
 * +d) 1.63E+01 amps
 * -e) 1.78E+01 amps

Key: P1
1) 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

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=2.42 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

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.1539,7.7549) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 5.23E-02 A/m
 * -b) 5.74E-02 A/m
 * -c) 6.29E-02 A/m
 * +d) 6.90E-02 A/m
 * -e) 7.56E-02 A/m

4) What is the sum of 0.2 apples plus 57 apples?


 * +a) 5.72E+01 apples
 * -b) 6.27E+01 apples
 * -c) 6.88E+01 apples
 * -d) 7.54E+01 apples
 * -e) 8.27E+01 apples

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 33A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.6, 6.6) to the point (6.6, 6.6).


 * -a) 5.71E+00 amps
 * -b) 6.26E+00 amps
 * -c) 6.86E+00 amps
 * -d) 7.52E+00 amps
 * +e) 8.25E+00 amps

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 38A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,6.7).


 * -a) 4.33E+00 amps
 * +b) 4.75E+00 amps
 * -c) 5.21E+00 amps
 * -d) 5.71E+00 amps
 * -e) 6.26E+00 amps

7) 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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 8.971E+05 m/s
 * -b) 9.868E+05 m/s
 * -c) 1.085E+06 m/s
 * +d) 1.194E+06 m/s
 * -e) 1.313E+06 m/s

8) 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

9) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

10) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

Key: P2
1) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

2) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

3) 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

4) What is the sum of 7.2 apples plus 9 apples?


 * +a) 1.62E+01 apples
 * -b) 1.78E+01 apples
 * -c) 1.95E+01 apples
 * -d) 2.14E+01 apples
 * -e) 2.34E+01 apples

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=2.84 kA, I2=3.3 kA, and I3=5.85 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 5.598E-03 T-m
 * -b) 6.158E-03 T-m
 * +c) 6.773E-03 T-m
 * -d) 7.451E-03 T-m
 * -e) 8.196E-03 T-m

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 3.34 mT and 7.430E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 1.671E+06 m/s
 * -b) 1.838E+06 m/s
 * -c) 2.022E+06 m/s
 * +d) 2.225E+06 m/s
 * -e) 2.447E+06 m/s

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.2) to the point (7.2,7.2).


 * +a) 7.38E+00 amps
 * -b) 8.09E+00 amps
 * -c) 8.87E+00 amps
 * -d) 9.72E+00 amps
 * -e) 1.07E+01 amps

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7.4, 7.4) to the point (7.4, 7.4).


 * -a) 1.69E+01 amps
 * +b) 1.85E+01 amps
 * -c) 2.03E+01 amps
 * -d) 2.22E+01 amps
 * -e) 2.44E+01 amps

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?


 * -a) 1.06E-01 A/m
 * -b) 1.16E-01 A/m
 * -c) 1.28E-01 A/m
 * -d) 1.40E-01 A/m
 * +e) 1.54E-01 A/m

Key: Q0
1) 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

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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 8.971E+05 m/s
 * -b) 9.868E+05 m/s
 * -c) 1.085E+06 m/s
 * +d) 1.194E+06 m/s
 * -e) 1.313E+06 m/s

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) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?


 * +a) 7.623E-03 T
 * -b) 8.385E-03 T
 * -c) 9.223E-03 T
 * -d) 1.015E-02 T
 * -e) 1.116E-02 T

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.2097,1.9209) if a current of 4.7A flows through a wire that runs along the z axis?


 * -a) 8.34E-02 A/m
 * -b) 9.14E-02 A/m
 * -c) 1.00E-01 A/m
 * +d) 1.10E-01 A/m
 * -e) 1.21E-01 A/m

8) A very long and thin solenoid has 2472 turns and is 144 meters long. The wire carrys a current of 8.4A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 87 meters from the center?


 * -a) 3.17E+03 A
 * -b) 3.48E+03 A
 * -c) 3.81E+03 A
 * +d) 4.18E+03 A
 * -e) 4.59E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * -a) 3.25E+01 amps
 * -b) 3.57E+01 amps
 * -c) 3.91E+01 amps
 * -d) 4.29E+01 amps
 * +e) 4.70E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.1) to the point (4.1,0).


 * -a) 1.28E+01 amps
 * -b) 1.40E+01 amps
 * -c) 1.54E+01 amps
 * -d) 1.69E+01 amps
 * +e) 1.85E+01 amps

Key: Q1
1) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * -b) 2.092E+00 Tesla
 * -c) 2.301E+00 Tesla
 * +d) 2.532E+00 Tesla
 * -e) 2.785E+00 Tesla

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * -a) 1.28E-01 A/m
 * -b) 1.40E-01 A/m
 * -c) 1.54E-01 A/m
 * +d) 1.68E-01 A/m
 * -e) 1.85E-01 A/m

3) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,6.9) to (+ &infin; ,6.9).


 * -a) 2.54E+01 amps
 * -b) 2.79E+01 amps
 * -c) 3.06E+01 amps
 * +d) 3.35E+01 amps
 * -e) 3.67E+01 amps

5) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * -a) 4.908E+00 N/m
 * +b) 5.399E+00 N/m
 * -c) 5.939E+00 N/m
 * -d) 6.533E+00 N/m
 * -e) 7.186E+00 N/m

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 1.85 mT and 5.080E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * +a) 2.746E+06 m/s
 * -b) 3.021E+06 m/s
 * -c) 3.323E+06 m/s
 * -d) 3.655E+06 m/s
 * -e) 4.020E+06 m/s

7) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 85A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.8) to the point (9.8,0).


 * -a) 1.77E+01 amps
 * -b) 1.94E+01 amps
 * +c) 2.13E+01 amps
 * -d) 2.33E+01 amps
 * -e) 2.55E+01 amps

9) 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

10) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * -a) 3.84E+03 A
 * -b) 4.21E+03 A
 * -c) 4.62E+03 A
 * +d) 5.06E+03 A
 * -e) 5.55E+03 A

Key: Q2
1) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * -a) 3.863E-02 T
 * +b) 4.249E-02 T
 * -c) 4.674E-02 T
 * -d) 5.141E-02 T
 * -e) 5.655E-02 T

2) 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

3) 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 6.97 mT and 2.240E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 2.656E+05 m/s
 * -b) 2.922E+05 m/s
 * +c) 3.214E+05 m/s
 * -d) 3.535E+05 m/s
 * -e) 3.889E+05 m/s

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 99A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.2) to the point (6.2,0).


