Quizbank/University Physics Semester 2/T6

University Physics Semester 2/T6 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-T6.pdf

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

T6 A0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?


 * a) 1.028E-14 N
 * b) 1.130E-14 N
 * c) 1.244E-14 N
 * d) 1.368E-14 N
 * e) 1.505E-14 N

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is, $$\vec E=4y^{1.4}\hat i +2x^{2.3}\hat j +4y^{2.3}\hat k$$


 * a) 2.694E+03 V&middot;m
 * b) 2.963E+03 V&middot;m
 * c) 3.259E+03 V&middot;m
 * d) 3.585E+03 V&middot;m
 * e) 3.944E+03 V&middot;m

3) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?


 * a) 7.825E+02 N/C
 * b) 8.607E+02 N/C
 * c) 9.468E+02 N/C
 * d) 1.041E+03 N/C
 * e) 1.146E+03 N/C

4) Assume that a 11 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (12 cm, 14&deg;).


 * a) 1.876E+02 V
 * b) 2.063E+02 V
 * c) 2.270E+02 V
 * d) 2.497E+02 V
 * e) 2.746E+02 V

5) A 3 C charge is separated from a 11 C charge by distance of 12 cm.  What is the work done by increasing this separation to 19 cm?


 * a) 8.278E-07 J
 * b) 9.106E-07 J
 * c) 1.002E-06 J
 * d) 1.102E-06 J
 * e) 1.212E-06 J

6) What is the net capacitance if C1=2.25 &mu;F, C2=4.16 &mu;F, and C3=2.49 &mu;F in the configuration shown?


 * a) 2.698E+00 &mu;F
 * b) 2.968E+00 &mu;F
 * c) 3.265E+00 &mu;F
 * d) 3.591E+00 &mu;F
 * e) 3.950E+00 &mu;F

7) A device requires consumes 81 W of power and requires 2.34 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * a) 3.342E+05 A/m2
 * b) 3.677E+05 A/m2
 * c) 4.044E+05 A/m2
 * d) 4.449E+05 A/m2
 * e) 4.894E+05 A/m2

8) What is the average current involved when a truck battery sets in motion 775 C of charge in 2.9 s while starting an engine?


 * a) 2.209E+02 A
 * b) 2.429E+02 A
 * c) 2.672E+02 A
 * d) 2.940E+02 A
 * e) 3.234E+02 A

9) A given battery has a 13 V emf and an internal resistance of 0.113 &Omega;. If it is connected to a 0.686 &Omega; resistor what is the power dissipated by that load?


 * a) 1.501E+02 W
 * b) 1.651E+02 W
 * c) 1.816E+02 W
 * d) 1.998E+02 W
 * e) 2.197E+02 W

10) The resistances in the figure shown are R1= 1.54 &Omega;, R2= 0.927 &Omega;, and R2= 2.46 &Omega;. V1 and V3 are text 0.632 V and 2.12 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.586 V. What is the absolute value of the current through R1?


 * a) 1.770E-01 A
 * b) 1.947E-01 A
 * c) 2.141E-01 A
 * d) 2.355E-01 A
 * e) 2.591E-01 A

T6 A1
1) Assume that a 24 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 27&deg;).


 * a) 5.540E+02 V
 * b) 6.095E+02 V
 * c) 6.704E+02 V
 * d) 7.374E+02 V
 * e) 8.112E+02 V

2) What is the net capacitance if C1=3.25 &mu;F, C2=4.87 &mu;F, and C3=2.19 &mu;F in the configuration shown?


 * a) 4.139E+00 &mu;F
 * b) 4.553E+00 &mu;F
 * c) 5.008E+00 &mu;F
 * d) 5.509E+00 &mu;F
 * e) 6.060E+00 &mu;F

3) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=2 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?


 * a) 1.123E+02 N/C
 * b) 1.235E+02 N/C
 * c) 1.358E+02 N/C
 * d) 1.494E+02 N/C
 * e) 1.644E+02 N/C

4) A device requires consumes 185 W of power and requires 10.1 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * a) 1.920E+06 A/m2
 * b) 2.112E+06 A/m2
 * c) 2.323E+06 A/m2
 * d) 2.556E+06 A/m2
 * e) 2.811E+06 A/m2

5) The resistances in the figure shown are R1= 1.6 &Omega;, R2= 1.3 &Omega;, and R2= 2.22 &Omega;. V1 and V3 are text 0.55 V and 3.18 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.743 V. What is the absolute value of the current through R1?


 * a) 1.721E-01 A
 * b) 1.893E-01 A
 * c) 2.082E-01 A
 * d) 2.291E-01 A
 * e) 2.520E-01 A

6) What is the average current involved when a truck battery sets in motion 622 C of charge in 5.69 s while starting an engine?


 * a) 9.034E+01 A
 * b) 9.938E+01 A
 * c) 1.093E+02 A
 * d) 1.202E+02 A
 * e) 1.323E+02 A

7) A given battery has a 11 V emf and an internal resistance of 0.0998 &Omega;. If it is connected to a 0.417 &Omega; resistor what is the power dissipated by that load?


 * a) 1.419E+02 W
 * b) 1.561E+02 W
 * c) 1.717E+02 W
 * d) 1.889E+02 W
 * e) 2.078E+02 W

8) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=3e$$?


 * a) 4.171E-14 N
 * b) 4.588E-14 N
 * c) 5.047E-14 N
 * d) 5.551E-14 N
 * e) 6.107E-14 N

9) A 7 C charge is separated from a 12 C charge by distance of 11 cm.  What is the work done by increasing this separation to 19 cm?


 * a) 2.890E-06 J
 * b) 3.179E-06 J
 * c) 3.497E-06 J
 * d) 3.846E-06 J
 * e) 4.231E-06 J

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.2}\hat i +3x^{2.1}\hat j +5y^{3.3}\hat k$$


 * a) 2.610E+03 V&middot;m
 * b) 2.871E+03 V&middot;m
 * c) 3.158E+03 V&middot;m
 * d) 3.474E+03 V&middot;m
 * e) 3.822E+03 V&middot;m

T6 A2
1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?


 * a) 2.777E+02 N/C
 * b) 3.055E+02 N/C
 * c) 3.361E+02 N/C
 * d) 3.697E+02 N/C
 * e) 4.066E+02 N/C

2) A 2 C charge is separated from a 10 C charge by distance of 10 cm.  What is the work done by increasing this separation to 16 cm?


 * a) 6.128E-07 J
 * b) 6.741E-07 J
 * c) 7.415E-07 J
 * d) 8.156E-07 J
 * e) 8.972E-07 J

3) The resistances in the figure shown are R1= 1.1 &Omega;, R2= 1.55 &Omega;, and R2= 2.11 &Omega;. V1 and V3 are text 0.545 V and 3.22 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.744 V. What is the absolute value of the current through R1?


 * a) 1.886E-01 A
 * b) 2.075E-01 A
 * c) 2.282E-01 A
 * d) 2.510E-01 A
 * e) 2.761E-01 A

4) A device requires consumes 126 W of power and requires 1.11 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * a) 2.110E+05 A/m2
 * b) 2.321E+05 A/m2
 * c) 2.553E+05 A/m2
 * d) 2.809E+05 A/m2
 * e) 3.090E+05 A/m2

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * a) 3.429E+03 V&middot;m
 * b) 3.771E+03 V&middot;m
 * c) 4.149E+03 V&middot;m
 * d) 4.564E+03 V&middot;m
 * e) 5.020E+03 V&middot;m

6) A given battery has a 12 V emf and an internal resistance of 0.107 &Omega;. If it is connected to a 0.814 &Omega; resistor what is the power dissipated by that load?


 * a) 1.382E+02 W
 * b) 1.520E+02 W
 * c) 1.672E+02 W
 * d) 1.839E+02 W
 * e) 2.023E+02 W

7) What is the net capacitance if C1=3.27 &mu;F, C2=2.87 &mu;F, and C3=3.23 &mu;F in the configuration shown?


 * a) 3.250E+00 &mu;F
 * b) 3.575E+00 &mu;F
 * c) 3.933E+00 &mu;F
 * d) 4.326E+00 &mu;F
 * e) 4.758E+00 &mu;F

8) What is the average current involved when a truck battery sets in motion 821 C of charge in 5.51 s while starting an engine?


 * a) 1.231E+02 A
 * b) 1.355E+02 A
 * c) 1.490E+02 A
 * d) 1.639E+02 A
 * e) 1.803E+02 A

9) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?


 * a) 1.028E-14 N
 * b) 1.130E-14 N
 * c) 1.244E-14 N
 * d) 1.368E-14 N
 * e) 1.505E-14 N

10) Assume that a 6 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (8 cm, 0&deg;) and  P2 is at (14 cm, 34&deg;).


 * a) 2.626E+02 V
 * b) 2.889E+02 V
 * c) 3.178E+02 V
 * d) 3.496E+02 V
 * e) 3.845E+02 V

T6 B0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.


 * a) 5.825E+00 V/m2
 * b) 6.407E+00 V/m2
 * c) 7.048E+00 V/m2
 * d) 7.753E+00 V/m2
 * e) 8.528E+00 V/m2

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?


 * a) 2.964E+00 N/C
 * b) 3.260E+00 N/C
 * c) 3.586E+00 N/C
 * d) 3.944E+00 N/C
 * e) 4.339E+00 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.924E+01 N&middot;m2/C
 * b) 4.316E+01 N&middot;m2/C
 * c) 4.748E+01 N&middot;m2/C
 * d) 5.222E+01 N&middot;m2/C
 * e) 5.745E+01 N&middot;m2/C

4) A Van de Graff generator has a 149 cm diameter metal sphere that produces 172 kV near its surface. What  is the excess charge on the sphere?


 * a) 1.071E+01 &mu;C
 * b) 1.178E+01 &mu;C
 * c) 1.296E+01 &mu;C
 * d) 1.426E+01 &mu;C
 * e) 1.568E+01 &mu;C

5) When a 5.65 V battery operates a 2.73 W bulb, how many electrons pass through it each second?


 * a) 3.016E+18 electrons
 * b) 3.317E+18 electrons
 * c) 3.649E+18 electrons
 * d) 4.014E+18 electrons
 * e) 4.415E+18 electrons

6) What is the net capacitance if C1=3.54 &mu;F, C2=3.53 &mu;F, and C3=3.65 &mu;F in the configuration shown?


 * a) 3.700E+00 &mu;F
 * b) 4.070E+00 &mu;F
 * c) 4.477E+00 &mu;F
 * d) 4.925E+00 &mu;F
 * e) 5.417E+00 &mu;F

7) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 2.292E+29 e&minus;/m3
 * b) 2.521E+29 e&minus;/m3
 * c) 2.773E+29 e&minus;/m3
 * d) 3.051E+29 e&minus;/m3
 * e) 3.356E+29 e&minus;/m3

8) What is the average current involved when a truck battery sets in motion 775 C of charge in 2.9 s while starting an engine?


 * a) 2.209E+02 A
 * b) 2.429E+02 A
 * c) 2.672E+02 A
 * d) 2.940E+02 A
 * e) 3.234E+02 A

9) A battery with a terminal voltage of 8.01 V is connected to a circuit consisting of 3 22.1 &Omega; resistors and one 14.5 &Omega; resistor. What is the voltage drop across the 14.5 &Omega; resistor?


 * a) 9.818E-01 V
 * b) 1.080E+00 V
 * c) 1.188E+00 V
 * d) 1.307E+00 V
 * e) 1.437E+00 V

10) Two sources of emf &epsilon;1=58.5 V, and  &epsilon;2=17.3 V are oriented as shownin the circuit. The resistances are R1=3.06 k&Omega; and  R2=1.88 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.25 mA and I4=1.25 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.981E+01 V
 * b) 2.179E+01 V
 * c) 2.397E+01 V
 * d) 2.637E+01 V
 * e) 2.901E+01 V

T6 B1
1) A make-believe metal has a density of 2.670E+03 kg/m3 and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 3.930E+28 e&minus;/m3
 * b) 4.323E+28 e&minus;/m3
 * c) 4.755E+28 e&minus;/m3
 * d) 5.231E+28 e&minus;/m3
 * e) 5.754E+28 e&minus;/m3

2) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.440E+01 V
 * b) 1.584E+01 V
 * c) 1.742E+01 V
 * d) 1.916E+01 V
 * e) 2.108E+01 V

3) A Van de Graff generator has a 76 cm diameter metal sphere that produces 193 kV near its surface. What  is the excess charge on the sphere?


 * a) 7.418E+00 &mu;C
 * b) 8.160E+00 &mu;C
 * c) 8.976E+00 &mu;C
 * d) 9.874E+00 &mu;C
 * e) 1.086E+01 &mu;C

4) When a 7.78 V battery operates a 1.35 W bulb, how many electrons pass through it each second?