 * +a) 2.48E+01 amps
 * -b) 2.71E+01 amps
 * -c) 2.98E+01 amps
 * -d) 3.26E+01 amps
 * -e) 3.58E+01 amps

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 44A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5) to (+ &infin; ,5).


 * -a) 1.67E+01 amps
 * -b) 1.83E+01 amps
 * -c) 2.01E+01 amps
 * +d) 2.20E+01 amps
 * -e) 2.41E+01 amps

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * -a) 1.23E-01 A/m
 * -b) 1.34E-01 A/m
 * -c) 1.47E-01 A/m
 * +d) 1.62E-01 A/m
 * -e) 1.77E-01 A/m

8) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * -a) 2.97E+03 A
 * -b) 3.26E+03 A
 * +c) 3.57E+03 A
 * -d) 3.92E+03 A
 * -e) 4.30E+03 A

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

10) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * -a) 4.908E+00 N/m
 * +b) 5.399E+00 N/m
 * -c) 5.939E+00 N/m
 * -d) 6.533E+00 N/m
 * -e) 7.186E+00 N/m

Key: R0
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 long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * -a) 4.908E+00 N/m
 * +b) 5.399E+00 N/m
 * -c) 5.939E+00 N/m
 * -d) 6.533E+00 N/m
 * -e) 7.186E+00 N/m

3) Two loops of wire carry the same current of 11 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.424 m while the other has a radius of 1.32 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 0.52 m from the first (smaller) loopif the disance between the loops is 1.25 m?


 * +a) 7.623E-03 T
 * -b) 8.385E-03 T
 * -c) 9.223E-03 T
 * -d) 1.015E-02 T
 * -e) 1.116E-02 T

4) 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

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * -c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * +e) 1.29E-01 A/m

8) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 7.9A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 4.2m.


 * -a) 1.83E+01 m
 * -b) 2.00E+01 m
 * -c) 2.19E+01 m
 * -d) 2.41E+01 m
 * +e) 2.64E+01 m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 5.8, 5.8) to the point (5.8, 5.8).


 * -a) 1.78E+01 amps
 * -b) 1.95E+01 amps
 * -c) 2.14E+01 amps
 * +d) 2.35E+01 amps
 * -e) 2.58E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * -a) 3.16E+01 amps
 * -b) 3.47E+01 amps
 * +c) 3.80E+01 amps
 * -d) 4.17E+01 amps
 * -e) 4.57E+01 amps

Key: R1
1) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 71A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.6, 8.6) to the point (8.6, 8.6).


 * -a) 1.62E+01 amps
 * +b) 1.78E+01 amps
 * -c) 1.95E+01 amps
 * -d) 2.13E+01 amps
 * -e) 2.34E+01 amps

3) 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

4) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.3) to (+ &infin; ,8.3).


 * -a) 1.50E+01 amps
 * -b) 1.64E+01 amps
 * +c) 1.80E+01 amps
 * -d) 1.97E+01 amps
 * -e) 2.16E+01 amps

5) 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

6) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.848 m while the other has a radius of 1.42 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 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?


 * -a) 7.952E-03 T
 * -b) 8.747E-03 T
 * -c) 9.622E-03 T
 * -d) 1.058E-02 T
 * +e) 1.164E-02 T

7) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

8) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 6.5A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 6.8m.


 * +a) 4.27E+01 m
 * -b) 4.68E+01 m
 * -c) 5.14E+01 m
 * -d) 5.63E+01 m
 * -e) 6.18E+01 m

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?


 * -a) 1.75E-01 A/m
 * -b) 1.92E-01 A/m
 * +c) 2.11E-01 A/m
 * -d) 2.31E-01 A/m
 * -e) 2.53E-01 A/m

10) 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

Key: R2
1) 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

2) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * -a) 3.863E-02 T
 * +b) 4.249E-02 T
 * -c) 4.674E-02 T
 * -d) 5.141E-02 T
 * -e) 5.655E-02 T

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.7803,5.3849) if a current of 6.8A flows through a wire that runs along the z axis?


 * -a) 6.93E-02 A/m
 * -b) 7.60E-02 A/m
 * -c) 8.34E-02 A/m
 * -d) 9.14E-02 A/m
 * +e) 1.00E-01 A/m

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) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * -a) 3.25E+01 amps
 * -b) 3.57E+01 amps
 * -c) 3.91E+01 amps
 * -d) 4.29E+01 amps
 * +e) 4.70E+01 amps

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.1, 6.1) to the point (6.1, 6.1).


 * -a) 1.50E+01 amps
 * -b) 1.65E+01 amps
 * -c) 1.81E+01 amps
 * -d) 1.98E+01 amps
 * +e) 2.18E+01 amps

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

10) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 9.6A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 9.8m.


 * -a) 4.26E+01 m
 * -b) 4.67E+01 m
 * -c) 5.12E+01 m
 * -d) 5.62E+01 m
 * +e) 6.16E+01 m

Key: S0
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 4.36 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (8.25 i + 7.71 j  + 2.91 k) x 104 m/s?


 * -a) 8.890E-14 N
 * -b) 9.779E-14 N
 * +c) 1.076E-13 N
 * -d) 1.183E-13 N
 * -e) 1.302E-13 N

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 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * -a) 3.863E-02 T
 * +b) 4.249E-02 T
 * -c) 4.674E-02 T
 * -d) 5.141E-02 T
 * -e) 5.655E-02 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 $$a=$$ 0.353 m and $$B_{max}=\,$$ 0.697 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) 5.479E+05 A
 * -b) 6.027E+05 A
 * -c) 6.630E+05 A
 * -d) 7.293E+05 A
 * -e) 8.022E+05 A

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

7) What is the sum of 0.8 apples plus 18 apples?


 * -a) 1.56E+01 apples
 * -b) 1.71E+01 apples
 * +c) 1.88E+01 apples
 * -d) 2.06E+01 apples
 * -e) 2.26E+01 apples

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?