 * a) 7.397E+17 electrons
 * b) 8.137E+17 electrons
 * c) 8.951E+17 electrons
 * d) 9.846E+17 electrons
 * e) 1.083E+18 electrons

5) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * a) 1.677E+00 V
 * b) 1.844E+00 V
 * c) 2.029E+00 V
 * d) 2.231E+00 V
 * e) 2.455E+00 V

6) What is the net capacitance if C1=4.7 &mu;F, C2=4.82 &mu;F, and C3=3.61 &mu;F in the configuration shown?


 * a) 5.445E+00 &mu;F
 * b) 5.990E+00 &mu;F
 * c) 6.589E+00 &mu;F
 * d) 7.247E+00 &mu;F
 * e) 7.972E+00 &mu;F

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.698E+01 N&middot;m2/C
 * b) 1.868E+01 N&middot;m2/C
 * c) 2.055E+01 N&middot;m2/C
 * d) 2.260E+01 N&middot;m2/C
 * e) 2.486E+01 N&middot;m2/C

8) What is the average current involved when a truck battery sets in motion 728 C of charge in 3.94 s while starting an engine?


 * a) 1.848E+02 A
 * b) 2.032E+02 A
 * c) 2.236E+02 A
 * d) 2.459E+02 A
 * e) 2.705E+02 A

9) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.1 m, b=1.4 m.  The total charge on the rod is 5 nC.


 * a) 4.602E+00 V/m2
 * b) 5.062E+00 V/m2
 * c) 5.568E+00 V/m2
 * d) 6.125E+00 V/m2
 * e) 6.738E+00 V/m2

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?


 * a) 2.601E+01 N/C
 * b) 2.861E+01 N/C
 * c) 3.147E+01 N/C
 * d) 3.462E+01 N/C
 * e) 3.808E+01 N/C

T6 B2
1) A Van de Graff generator has a 141 cm diameter metal sphere that produces 280 kV near its surface. What  is the excess charge on the sphere?


 * a) 1.500E+01 &mu;C
 * b) 1.650E+01 &mu;C
 * c) 1.815E+01 &mu;C
 * d) 1.997E+01 &mu;C
 * e) 2.196E+01 &mu;C

2) When a 6.24 V battery operates a 2.1 W bulb, how many electrons pass through it each second?


 * a) 1.435E+18 electrons
 * b) 1.578E+18 electrons
 * c) 1.736E+18 electrons
 * d) 1.910E+18 electrons
 * e) 2.101E+18 electrons

3) What is the average current involved when a truck battery sets in motion 821 C of charge in 5.51 s while starting an engine?


 * a) 1.231E+02 A
 * b) 1.355E+02 A
 * c) 1.490E+02 A
 * d) 1.639E+02 A
 * e) 1.803E+02 A

4) A battery with a terminal voltage of 8.41 V is connected to a circuit consisting of 3 16.1 &Omega; resistors and one 10.9 &Omega; resistor. What is the voltage drop across the 10.9 &Omega; resistor?


 * a) 1.058E+00 V
 * b) 1.163E+00 V
 * c) 1.280E+00 V
 * d) 1.408E+00 V
 * e) 1.548E+00 V

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.385E+01 N&middot;m2/C
 * b) 5.923E+01 N&middot;m2/C
 * c) 6.516E+01 N&middot;m2/C
 * d) 7.167E+01 N&middot;m2/C
 * e) 7.884E+01 N&middot;m2/C

6) What is the net capacitance if C1=4.75 &mu;F, C2=2.77 &mu;F, and C3=2.47 &mu;F in the configuration shown?


 * a) 4.220E+00 &mu;F
 * b) 4.642E+00 &mu;F
 * c) 5.106E+00 &mu;F
 * d) 5.616E+00 &mu;F
 * e) 6.178E+00 &mu;F

7) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.1 m, b=1.4 m.  The total charge on the rod is 5 nC.


 * a) 4.602E+00 V/m2
 * b) 5.062E+00 V/m2
 * c) 5.568E+00 V/m2
 * d) 6.125E+00 V/m2
 * e) 6.738E+00 V/m2

8) Two sources of emf &epsilon;1=27.9 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=2.82 k&Omega; and  R2=2.25 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.1 mA and I4=0.676 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 8.334E+00 V
 * b) 9.167E+00 V
 * c) 1.008E+01 V
 * d) 1.109E+01 V
 * e) 1.220E+01 V

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?


 * a) 6.641E+00 N/C
 * b) 7.305E+00 N/C
 * c) 8.036E+00 N/C
 * d) 8.839E+00 N/C
 * e) 9.723E+00 N/C

10) A make-believe metal has a density of 1.300E+04 kg/m3 and an atomic mass of 75.7 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 9.398E+28 e&minus;/m3
 * b) 1.034E+29 e&minus;/m3
 * c) 1.137E+29 e&minus;/m3
 * d) 1.251E+29 e&minus;/m3
 * e) 1.376E+29 e&minus;/m3

T6 C0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.


 * a) 5.825E+00 V/m2
 * b) 6.407E+00 V/m2
 * c) 7.048E+00 V/m2
 * d) 7.753E+00 V/m2
 * e) 8.528E+00 V/m2

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?


 * a) 9.592E+00 N/C
 * b) 1.055E+01 N/C
 * c) 1.161E+01 N/C
 * d) 1.277E+01 N/C
 * e) 1.404E+01 N/C

3) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?


 * a) 7.825E+02 N/C
 * b) 8.607E+02 N/C
 * c) 9.468E+02 N/C
 * d) 1.041E+03 N/C
 * e) 1.146E+03 N/C

4) Calculate the final speed of a free electron accelerated from rest through a potential difference of 19 V.


 * a) 1.942E+06 m/s
 * b) 2.137E+06 m/s
 * c) 2.350E+06 m/s
 * d) 2.585E+06 m/s
 * e) 2.844E+06 m/s

5) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=10 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 1.194E+02 J
 * b) 1.314E+02 J
 * c) 1.445E+02 J
 * d) 1.589E+02 J
 * e) 1.748E+02 J

6) What is the net capacitance if C1=2.3 &mu;F, C2=2.84 &mu;F, and C3=3.41 &mu;F in the configuration shown?