 * -a) 8.90E-02 A/m
 * -b) 9.76E-02 A/m
 * -c) 1.07E-01 A/m
 * -d) 1.17E-01 A/m
 * +e) 1.29E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 8.72E+00 amps
 * -b) 9.57E+00 amps
 * -c) 1.05E+01 amps
 * +d) 1.15E+01 amps
 * -e) 1.26E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * -a) 1.21E+01 amps
 * -b) 1.33E+01 amps
 * -c) 1.46E+01 amps
 * -d) 1.60E+01 amps
 * +e) 1.75E+01 amps

Key: S1
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * -a) 7.68E+00 amps
 * -b) 8.42E+00 amps
 * -c) 9.23E+00 amps
 * +d) 1.01E+01 amps
 * -e) 1.11E+01 amps

2) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

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 5.75 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.81 i + 2.05 j  + 4.49 k) x 104 m/s?


 * -a) 2.576E-14 N
 * -b) 2.834E-14 N
 * -c) 3.117E-14 N
 * -d) 3.429E-14 N
 * +e) 3.772E-14 N

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (6.4963,2.0095) if a current of 6.5A flows through a wire that runs along the z axis?


 * -a) 1.33E-01 A/m
 * +b) 1.45E-01 A/m
 * -c) 1.59E-01 A/m
 * -d) 1.75E-01 A/m
 * -e) 1.92E-01 A/m

5) What is the sum of 3.4 apples plus 62 apples?


 * -a) 4.96E+01 apples
 * -b) 5.44E+01 apples
 * -c) 5.96E+01 apples
 * +d) 6.54E+01 apples
 * -e) 7.17E+01 apples

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7, 7) to the point (7, 7).


 * -a) 9.67E+00 amps
 * -b) 1.06E+01 amps
 * -c) 1.16E+01 amps
 * +d) 1.28E+01 amps
 * -e) 1.40E+01 amps

7) 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

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 $$a=$$ 0.547 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

9) Two loops of wire carry the same current of 64 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.838 m while the other has a radius of 1.17 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 0.528 m from the first (smaller) loopif the disance between the loops is 1.62 m?


 * -a) 3.863E-02 T
 * +b) 4.249E-02 T
 * -c) 4.674E-02 T
 * -d) 5.141E-02 T
 * -e) 5.655E-02 T

10) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

Key: S2
1) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7.4, 7.4) to the point (7.4, 7.4).


 * -a) 1.69E+01 amps
 * +b) 1.85E+01 amps
 * -c) 2.03E+01 amps
 * -d) 2.22E+01 amps
 * -e) 2.44E+01 amps

3) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

4) What is the sum of 0.2 apples plus 57 apples?


 * +a) 5.72E+01 apples
 * -b) 6.27E+01 apples
 * -c) 6.88E+01 apples
 * -d) 7.54E+01 apples
 * -e) 8.27E+01 apples

5) Two loops of wire carry the same current of 18 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.848 m while the other has a radius of 1.42 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 0.625 m from the first (smaller) loopif the disance between the loops is 1.55 m?


 * -a) 7.952E-03 T
 * -b) 8.747E-03 T
 * -c) 9.622E-03 T
 * -d) 1.058E-02 T
 * +e) 1.164E-02 T

6) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 7.22 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (2.85 i + 1.28 j  + 8.49 k) x 104 m/s?


 * -a) 2.222E-14 N
 * -b) 2.444E-14 N
 * -c) 2.688E-14 N
 * +d) 2.957E-14 N
 * -e) 3.253E-14 N

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 58A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.5) to the point (8.5,8.5).


 * -a) 6.03E+00 amps
 * -b) 6.61E+00 amps
 * +c) 7.25E+00 amps
 * -d) 7.95E+00 amps
 * -e) 8.72E+00 amps

9) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.783 T magnetic field is directed 77&deg; away from the wire?


 * -a) 3.648E+00 N/m
 * -b) 4.012E+00 N/m
 * -c) 4.414E+00 N/m
 * -d) 4.855E+00 N/m
 * +e) 5.341E+00 N/m

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * -a) 1.13E-01 A/m
 * -b) 1.24E-01 A/m
 * -c) 1.36E-01 A/m
 * +d) 1.49E-01 A/m
 * -e) 1.63E-01 A/m

Key: T0
1) A 97 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 0.753 T. What current is required to maintain this balance?


 * -a) 7.056E-02 A
 * -b) 7.762E-02 A
 * -c) 8.538E-02 A
 * +d) 9.392E-02 A
 * -e) 1.033E-01 A

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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 8.971E+05 m/s
 * -b) 9.868E+05 m/s
 * -c) 1.085E+06 m/s
 * +d) 1.194E+06 m/s
 * -e) 1.313E+06 m/s

3) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?


 * +a) 1.434E-10 N/m
 * -b) 1.578E-10 N/m
 * -c) 1.736E-10 N/m
 * -d) 1.909E-10 N/m
 * -e) 2.100E-10 N/m

4) 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

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) A very long and thin solenoid has 2543 turns and is 166 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * -a) 1.34E-04 Tesla
 * -b) 1.47E-04 Tesla
 * -c) 1.62E-04 Tesla
 * +d) 1.77E-04 Tesla
 * -e) 1.94E-04 Tesla

8) A very long and thin solenoid has 1292 turns and is 122 meters long. The wire carrys a current of 8.4A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 39 meters from the center and stops 75 meters from the center?


 * -a) 1.63E+03 A
 * -b) 1.78E+03 A
 * +c) 1.96E+03 A
 * -d) 2.15E+03 A
 * -e) 2.35E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * -a) 7.44E+00 amps
 * -b) 8.15E+00 amps
 * -c) 8.94E+00 amps
 * -d) 9.80E+00 amps
 * +e) 1.08E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * +a) 1.55E+01 amps
 * -b) 1.70E+01 amps
 * -c) 1.86E+01 amps
 * -d) 2.04E+01 amps
 * -e) 2.24E+01 amps

Key: T1
1) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.81 mm from the center of a wire of radius 3 mm if the current is 1A?


 * -a) 3.324E-05 T
 * -b) 3.657E-05 T
 * +c) 4.022E-05 T
 * -d) 4.424E-05 T
 * -e) 4.867E-05 T

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.4) to (+ &infin; ,9.4).