 * a) 4.255E+00 &mu;F
 * b) 4.681E+00 &mu;F
 * c) 5.149E+00 &mu;F
 * d) 5.664E+00 &mu;F
 * e) 6.230E+00 &mu;F

7) A make-believe metal has a density of 1.430E+04 kg/m3 and an atomic mass of 37.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 1.882E+29 e&minus;/m3
 * b) 2.070E+29 e&minus;/m3
 * c) 2.277E+29 e&minus;/m3
 * d) 2.505E+29 e&minus;/m3
 * e) 2.756E+29 e&minus;/m3

8) Calculate the drift speed of electrons in a copper wire with a diameter of 4.38 mm carrying a 5.79 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.615E-05 m/s
 * b) 2.876E-05 m/s
 * c) 3.164E-05 m/s
 * d) 3.480E-05 m/s
 * e) 3.828E-05 m/s

9) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 k&Omega; and  R2=2.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.34 mA and I4=0.955 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 7.031E+00 V
 * b) 7.734E+00 V
 * c) 8.507E+00 V
 * d) 9.358E+00 V
 * e) 1.029E+01 V

10) Two sources of emf &epsilon;1=13.6 V, and  &epsilon;2=6.53 V are oriented as shownin the circuit. The resistances are R1=2.89 k&Omega; and  R2=2.12 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.11 mA and I4=0.311 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 7.264E-01 mA
 * b) 7.990E-01 mA
 * c) 8.789E-01 mA
 * d) 9.668E-01 mA
 * e) 1.063E+00 mA

T6 C1
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.


 * a) 5.825E+00 V/m2
 * b) 6.407E+00 V/m2
 * c) 7.048E+00 V/m2
 * d) 7.753E+00 V/m2
 * e) 8.528E+00 V/m2

2) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=8 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 3.444E+01 J
 * b) 3.789E+01 J
 * c) 4.168E+01 J
 * d) 4.585E+01 J
 * e) 5.043E+01 J

3) Calculate the drift speed of electrons in a copper wire with a diameter of 4.9 mm carrying a 6.43 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.109E-05 m/s
 * b) 2.320E-05 m/s
 * c) 2.552E-05 m/s
 * d) 2.807E-05 m/s
 * e) 3.088E-05 m/s

4) What is the net capacitance if C1=3.56 &mu;F, C2=4.23 &mu;F, and C3=2.61 &mu;F in the configuration shown?


 * a) 3.755E+00 &mu;F
 * b) 4.130E+00 &mu;F
 * c) 4.543E+00 &mu;F
 * d) 4.997E+00 &mu;F
 * e) 5.497E+00 &mu;F

5) Two sources of emf &epsilon;1=24.8 V, and  &epsilon;2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 k&Omega; and  R2=1.6 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.49 mA and I4=0.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.660E+00 mA
 * b) 1.826E+00 mA
 * c) 2.009E+00 mA
 * d) 2.209E+00 mA
 * e) 2.430E+00 mA

6) A make-believe metal has a density of 1.810E+04 kg/m3 and an atomic mass of 14.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 5.847E+29 e&minus;/m3
 * b) 6.432E+29 e&minus;/m3
 * c) 7.075E+29 e&minus;/m3
 * d) 7.783E+29 e&minus;/m3
 * e) 8.561E+29 e&minus;/m3

7) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.945E+00 V
 * b) 9.840E+00 V
 * c) 1.082E+01 V
 * d) 1.191E+01 V
 * e) 1.310E+01 V

8) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?


 * a) 3.604E+02 N/C
 * b) 3.964E+02 N/C
 * c) 4.360E+02 N/C
 * d) 4.796E+02 N/C
 * e) 5.276E+02 N/C

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?


 * a) 9.592E+00 N/C
 * b) 1.055E+01 N/C
 * c) 1.161E+01 N/C
 * d) 1.277E+01 N/C
 * e) 1.404E+01 N/C

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * a) 4.638E+06 m/s
 * b) 5.102E+06 m/s
 * c) 5.612E+06 m/s
 * d) 6.173E+06 m/s
 * e) 6.791E+06 m/s

T6 C2
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?


 * a) 2.988E+00 N/C
 * b) 3.287E+00 N/C
 * c) 3.616E+00 N/C
 * d) 3.977E+00 N/C
 * e) 4.375E+00 N/C

2) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=10 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 1.194E+02 J
 * b) 1.314E+02 J
 * c) 1.445E+02 J
 * d) 1.589E+02 J
 * e) 1.748E+02 J

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 53 V.


 * a) 3.244E+06 m/s
 * b) 3.568E+06 m/s
 * c) 3.925E+06 m/s
 * d) 4.318E+06 m/s
 * e) 4.750E+06 m/s

4) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=2 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?


 * a) 2.406E+01 N/C
 * b) 2.646E+01 N/C
 * c) 2.911E+01 N/C
 * d) 3.202E+01 N/C
 * e) 3.522E+01 N/C

5) A make-believe metal has a density of 3.470E+03 kg/m3 and an atomic mass of 33.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 6.180E+28 e&minus;/m3
 * b) 6.798E+28 e&minus;/m3
 * c) 7.478E+28 e&minus;/m3
 * d) 8.226E+28 e&minus;/m3
 * e) 9.049E+28 e&minus;/m3

6) Two sources of emf &epsilon;1=39.2 V, and  &epsilon;2=12.6 V are oriented as shownin the circuit. The resistances are R1=3.86 k&Omega; and  R2=1.89 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.05 mA and I4=0.701 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.687E+00 V
 * b) 9.555E+00 V
 * c) 1.051E+01 V
 * d) 1.156E+01 V
 * e) 1.272E+01 V

7) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.96 m if a=0.63 m, b=1.4 m.  The total charge on the rod is 3 nC.


 * a) 3.719E+00 V/m2
 * b) 4.091E+00 V/m2
 * c) 4.500E+00 V/m2
 * d) 4.950E+00 V/m2
 * e) 5.445E+00 V/m2

8) Calculate the drift speed of electrons in a copper wire with a diameter of 5.47 mm carrying a 3.48 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.008E-05 m/s
 * b) 1.108E-05 m/s
 * c) 1.219E-05 m/s
 * d) 1.341E-05 m/s
 * e) 1.475E-05 m/s

9) What is the net capacitance if C1=4.75 &mu;F, C2=2.77 &mu;F, and C3=2.47 &mu;F in the configuration shown?