 * -a) 2.32E+01 amps
 * -b) 2.54E+01 amps
 * -c) 2.79E+01 amps
 * -d) 3.06E+01 amps
 * +e) 3.35E+01 amps

3) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

4) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

5) 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

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 2.68 mT and 3.200E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 8.971E+05 m/s
 * -b) 9.868E+05 m/s
 * -c) 1.085E+06 m/s
 * +d) 1.194E+06 m/s
 * -e) 1.313E+06 m/s

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 8.72E+00 amps
 * -b) 9.57E+00 amps
 * -c) 1.05E+01 amps
 * +d) 1.15E+01 amps
 * -e) 1.26E+01 amps

8) A very long and thin solenoid has 1982 turns and is 154 meters long. The wire carrys a current of 9.1A. What is the magnetic field in the center?


 * -a) 1.12E-04 Tesla
 * -b) 1.22E-04 Tesla
 * -c) 1.34E-04 Tesla
 * +d) 1.47E-04 Tesla
 * -e) 1.61E-04 Tesla

9) A very long and thin solenoid has 1259 turns and is 156 meters long. The wire carrys a current of 8.9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 35 meters from the center and stops 90 meters from the center?


 * -a) 2.82E+03 A
 * +b) 3.09E+03 A
 * -c) 3.39E+03 A
 * -d) 3.71E+03 A
 * -e) 4.07E+03 A

10) Two parallel wires each carry a 7.75 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.62 cm, 1.31 cm), while the other is located at (4.63 cm, 5.53 cm). What is the force per unit length between the wires?


 * -a) 2.588E-10 N/m
 * +b) 2.847E-10 N/m
 * -c) 3.131E-10 N/m
 * -d) 3.444E-10 N/m
 * -e) 3.789E-10 N/m

Key: T2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

2) A 82 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 0.459 T. What current is required to maintain this balance?


 * -a) 1.956E-01 A
 * -b) 2.152E-01 A
 * -c) 2.367E-01 A
 * -d) 2.604E-01 A
 * +e) 2.864E-01 A

3) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * -a) 3.84E+03 A
 * -b) 4.21E+03 A
 * -c) 4.62E+03 A
 * +d) 5.06E+03 A
 * -e) 5.55E+03 A

4) 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 4.66 mT and 2.860E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?


 * -a) 5.072E+05 m/s
 * -b) 5.579E+05 m/s
 * +c) 6.137E+05 m/s
 * -d) 6.751E+05 m/s
 * -e) 7.426E+05 m/s

5) A very long and thin solenoid has 2175 turns and is 134 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?


 * -a) 1.29E-04 Tesla
 * -b) 1.41E-04 Tesla
 * +c) 1.55E-04 Tesla
 * -d) 1.70E-04 Tesla
 * -e) 1.86E-04 Tesla

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 8.72E+00 amps
 * -b) 9.57E+00 amps
 * -c) 1.05E+01 amps
 * +d) 1.15E+01 amps
 * -e) 1.26E+01 amps

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 85A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8) to (+ &infin; ,8).


 * -a) 2.94E+01 amps
 * -b) 3.22E+01 amps
 * -c) 3.53E+01 amps
 * -d) 3.88E+01 amps
 * +e) 4.25E+01 amps

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

10) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.03 mm from the center of a wire of radius 3 mm if the current is 1A?


 * -a) 1.720E-05 T
 * -b) 1.892E-05 T
 * -c) 2.081E-05 T
 * +d) 2.289E-05 T
 * -e) 2.518E-05 T

Key: U0
1) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0482 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 4.629E-07 s
 * -b) 5.092E-07 s
 * -c) 5.601E-07 s
 * +d) 6.161E-07 s
 * -e) 6.777E-07 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 0.157 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

3) Three wires sit at the corners of a square of length 0.739 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 (1.93 A, 2.48 A, 1.36 A), respectively. What is the x-component of the magnetic field at point P?


 * -a) Bx= 6.397E-05 T
 * +b) Bx= 7.037E-05 T
 * -c) Bx= 7.740E-05 T
 * -d) Bx= 8.514E-05 T
 * -e) Bx= 9.366E-05 T

4) Two parallel wires each carry a 2.58 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.79 cm, 1.03 cm), while the other is located at (5.64 cm, 5.12 cm). What is the force per unit length between the wires?


 * -a) 2.634E-11 N/m
 * -b) 2.897E-11 N/m
 * +c) 3.187E-11 N/m
 * -d) 3.506E-11 N/m
 * -e) 3.856E-11 N/m

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 5.8A?


 * -a) 1.91E-01 A/m
 * +b) 2.10E-01 A/m
 * -c) 2.30E-01 A/m
 * -d) 2.52E-01 A/m
 * -e) 2.77E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * -a) 1.28E-01 A/m
 * -b) 1.40E-01 A/m
 * -c) 1.54E-01 A/m
 * +d) 1.68E-01 A/m
 * -e) 1.85E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.2) to the point (7.2,7.2).


 * +a) 7.38E+00 amps
 * -b) 8.09E+00 amps
 * -c) 8.87E+00 amps
 * -d) 9.72E+00 amps
 * -e) 1.07E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).


 * -a) 9.34E+00 amps
 * -b) 1.02E+01 amps
 * -c) 1.12E+01 amps
 * -d) 1.23E+01 amps
 * +e) 1.35E+01 amps

Key: U1
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?


 * -a) 1.75E-01 A/m
 * -b) 1.92E-01 A/m
 * +c) 2.11E-01 A/m
 * -d) 2.31E-01 A/m
 * -e) 2.53E-01 A/m

2) 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

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 55A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.7) to the point (8.7,0).


 * +a) 1.38E+01 amps
 * -b) 1.51E+01 amps
 * -c) 1.65E+01 amps
 * -d) 1.81E+01 amps
 * -e) 1.99E+01 amps

4) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0482 T . It emerges after being deflected by 82&deg; from its original direction. How much time did it spend in that magnetic field?


 * -a) 4.629E-07 s
 * -b) 5.092E-07 s
 * -c) 5.601E-07 s
 * +d) 6.161E-07 s
 * -e) 6.777E-07 s

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 42A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.2) to the point (4.2,4.2).


 * -a) 3.98E+00 amps
 * -b) 4.37E+00 amps
 * -c) 4.79E+00 amps
 * +d) 5.25E+00 amps
 * -e) 5.76E+00 amps

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 0.388 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

9) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.9m from a wire carrying a current of 6.8A?


 * -a) 1.14E-01 A/m
 * -b) 1.25E-01 A/m
 * +c) 1.37E-01 A/m
 * -d) 1.50E-01 A/m
 * -e) 1.65E-01 A/m

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

Key: U2
1) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * -a) 1.13E-01 A/m
 * -b) 1.24E-01 A/m
 * -c) 1.36E-01 A/m
 * +d) 1.49E-01 A/m
 * -e) 1.63E-01 A/m

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 9.77E+00 amps
 * -b) 1.07E+01 amps
 * +c) 1.18E+01 amps
 * -d) 1.29E+01 amps
 * -e) 1.41E+01 amps

3) Three wires sit at the corners of a square of length 0.784 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 (1.19 A, 1.51 A, 2.18 A), respectively. What is the x-component of the magnetic field at point P?


 * +a) Bx= 7.487E-05 T
 * -b) Bx= 8.236E-05 T
 * -c) Bx= 9.060E-05 T
 * -d) Bx= 9.966E-05 T
 * -e) Bx= 1.096E-04 T

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 8.2m from a wire carrying a current of 7.2A?


 * -a) 9.67E-02 A/m
 * -b) 1.06E-01 A/m
 * -c) 1.16E-01 A/m
 * -d) 1.27E-01 A/m
 * +e) 1.40E-01 A/m

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 0.118 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

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

8) 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

9) 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

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.4) to the point (6.4,0).


 * -a) 2.10E+01 amps
 * +b) 2.30E+01 amps
 * -c) 2.52E+01 amps
 * -d) 2.77E+01 amps
 * -e) 3.03E+01 amps

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) 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) 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) 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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.6m from a wire carrying a current of 9.8A?


 * -a) 2.57E-01 A/m
 * -b) 2.82E-01 A/m
 * -c) 3.09E-01 A/m
 * +d) 3.39E-01 A/m
 * -e) 3.72E-01 A/m

8) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * -a) 2.97E+03 A
 * -b) 3.26E+03 A
 * +c) 3.57E+03 A
 * -d) 3.92E+03 A
 * -e) 4.30E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.1) to the point (4.1,0).


 * -a) 1.28E+01 amps
 * -b) 1.40E+01 amps
 * -c) 1.54E+01 amps
 * -d) 1.69E+01 amps
 * +e) 1.85E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 38A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,6.7).


 * -a) 4.33E+00 amps
 * +b) 4.75E+00 amps
 * -c) 5.21E+00 amps
 * -d) 5.71E+00 amps
 * -e) 6.26E+00 amps

Key: V1
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=2.31 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

2) 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

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 46A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * -a) 5.24E+00 amps
 * +b) 5.75E+00 amps
 * -c) 6.30E+00 amps
 * -d) 6.91E+00 amps
 * -e) 7.58E+00 amps

4) A long rigid wire carries a 7 A current. What is the magnetic force per unit length on the wire if a 0.851 T magnetic field is directed 65&deg; away from the wire?


 * -a) 4.908E+00 N/m
 * +b) 5.399E+00 N/m
 * -c) 5.939E+00 N/m
 * -d) 6.533E+00 N/m
 * -e) 7.186E+00 N/m

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 0.157 m and a magneticfield of 0.512 T. What is their maximum kinetic energy?


 * -a) 2.574E-01 MeV
 * -b) 2.831E-01 MeV
 * +c) 3.114E-01 MeV
 * -d) 3.425E-01 MeV
 * -e) 3.768E-01 MeV

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.4m from a wire carrying a current of 5.8A?


 * -a) 1.91E-01 A/m
 * +b) 2.10E-01 A/m
 * -c) 2.30E-01 A/m
 * -d) 2.52E-01 A/m
 * -e) 2.77E-01 A/m

8) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

9) A very long and thin solenoid has 1397 turns and is 154 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 31 meters from the center and stops 93 meters from the center?


 * +a) 3.76E+03 A
 * -b) 4.12E+03 A
 * -c) 4.52E+03 A
 * -d) 4.95E+03 A
 * -e) 5.43E+03 A

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.1) to the point (4.1,0).


 * -a) 1.28E+01 amps
 * -b) 1.40E+01 amps
 * -c) 1.54E+01 amps
 * -d) 1.69E+01 amps
 * +e) 1.85E+01 amps

Key: V2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 40A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.6) to the point (6.6,0).


 * +a) 1.00E+01 amps
 * -b) 1.10E+01 amps
 * -c) 1.20E+01 amps
 * -d) 1.32E+01 amps
 * -e) 1.45E+01 amps

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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 6.2m from a wire carrying a current of 4.8A?


 * -a) 9.35E-02 A/m
 * -b) 1.02E-01 A/m
 * -c) 1.12E-01 A/m
 * +d) 1.23E-01 A/m
 * -e) 1.35E-01 A/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=2.89 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

6) 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

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 9.77E+00 amps
 * -b) 1.07E+01 amps
 * +c) 1.18E+01 amps
 * -d) 1.29E+01 amps
 * -e) 1.41E+01 amps

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 0.388 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

9) A very long and thin solenoid has 1847 turns and is 162 meters long. The wire carrys a current of 8.7A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 42 meters from the center and stops 103 meters from the center?


 * -a) 2.68E+03 A
 * -b) 2.93E+03 A
 * -c) 3.22E+03 A
 * -d) 3.53E+03 A
 * +e) 3.87E+03 A

10) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

Key: W0
1) 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

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 wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * -b) 2.092E+00 Tesla
 * -c) 2.301E+00 Tesla
 * +d) 2.532E+00 Tesla
 * -e) 2.785E+00 Tesla

4) 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

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.1m from a wire carrying a current of 6.7A?


 * +a) 2.60E-01 A/m
 * -b) 2.85E-01 A/m
 * -c) 3.13E-01 A/m
 * -d) 3.43E-01 A/m
 * -e) 3.76E-01 A/m

8) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * -a) 1.13E-01 A/m
 * -b) 1.24E-01 A/m
 * -c) 1.36E-01 A/m
 * +d) 1.49E-01 A/m
 * -e) 1.63E-01 A/m

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.9) to the point (7.9,7.9).