 * a) 4.220E+00 &mu;F
 * b) 4.642E+00 &mu;F
 * c) 5.106E+00 &mu;F
 * d) 5.616E+00 &mu;F
 * e) 6.178E+00 &mu;F

10) Two sources of emf &epsilon;1=36.3 V, and  &epsilon;2=12.9 V are oriented as shownin the circuit. The resistances are R1=4.28 k&Omega; and  R2=1.58 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.16 mA and I4=1.2 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.224E+00 mA
 * b) 2.446E+00 mA
 * c) 2.691E+00 mA
 * d) 2.960E+00 mA
 * e) 3.256E+00 mA

T6 D0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * a) 5.569E+01 degrees
 * b) 6.125E+01 degrees
 * c) 6.738E+01 degrees
 * d) 7.412E+01 degrees
 * e) 8.153E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.2 m, and z=z1=4.1 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 5.8m2. An electric field has the xyz components (0, 8.4, 5.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.328E+01 N&middot;m2/C
 * b) 3.660E+01 N&middot;m2/C
 * c) 4.026E+01 N&middot;m2/C
 * d) 4.429E+01 N&middot;m2/C
 * e) 4.872E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.777E+01 N&middot;m2/C
 * b) 5.254E+01 N&middot;m2/C
 * c) 5.780E+01 N&middot;m2/C
 * d) 6.358E+01 N&middot;m2/C
 * e) 6.993E+01 N&middot;m2/C

4) When a 4.89 V battery operates a 1.44 W bulb, how many electrons pass through it each second?


 * a) 1.838E+18 electrons
 * b) 2.022E+18 electrons
 * c) 2.224E+18 electrons
 * d) 2.446E+18 electrons
 * e) 2.691E+18 electrons

5) Two large parallel conducting plates are separated by 9.6 mm. Equal and opposite surface charges of 7.610E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 71 V?


 * a) 4.723E-01 mm
 * b) 5.432E-01 mm
 * c) 6.246E-01 mm
 * d) 7.183E-01 mm
 * e) 8.261E-01 mm

6) In the figure shown C1=17.9 &mu;F, C2=2.71 &mu;F, and C3=4.14 &mu;F. The voltage source provides &epsilon;=7.12 V. What is the charge on C1?


 * a) 3.527E+01 &mu;C
 * b) 3.880E+01 &mu;C
 * c) 4.268E+01 &mu;C
 * d) 4.695E+01 &mu;C
 * e) 5.164E+01 &mu;C

7) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.631E-01 &Omega;
 * b) 2.894E-01 &Omega;
 * c) 3.184E-01 &Omega;
 * d) 3.502E-01 &Omega;
 * e) 3.852E-01 &Omega;

8) What is consumer cost to operate one 76&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.144 per kilowatt-hour?


 * a) $3.595E+01
 * b) $3.955E+01
 * c) $4.350E+01
 * d) $4.785E+01
 * e) $5.264E+01

9) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * a) 1.677E+00 V
 * b) 1.844E+00 V
 * c) 2.029E+00 V
 * d) 2.231E+00 V
 * e) 2.455E+00 V

10) Three resistors, R1 = 1.43 &Omega;, and R2 = R2 = 3.25 &Omega;, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 5.184E+01 W
 * b) 5.702E+01 W
 * c) 6.272E+01 W
 * d) 6.900E+01 W
 * e) 7.590E+01 W

T6 D1
1) Three resistors, R1 = 1.31 &Omega;, and R2 = R2 = 2.91 &Omega;, are connected in parallel to a 6.03 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 2.294E+01 W
 * b) 2.523E+01 W
 * c) 2.776E+01 W
 * d) 3.053E+01 W
 * e) 3.359E+01 W

2) Calculate the resistance of a 12-gauge copper wire that is 81 m long and carries a current of 32 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 3.737E-01 &Omega;
 * b) 4.111E-01 &Omega;
 * c) 4.522E-01 &Omega;
 * d) 4.975E-01 &Omega;
 * e) 5.472E-01 &Omega;

3) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * a) $2.791E+01
 * b) $3.071E+01
 * c) $3.378E+01
 * d) $3.715E+01
 * e) $4.087E+01

4) When a 3.63 V battery operates a 1.34 W bulb, how many electrons pass through it each second?


 * a) 2.095E+18 electrons
 * b) 2.304E+18 electrons
 * c) 2.534E+18 electrons
 * d) 2.788E+18 electrons
 * e) 3.067E+18 electrons

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.2 m, z=z0=1.9 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 8.1m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 7.081E+01 N&middot;m2/C
 * b) 7.789E+01 N&middot;m2/C
 * c) 8.568E+01 N&middot;m2/C
 * d) 9.425E+01 N&middot;m2/C
 * e) 1.037E+02 N&middot;m2/C

6) In the figure shown C1=17.7 &mu;F, C2=2.5 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=12.8 V. What is the charge on C1?


 * a) 5.066E+01 &mu;C
 * b) 5.573E+01 &mu;C
 * c) 6.130E+01 &mu;C
 * d) 6.743E+01 &mu;C
 * e) 7.417E+01 &mu;C

7) A battery with a terminal voltage of 7.82 V is connected to a circuit consisting of 2 19.3 &Omega; resistors and one 12.2 &Omega; resistor. What is the voltage drop across the 12.2 &Omega; resistor?


 * a) 1.552E+00 V
 * b) 1.707E+00 V
 * c) 1.878E+00 V
 * d) 2.066E+00 V
 * e) 2.272E+00 V

8) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * a) 5.569E+01 degrees
 * b) 6.125E+01 degrees
 * c) 6.738E+01 degrees
 * d) 7.412E+01 degrees
 * e) 8.153E+01 degrees

9) Two large parallel conducting plates are separated by 7.01 mm. Equal and opposite surface charges of 7.330E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 55 V?


 * a) 3.799E-01 mm
 * b) 4.368E-01 mm
 * c) 5.024E-01 mm
 * d) 5.777E-01 mm
 * e) 6.644E-01 mm

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.134E+01 N&middot;m2/C
 * b) 2.347E+01 N&middot;m2/C
 * c) 2.582E+01 N&middot;m2/C
 * d) 2.840E+01 N&middot;m2/C
 * e) 3.124E+01 N&middot;m2/C

T6 D2
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.614E+01 N&middot;m2/C
 * b) 7.275E+01 N&middot;m2/C
 * c) 8.003E+01 N&middot;m2/C
 * d) 8.803E+01 N&middot;m2/C
 * e) 9.683E+01 N&middot;m2/C

2) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 4.957E-02 &Omega;
 * b) 5.453E-02 &Omega;
 * c) 5.998E-02 &Omega;
 * d) 6.598E-02 &Omega;
 * e) 7.258E-02 &Omega;

3) A battery with a terminal voltage of 13.2 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * a) 1.958E+00 V
 * b) 2.153E+00 V
 * c) 2.369E+00 V
 * d) 2.606E+00 V
 * e) 2.866E+00 V

4) Two large parallel conducting plates are separated by 6.95 mm. Equal and opposite surface charges of 7.360E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 83 V?