 * -a) 7.68E+00 amps
 * -b) 8.42E+00 amps
 * -c) 9.23E+00 amps
 * +d) 1.01E+01 amps
 * -e) 1.11E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.7) to (+ &infin; ,8.7).


 * -a) 4.01E+01 amps
 * +b) 4.40E+01 amps
 * -c) 4.82E+01 amps
 * -d) 5.29E+01 amps
 * -e) 5.80E+01 amps

Key: W1
1) A circular current loop of radius 1.56 cm carries a current of 2.57 mA. What is the magnitude of the torque if the dipole is oriented at 38 &deg; to a uniform magnetic fied of 0.79 T?


 * -a) 7.898E-07 N m
 * -b) 8.688E-07 N m
 * +c) 9.557E-07 N m
 * -d) 1.051E-06 N m
 * -e) 1.156E-06 N m

2) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?


 * -a) 1.13E-01 A/m
 * -b) 1.24E-01 A/m
 * -c) 1.36E-01 A/m
 * +d) 1.49E-01 A/m
 * -e) 1.63E-01 A/m

3) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * -b) 2.092E+00 Tesla
 * -c) 2.301E+00 Tesla
 * +d) 2.532E+00 Tesla
 * -e) 2.785E+00 Tesla

4) 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

5) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 7.7m from a wire carrying a current of 4.8A?


 * +a) 9.92E-02 A/m
 * -b) 1.09E-01 A/m
 * -c) 1.19E-01 A/m
 * -d) 1.31E-01 A/m
 * -e) 1.43E-01 A/m

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5) to the point (5,5).


 * -a) 7.44E+00 amps
 * -b) 8.15E+00 amps
 * -c) 8.94E+00 amps
 * -d) 9.80E+00 amps
 * +e) 1.08E+01 amps

8) 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

9) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9.6) to (+ &infin; ,9.6).


 * -a) 3.16E+01 amps
 * -b) 3.47E+01 amps
 * +c) 3.80E+01 amps
 * -d) 4.17E+01 amps
 * -e) 4.57E+01 amps

Key: W2
1) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * +a) 3.88E+00 amps
 * -b) 4.25E+00 amps
 * -c) 4.66E+00 amps
 * -d) 5.11E+00 amps
 * -e) 5.60E+00 amps

2) H is defined by, B=&mu;0H, where B is magnetic field. A current of 44A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5) to (+ &infin; ,5).


 * -a) 1.67E+01 amps
 * -b) 1.83E+01 amps
 * -c) 2.01E+01 amps
 * +d) 2.20E+01 amps
 * -e) 2.41E+01 amps

3) 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

4) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?


 * -a) 1.28E-01 A/m
 * -b) 1.40E-01 A/m
 * -c) 1.54E-01 A/m
 * +d) 1.68E-01 A/m
 * -e) 1.85E-01 A/m

5) 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

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

9) A wire carries a current of 343 A in a circular arc with radius 2.95 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) 1.902E+00 Tesla
 * -b) 2.092E+00 Tesla
 * -c) 2.301E+00 Tesla
 * +d) 2.532E+00 Tesla
 * -e) 2.785E+00 Tesla

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 4.2m from a wire carrying a current of 4.9A?


 * -a) 1.28E-01 A/m
 * -b) 1.41E-01 A/m
 * -c) 1.54E-01 A/m
 * -d) 1.69E-01 A/m
 * +e) 1.86E-01 A/m

Key: X0
1) 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

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) 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

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) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

7) A very long and thin solenoid has 2762 turns and is 142 meters long. The wire carrys a current of 9.7A. What is the magnetic field in the center?


 * +a) 2.37E-04 Tesla
 * -b) 2.60E-04 Tesla
 * -c) 2.85E-04 Tesla
 * -d) 3.13E-04 Tesla
 * -e) 3.43E-04 Tesla

8) A very long and thin solenoid has 2850 turns and is 164 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 108 meters from the center?


 * -a) 5.16E+03 A
 * +b) 5.66E+03 A
 * -c) 6.20E+03 A
 * -d) 6.80E+03 A
 * -e) 7.46E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.3) to (+ &infin; ,8.3).


 * -a) 1.50E+01 amps
 * -b) 1.64E+01 amps
 * +c) 1.80E+01 amps
 * -d) 1.97E+01 amps
 * -e) 2.16E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.3) to the point (5.3,5.3).


 * -a) 8.72E+00 amps
 * -b) 9.57E+00 amps
 * -c) 1.05E+01 amps
 * +d) 1.15E+01 amps
 * -e) 1.26E+01 amps

Key: X1
1) A very long and thin solenoid has 1292 turns and is 122 meters long. The wire carrys a current of 8.4A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 39 meters from the center and stops 75 meters from the center?


 * -a) 1.63E+03 A
 * -b) 1.78E+03 A
 * +c) 1.96E+03 A
 * -d) 2.15E+03 A
 * -e) 2.35E+03 A

2) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

3) A 82 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 0.459 T. What current is required to maintain this balance?


 * -a) 1.956E-01 A
 * -b) 2.152E-01 A
 * -c) 2.367E-01 A
 * -d) 2.604E-01 A
 * +e) 2.864E-01 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=2.85 kA, I2=1.8 kA, and I3=4.89 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 3.530E-03 T-m
 * +b) 3.883E-03 T-m
 * -c) 4.271E-03 T-m
 * -d) 4.698E-03 T-m
 * -e) 5.168E-03 T-m

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * -a) 3.16E+01 amps
 * -b) 3.47E+01 amps
 * +c) 3.80E+01 amps
 * -d) 4.17E+01 amps
 * -e) 4.57E+01 amps

7) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?


 * +a) 1.434E-10 N/m
 * -b) 1.578E-10 N/m
 * -c) 1.736E-10 N/m
 * -d) 1.909E-10 N/m
 * -e) 2.100E-10 N/m

8) A very long and thin solenoid has 2543 turns and is 166 meters long. The wire carrys a current of 9.2A. What is the magnetic field in the center?