 * a) 6.565E-01 mm
 * b) 7.550E-01 mm
 * c) 8.683E-01 mm
 * d) 9.985E-01 mm
 * e) 1.148E+00 mm

5) Three resistors, R1 = 1.2 &Omega;, and R2 = R2 = 2.75 &Omega;, are connected in parallel to a 6.42 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 2.581E+01 W
 * b) 2.839E+01 W
 * c) 3.122E+01 W
 * d) 3.435E+01 W
 * e) 3.778E+01 W

6) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * a) $2.791E+01
 * b) $3.071E+01
 * c) $3.378E+01
 * d) $3.715E+01
 * e) $4.087E+01

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 8.921E+01 N&middot;m2/C
 * b) 9.813E+01 N&middot;m2/C
 * c) 1.079E+02 N&middot;m2/C
 * d) 1.187E+02 N&middot;m2/C
 * e) 1.306E+02 N&middot;m2/C

8) In the figure shown C1=15.4 &mu;F, C2=2.22 &mu;F, and C3=4.77 &mu;F. The voltage source provides &epsilon;=6.8 V. What is the charge on C1?


 * a) 2.702E+01 &mu;C
 * b) 2.972E+01 &mu;C
 * c) 3.269E+01 &mu;C
 * d) 3.596E+01 &mu;C
 * e) 3.956E+01 &mu;C

9) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=5e$$?


 * a) 6.125E+01 degrees
 * b) 6.738E+01 degrees
 * c) 7.412E+01 degrees
 * d) 8.153E+01 degrees
 * e) 8.968E+01 degrees

10) When a 4.91 V battery operates a 1.43 W bulb, how many electrons pass through it each second?


 * a) 1.242E+18 electrons
 * b) 1.366E+18 electrons
 * c) 1.502E+18 electrons
 * d) 1.653E+18 electrons
 * e) 1.818E+18 electrons

T6 E0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.


 * a) 5.134E-01 V/m2
 * b) 5.648E-01 V/m2
 * c) 6.212E-01 V/m2
 * d) 6.834E-01 V/m2
 * e) 7.517E-01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.740E+01 N&middot;m2/C
 * b) 1.914E+01 N&middot;m2/C
 * c) 2.106E+01 N&middot;m2/C
 * d) 2.316E+01 N&middot;m2/C
 * e) 2.548E+01 N&middot;m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.8 m from the center of the shells?


 * a) 5.865E+00 N/C
 * b) 6.451E+00 N/C
 * c) 7.096E+00 N/C
 * d) 7.806E+00 N/C
 * e) 8.587E+00 N/C

4) Two large parallel conducting plates are separated by 7.77 mm. Equal and opposite surface charges of 7.310E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?


 * a) 5.814E-01 mm
 * b) 6.686E-01 mm
 * c) 7.689E-01 mm
 * d) 8.842E-01 mm
 * e) 1.017E+00 mm

5) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 4.324E+02 V
 * b) 4.757E+02 V
 * c) 5.232E+02 V
 * d) 5.755E+02 V
 * e) 6.331E+02 V

6) In the figure shown C1=16.1 &mu;F, C2=2.14 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * a) 1.199E+01 &mu;J
 * b) 1.319E+01 &mu;J
 * c) 1.450E+01 &mu;J
 * d) 1.595E+01 &mu;J
 * e) 1.755E+01 &mu;J

7) A make-believe metal has a density of 3.530E+03 kg/m3 and an atomic mass of 10.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 1.673E+29 e&minus;/m3
 * b) 1.840E+29 e&minus;/m3
 * c) 2.024E+29 e&minus;/m3
 * d) 2.226E+29 e&minus;/m3
 * e) 2.449E+29 e&minus;/m3

8) Calculate the resistance of a 12-gauge copper wire that is 52 m long and carries a current of 99 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 1.983E-01 &Omega;
 * b) 2.181E-01 &Omega;
 * c) 2.399E-01 &Omega;
 * d) 2.639E-01 &Omega;
 * e) 2.903E-01 &Omega;

9) A given battery has a 14 V emf and an internal resistance of 0.192 &Omega;. If it is connected to a 0.766 &Omega; resistor what is the power dissipated by that load?


 * a) 1.229E+02 W
 * b) 1.352E+02 W
 * c) 1.487E+02 W
 * d) 1.636E+02 W
 * e) 1.799E+02 W

10) Two sources of emf &epsilon;1=31.0 V, and  &epsilon;2=10.0 V are oriented as shownin the circuit. The resistances are R1=4.22 k&Omega; and  R2=1.37 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.32 mA and I4=1.03 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.290E+00 mA
 * b) 2.519E+00 mA
 * c) 2.771E+00 mA
 * d) 3.048E+00 mA
 * e) 3.353E+00 mA

T6 E1
1) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 4.957E-02 &Omega;
 * b) 5.453E-02 &Omega;
 * c) 5.998E-02 &Omega;
 * d) 6.598E-02 &Omega;
 * e) 7.258E-02 &Omega;

2) A given battery has a 14 V emf and an internal resistance of 0.192 &Omega;. If it is connected to a 0.766 &Omega; resistor what is the power dissipated by that load?


 * a) 1.229E+02 W
 * b) 1.352E+02 W
 * c) 1.487E+02 W
 * d) 1.636E+02 W
 * e) 1.799E+02 W

3) Two sources of emf &epsilon;1=24.9 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 k&Omega; and  R2=2.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.74 mA and I4=0.444 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.725E+00 mA
 * b) 1.898E+00 mA
 * c) 2.087E+00 mA
 * d) 2.296E+00 mA
 * e) 2.526E+00 mA

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=6.8\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.6\text{ m}$$.


 * a) 1.258E+00 V/m2
 * b) 1.384E+00 V/m2
 * c) 1.522E+00 V/m2
 * d) 1.674E+00 V/m2
 * e) 1.842E+00 V/m2

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 8.5m2. Those in the xy plane have area 2.8m2 ,and those in the zx plane have area 3.7m2. An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.079E+01 N&middot;m2/C
 * b) 2.287E+01 N&middot;m2/C
 * c) 2.516E+01 N&middot;m2/C
 * d) 2.768E+01 N&middot;m2/C
 * e) 3.044E+01 N&middot;m2/C

6) A make-believe metal has a density of 3.230E+03 kg/m3 and an atomic mass of 116.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 1.385E+28 e&minus;/m3
 * b) 1.524E+28 e&minus;/m3
 * c) 1.676E+28 e&minus;/m3
 * d) 1.844E+28 e&minus;/m3
 * e) 2.028E+28 e&minus;/m3

7) In the figure shown C1=18.7 &mu;F, C2=2.15 &mu;F, and C3=4.88 &mu;F. The voltage source provides &epsilon;=11.9 V. What is the energy stored in C2?