 * -a) 1.34E-04 Tesla
 * -b) 1.47E-04 Tesla
 * -c) 1.62E-04 Tesla
 * +d) 1.77E-04 Tesla
 * -e) 1.94E-04 Tesla

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 50A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7) to the point (7,7).


 * +a) 6.25E+00 amps
 * -b) 6.85E+00 amps
 * -c) 7.51E+00 amps
 * -d) 8.24E+00 amps
 * -e) 9.03E+00 amps

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

Key: X2
1) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?


 * +a) 1.60E-04 Tesla
 * -b) 1.75E-04 Tesla
 * -c) 1.92E-04 Tesla
 * -d) 2.11E-04 Tesla
 * -e) 2.31E-04 Tesla

2) A very long and thin solenoid has 1880 turns and is 166 meters long. The wire carrys a current of 9.2A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 48 meters from the center and stops 102 meters from the center?


 * +a) 3.65E+03 A
 * -b) 4.00E+03 A
 * -c) 4.38E+03 A
 * -d) 4.81E+03 A
 * -e) 5.27E+03 A

3) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

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=2.32 kA, I2=2.0 kA, and I3=3.66 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.724E-03 T-m
 * -b) 1.896E-03 T-m
 * +c) 2.086E-03 T-m
 * -d) 2.295E-03 T-m
 * -e) 2.524E-03 T-m

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) Two parallel wires each carry a 4.15 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.19 cm, 1.78 cm), while the other is located at (3.73 cm, 4.12 cm). What is the force per unit length between the wires?


 * +a) 1.434E-10 N/m
 * -b) 1.578E-10 N/m
 * -c) 1.736E-10 N/m
 * -d) 1.909E-10 N/m
 * -e) 2.100E-10 N/m

7) 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

8) H is defined by, B=&mu;0H, where B is magnetic field. A current of 93A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,4.1) to (+ &infin; ,4.1).


 * -a) 3.53E+01 amps
 * -b) 3.87E+01 amps
 * -c) 4.24E+01 amps
 * +d) 4.65E+01 amps
 * -e) 5.10E+01 amps

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.3) to the point (7.3,7.3).


 * +a) 3.88E+00 amps
 * -b) 4.25E+00 amps
 * -c) 4.66E+00 amps
 * -d) 5.11E+00 amps
 * -e) 5.60E+00 amps

10) 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

Key: Y0
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) 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) 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=2.49 kA, I2=0.996 kA, and I3=2.61 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.385E-03 T-m
 * -b) 1.524E-03 T-m
 * -c) 1.676E-03 T-m
 * -d) 1.844E-03 T-m
 * +e) 2.028E-03 T-m

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

7) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (2.5486,3.2116) if a current of 6.7A flows through a wire that runs along the z axis?


 * -a) 1.23E-01 A/m
 * -b) 1.34E-01 A/m
 * -c) 1.47E-01 A/m
 * +d) 1.62E-01 A/m
 * -e) 1.77E-01 A/m

8) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * -a) 2.97E+03 A
 * -b) 3.26E+03 A
 * +c) 3.57E+03 A
 * -d) 3.92E+03 A
 * -e) 4.30E+03 A

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.6, 9.6) to the point (9.6, 9.6).


 * -a) 1.73E+01 amps
 * -b) 1.89E+01 amps
 * -c) 2.07E+01 amps
 * +d) 2.28E+01 amps
 * -e) 2.49E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 43A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,5.8) to (+ &infin; ,5.8).


 * -a) 1.63E+01 amps
 * -b) 1.79E+01 amps
 * -c) 1.96E+01 amps
 * +d) 2.15E+01 amps
 * -e) 2.36E+01 amps

Key: Y1
1) A very long and thin solenoid has 2994 turns and is 180 meters long. The wire carrys a current of 9.3A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 101 meters from the center?


 * -a) 6.63E+03 A
 * +b) 7.27E+03 A
 * -c) 7.97E+03 A
 * -d) 8.74E+03 A
 * -e) 9.58E+03 A

2) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

3) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.1, 8.1) to the point (8.1, 8.1).


 * -a) 2.01E+01 amps
 * +b) 2.20E+01 amps
 * -c) 2.41E+01 amps
 * -d) 2.64E+01 amps
 * -e) 2.90E+01 amps

4) A wire carries a current of 280 A in a circular arc with radius 2.48 cm swept through 46 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) 2.032E+00 Tesla
 * -b) 2.236E+00 Tesla
 * -c) 2.459E+00 Tesla
 * -d) 2.705E+00 Tesla
 * +e) 2.976E+00 Tesla

5) 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

6) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.2) to (+ &infin; ,8.2).


 * -a) 3.37E+01 amps
 * +b) 3.70E+01 amps
 * -c) 4.06E+01 amps
 * -d) 4.45E+01 amps
 * -e) 4.88E+01 amps

7) 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

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=2.55 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

9) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

10) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (1.5944,4.101) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 6.86E-02 A/m
 * -b) 7.52E-02 A/m
 * -c) 8.25E-02 A/m
 * +d) 9.04E-02 A/m
 * -e) 9.92E-02 A/m

Key: Y2
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) H is defined by, B=&mu;0H, where B is magnetic field. A current of 85A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8) to (+ &infin; ,8).


 * -a) 2.94E+01 amps
 * -b) 3.22E+01 amps
 * -c) 3.53E+01 amps
 * -d) 3.88E+01 amps
 * +e) 4.25E+01 amps

3) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?


 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 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=2.4 kA, I2=2.64 kA, and I3=3.96 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:


 * -a) 1.133E-03 T-m
 * -b) 1.246E-03 T-m
 * -c) 1.371E-03 T-m
 * -d) 1.508E-03 T-m
 * +e) 1.659E-03 T-m

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?


 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

6) A very long and thin solenoid has 2682 turns and is 146 meters long. The wire carrys a current of 9.5A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?


 * -a) 3.84E+03 A
 * -b) 4.21E+03 A
 * -c) 4.62E+03 A
 * +d) 5.06E+03 A
 * -e) 5.55E+03 A

7) A wire carries a current of 193 A in a circular arc with radius 3.13 cm swept through 40 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) 1.285E+00 Tesla
 * +b) 1.413E+00 Tesla
 * -c) 1.554E+00 Tesla
 * -d) 1.710E+00 Tesla
 * -e) 1.881E+00 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) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (1.5944,4.101) if a current of 6.9A flows through a wire that runs along the z axis?