 * a) 1.270E+01 &mu;J
 * b) 1.397E+01 &mu;J
 * c) 1.537E+01 &mu;J
 * d) 1.690E+01 &mu;J
 * e) 1.859E+01 &mu;J

8) Two large parallel conducting plates are separated by 8.0 mm. Equal and opposite surface charges of 7.520E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?


 * a) 5.431E-01 mm
 * b) 6.245E-01 mm
 * c) 7.182E-01 mm
 * d) 8.260E-01 mm
 * e) 9.499E-01 mm

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?


 * a) 2.964E+00 N/C
 * b) 3.260E+00 N/C
 * c) 3.586E+00 N/C
 * d) 3.944E+00 N/C
 * e) 4.339E+00 N/C

10) A diploe has a charge magnitude of q=6 nC and a separation distance of d=3.89 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.24 cm, y=1.95 cm)? Note that following the textbook's example, the y-value of the field point at 1.95 cm matches the disance of the positive charge above the x-axis.


 * a) 4.104E+02 V
 * b) 4.514E+02 V
 * c) 4.965E+02 V
 * d) 5.462E+02 V
 * e) 6.008E+02 V

T6 E2
1) Two sources of emf &epsilon;1=24.8 V, and  &epsilon;2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 k&Omega; and  R2=1.6 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.49 mA and I4=0.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.660E+00 mA
 * b) 1.826E+00 mA
 * c) 2.009E+00 mA
 * d) 2.209E+00 mA
 * e) 2.430E+00 mA

2) In the figure shown C1=16.3 &mu;F, C2=2.17 &mu;F, and C3=4.67 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * a) 8.718E+00 &mu;J
 * b) 9.589E+00 &mu;J
 * c) 1.055E+01 &mu;J
 * d) 1.160E+01 &mu;J
 * e) 1.276E+01 &mu;J

3) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.


 * a) 5.261E+02 V
 * b) 5.787E+02 V
 * c) 6.365E+02 V
 * d) 7.002E+02 V
 * e) 7.702E+02 V

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?


 * a) 9.144E+00 N/C
 * b) 1.006E+01 N/C
 * c) 1.106E+01 N/C
 * d) 1.217E+01 N/C
 * e) 1.339E+01 N/C

5) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=2.0\text{ m}$$ and the surface charge density is $$\sigma=9\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.2\text{ m}$$.


 * a) 8.933E+00 V/m2
 * b) 9.826E+00 V/m2
 * c) 1.081E+01 V/m2
 * d) 1.189E+01 V/m2
 * e) 1.308E+01 V/m2

6) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.631E-01 &Omega;
 * b) 2.894E-01 &Omega;
 * c) 3.184E-01 &Omega;
 * d) 3.502E-01 &Omega;
 * e) 3.852E-01 &Omega;

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.891E+01 N&middot;m2/C
 * b) 2.080E+01 N&middot;m2/C
 * c) 2.288E+01 N&middot;m2/C
 * d) 2.517E+01 N&middot;m2/C
 * e) 2.768E+01 N&middot;m2/C

8) A make-believe metal has a density of 1.180E+04 kg/m3 and an atomic mass of 121.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 4.010E+28 e&minus;/m3
 * b) 4.411E+28 e&minus;/m3
 * c) 4.852E+28 e&minus;/m3
 * d) 5.337E+28 e&minus;/m3
 * e) 5.871E+28 e&minus;/m3

9) Two large parallel conducting plates are separated by 7.77 mm. Equal and opposite surface charges of 7.310E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?


 * a) 5.814E-01 mm
 * b) 6.686E-01 mm
 * c) 7.689E-01 mm
 * d) 8.842E-01 mm
 * e) 1.017E+00 mm

10) A given battery has a 15 V emf and an internal resistance of 0.113 &Omega;. If it is connected to a 0.645 &Omega; resistor what is the power dissipated by that load?


 * a) 1.898E+02 W
 * b) 2.087E+02 W
 * c) 2.296E+02 W
 * d) 2.526E+02 W
 * e) 2.778E+02 W

T6 F0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * a) 8.690E+00 V/m2
 * b) 9.559E+00 V/m2
 * c) 1.051E+01 V/m2
 * d) 1.157E+01 V/m2
 * e) 1.272E+01 V/m2

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * a) 1.969E+02 V&middot;m
 * b) 2.166E+02 V&middot;m
 * c) 2.383E+02 V&middot;m
 * d) 2.621E+02 V&middot;m
 * e) 2.883E+02 V&middot;m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.920E+01 N&middot;m2/C
 * b) 7.612E+01 N&middot;m2/C
 * c) 8.373E+01 N&middot;m2/C
 * d) 9.210E+01 N&middot;m2/C
 * e) 1.013E+02 N&middot;m2/C

4) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.39 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.56 cm, y=2.19 cm)? Note that following the textbook's example, the y-value of the field point at 2.19 cm matches the disance of the positive charge above the x-axis.


 * a) 3.852E+02 V
 * b) 4.238E+02 V
 * c) 4.661E+02 V
 * d) 5.127E+02 V
 * e) 5.640E+02 V

5) When a 6.32 V battery operates a 1.94 W bulb, how many electrons pass through it each second?


 * a) 1.439E+18 electrons
 * b) 1.583E+18 electrons
 * c) 1.742E+18 electrons
 * d) 1.916E+18 electrons
 * e) 2.107E+18 electrons

6) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * a) 5.969E+01 &mu;C
 * b) 6.566E+01 &mu;C
 * c) 7.222E+01 &mu;C
 * d) 7.944E+01 &mu;C
 * e) 8.739E+01 &mu;C

7) Calculate the electric field in a 12-gauge copper wire that is 13 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.250E-04 V/m
 * b) 2.475E-04 V/m
 * c) 2.722E-04 V/m
 * d) 2.995E-04 V/m
 * e) 3.294E-04 V/m

8) Calculate the resistance of a 12-gauge copper wire that is 59 m long and carries a current of 26 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.995E-01 &Omega;
 * b) 3.294E-01 &Omega;
 * c) 3.623E-01 &Omega;
 * d) 3.986E-01 &Omega;
 * e) 4.384E-01 &Omega;

9) A battery with a terminal voltage of 7.63 V is connected to a circuit consisting of 3 20.9 &Omega; resistors and one 12.1 &Omega; resistor. What is the voltage drop across the 12.1 &Omega; resistor?