 * -a) 6.86E-02 A/m
 * -b) 7.52E-02 A/m
 * -c) 8.25E-02 A/m
 * +d) 9.04E-02 A/m
 * -e) 9.92E-02 A/m

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.1, 6.1) to the point (6.1, 6.1).


 * -a) 1.50E+01 amps
 * -b) 1.65E+01 amps
 * -c) 1.81E+01 amps
 * -d) 1.98E+01 amps
 * +e) 2.18E+01 amps

Key: Z0
1) 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

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 3.78 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (1.43 i + 8.8 j  + 4.16 k) x 104 m/s?


 * +a) 1.064E-13 N
 * -b) 1.171E-13 N
 * -c) 1.288E-13 N
 * -d) 1.417E-13 N
 * -e) 1.558E-13 N

3) Two parallel wires each carry a 9.68 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.55 cm, 1.79 cm), while the other is located at (3.16 cm, 4.78 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) 5.684E-10 N/m

4) Two loops of wire carry the same current of 88 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.655 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 0.531 m from the first (smaller) loopif the disance between the loops is 1.72 m?


 * -a) 4.162E-02 T
 * -b) 4.578E-02 T
 * -c) 5.036E-02 T
 * +d) 5.540E-02 T
 * -e) 6.094E-02 T

5) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

6) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

7) A very long and thin solenoid has 1259 turns and is 156 meters long. The wire carrys a current of 8.9A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 35 meters from the center and stops 90 meters from the center?


 * -a) 2.82E+03 A
 * +b) 3.09E+03 A
 * -c) 3.39E+03 A
 * -d) 3.71E+03 A
 * -e) 4.07E+03 A

8) What is the sum of 0.2 apples plus 57 apples?


 * +a) 5.72E+01 apples
 * -b) 6.27E+01 apples
 * -c) 6.88E+01 apples
 * -d) 7.54E+01 apples
 * -e) 8.27E+01 apples

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.6) to the point (8.6,8.6).


 * +a) 4.50E+00 amps
 * -b) 4.93E+00 amps
 * -c) 5.41E+00 amps
 * -d) 5.93E+00 amps
 * -e) 6.50E+00 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 63A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 9.3, 9.3) to the point (9.3, 9.3).


 * -a) 1.19E+01 amps
 * -b) 1.31E+01 amps
 * -c) 1.44E+01 amps
 * +d) 1.58E+01 amps
 * -e) 1.73E+01 amps

Key: Z1
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) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

3) 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

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 very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?


 * -a) 2.97E+03 A
 * -b) 3.26E+03 A
 * +c) 3.57E+03 A
 * -d) 3.92E+03 A
 * -e) 4.30E+03 A

6) A torus is centered around the x-y plane, with major radius, a = 3.24 m, and  minor radius, r = 1.35m.  A wire carrying 4.9A is uniformly wrapped with 731 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.81m from the outermost edge of the torus?


 * +a) 1.11E+02 amps per meter
 * -b) 1.20E+02 amps per meter
 * -c) 1.30E+02 amps per meter
 * -d) 1.40E+02 amps per meter
 * -e) 1.51E+02 amps per meter

7) Two parallel wires each carry a 7.68 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (3.36 cm, 1.58 cm), while the other is located at (5.29 cm, 5.18 cm). What is the force per unit length between the wires?


 * -a) 1.973E-10 N/m
 * -b) 2.170E-10 N/m
 * -c) 2.387E-10 N/m
 * -d) 2.625E-10 N/m
 * +e) 2.888E-10 N/m

8) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

9) H is defined by, B=&mu;0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 7, 7) to the point (7, 7).


 * -a) 9.67E+00 amps
 * -b) 1.06E+01 amps
 * -c) 1.16E+01 amps
 * +d) 1.28E+01 amps
 * -e) 1.40E+01 amps

10) H is defined by, B=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,7.2) to the point (7.2,7.2).


 * +a) 7.38E+00 amps
 * -b) 8.09E+00 amps
 * -c) 8.87E+00 amps
 * -d) 9.72E+00 amps
 * -e) 1.07E+01 amps

Key: Z2
1) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?


 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

2) Two parallel wires each carry a 3.8 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.74 cm, 1.47 cm), while the other is located at (5.26 cm, 5.87 cm). What is the force per unit length between the wires?


 * -a) 5.926E-11 N/m
 * +b) 6.518E-11 N/m
 * -c) 7.170E-11 N/m
 * -d) 7.887E-11 N/m
 * -e) 8.676E-11 N/m

3) A very long and thin solenoid has 1409 turns and is 170 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 37 meters from the center and stops 100 meters from the center?


 * -a) 2.94E+03 A
 * +b) 3.22E+03 A
 * -c) 3.53E+03 A
 * -d) 3.87E+03 A
 * -e) 4.25E+03 A

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?


 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,8.4) to the point (8.4,8.4).


 * -a) 5.47E+00 amps
 * +b) 6.00E+00 amps
 * -c) 6.58E+00 amps
 * -d) 7.21E+00 amps
 * -e) 7.91E+00 amps

6) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and  minor radius, r = 2.16m.  A wire carrying 5A is uniformly wrapped with 930 turns.  If  B=&mu;0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?


 * -a) 5.31E+01 amps per meter
 * -b) 5.73E+01 amps per meter
 * -c) 6.19E+01 amps per meter
 * -d) 6.68E+01 amps per meter
 * +e) 7.21E+01 amps per meter

7) H is defined by, B=&mu;0H, where B is magnetic field. A current of 70A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 8.7, 8.7) to the point (8.7, 8.7).


 * -a) 1.21E+01 amps
 * -b) 1.33E+01 amps
 * -c) 1.46E+01 amps
 * -d) 1.60E+01 amps
 * +e) 1.75E+01 amps

8) A 11 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 0.809 T. What current is required to maintain this balance?


 * +a) 1.432E+00 A
 * -b) 1.575E+00 A
 * -c) 1.732E+00 A
 * -d) 1.905E+00 A
 * -e) 2.096E+00 A

9) 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

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 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