 * a) 1.234E+00 V
 * b) 1.358E+00 V
 * c) 1.493E+00 V
 * d) 1.643E+00 V
 * e) 1.807E+00 V

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 569 V.  If the combined external and internal resistance is 137 &Omega and the capacitance is  76 mF, how long will it take for the capacitor's voltage to reach 419.0 V?


 * a) 1.043E+01 s
 * b) 1.147E+01 s
 * c) 1.262E+01 s
 * d) 1.388E+01 s
 * e) 1.527E+01 s

T6 F1
1) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 190 V.  If the combined external and internal resistance is 255 &Omega and the capacitance is  54 mF, how long will it take for the capacitor's voltage to reach 101.0 V?


 * a) 1.044E+01 s
 * b) 1.149E+01 s
 * c) 1.264E+01 s
 * d) 1.390E+01 s
 * e) 1.529E+01 s

2) Calculate the electric field in a 12-gauge copper wire that is 23 m long and carries a current of 64 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.953E-04 V/m
 * b) 3.248E-04 V/m
 * c) 3.573E-04 V/m
 * d) 3.930E-04 V/m
 * e) 4.324E-04 V/m

3) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.3 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.86 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 6.325E+02 V
 * b) 6.957E+02 V
 * c) 7.653E+02 V
 * d) 8.418E+02 V
 * e) 9.260E+02 V

4) When a 4.89 V battery operates a 1.44 W bulb, how many electrons pass through it each second?


 * a) 1.838E+18 electrons
 * b) 2.022E+18 electrons
 * c) 2.224E+18 electrons
 * d) 2.446E+18 electrons
 * e) 2.691E+18 electrons

5) Calculate the resistance of a 12-gauge copper wire that is 19 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 7.970E-02 &Omega;
 * b) 8.767E-02 &Omega;
 * c) 9.644E-02 &Omega;
 * d) 1.061E-01 &Omega;
 * e) 1.167E-01 &Omega;

6) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.0 m, b=1.8 m.  The total charge on the rod is 6 nC.


 * a) 3.610E+00 V/m2
 * b) 3.971E+00 V/m2
 * c) 4.368E+00 V/m2
 * d) 4.804E+00 V/m2
 * e) 5.285E+00 V/m2

7) In the figure shown C1=17.7 &mu;F, C2=2.5 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=12.8 V. What is the charge on C1?


 * a) 5.066E+01 &mu;C
 * b) 5.573E+01 &mu;C
 * c) 6.130E+01 &mu;C
 * d) 6.743E+01 &mu;C
 * e) 7.417E+01 &mu;C

8) A battery with a terminal voltage of 10.6 V is connected to a circuit consisting of 2 21.1 &Omega; resistors and one 12.8 &Omega; resistor. What is the voltage drop across the 12.8 &Omega; resistor?


 * a) 2.467E+00 V
 * b) 2.714E+00 V
 * c) 2.985E+00 V
 * d) 3.283E+00 V
 * e) 3.612E+00 V

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.920E+01 N&middot;m2/C
 * b) 7.612E+01 N&middot;m2/C
 * c) 8.373E+01 N&middot;m2/C
 * d) 9.210E+01 N&middot;m2/C
 * e) 1.013E+02 N&middot;m2/C

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * a) 3.429E+03 V&middot;m
 * b) 3.771E+03 V&middot;m
 * c) 4.149E+03 V&middot;m
 * d) 4.564E+03 V&middot;m
 * e) 5.020E+03 V&middot;m

T6 F2
1) Calculate the electric field in a 12-gauge copper wire that is 21 m long and carries a current of 42 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 1.602E-04 V/m
 * b) 1.762E-04 V/m
 * c) 1.938E-04 V/m
 * d) 2.132E-04 V/m
 * e) 2.345E-04 V/m

2) Calculate the resistance of a 12-gauge copper wire that is 48 m long and carries a current of 50 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.215E-01 &Omega;
 * b) 2.436E-01 &Omega;
 * c) 2.680E-01 &Omega;
 * d) 2.948E-01 &Omega;
 * e) 3.243E-01 &Omega;

3) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 467 V.  If the combined external and internal resistance is 172 &Omega and the capacitance is  74 mF, how long will it take for the capacitor's voltage to reach 258.0 V?


 * a) 7.688E+00 s
 * b) 8.457E+00 s
 * c) 9.303E+00 s
 * d) 1.023E+01 s
 * e) 1.126E+01 s

4) In the figure shown C1=17.9 &mu;F, C2=2.71 &mu;F, and C3=4.14 &mu;F. The voltage source provides &epsilon;=7.12 V. What is the charge on C1?


 * a) 3.527E+01 &mu;C
 * b) 3.880E+01 &mu;C
 * c) 4.268E+01 &mu;C
 * d) 4.695E+01 &mu;C
 * e) 5.164E+01 &mu;C

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.186E+01 N&middot;m2/C
 * b) 2.404E+01 N&middot;m2/C
 * c) 2.645E+01 N&middot;m2/C
 * d) 2.909E+01 N&middot;m2/C
 * e) 3.200E+01 N&middot;m2/C

6) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.62 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * a) 6.311E+00 V/m2
 * b) 6.943E+00 V/m2
 * c) 7.637E+00 V/m2
 * d) 8.401E+00 V/m2
 * e) 9.241E+00 V/m2

7) A battery with a terminal voltage of 14.6 V is connected to a circuit consisting of 2 21.7 &Omega; resistors and one 14.4 &Omega; resistor. What is the voltage drop across the 14.4 &Omega; resistor?


 * a) 3.637E+00 V
 * b) 4.001E+00 V
 * c) 4.401E+00 V
 * d) 4.841E+00 V
 * e) 5.325E+00 V

8) A diploe has a charge magnitude of q=6 nC and a separation distance of d=3.89 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.24 cm, y=1.95 cm)? Note that following the textbook's example, the y-value of the field point at 1.95 cm matches the disance of the positive charge above the x-axis.


 * a) 4.104E+02 V
 * b) 4.514E+02 V
 * c) 4.965E+02 V
 * d) 5.462E+02 V
 * e) 6.008E+02 V

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.8}\hat i +1x^{2.3}\hat j +2y^{2.9}\hat k$$


 * a) 2.210E+04 V&middot;m
 * b) 2.431E+04 V&middot;m
 * c) 2.674E+04 V&middot;m
 * d) 2.941E+04 V&middot;m
 * e) 3.235E+04 V&middot;m

10) When a 4.21 V battery operates a 2.17 W bulb, how many electrons pass through it each second?


 * a) 2.659E+18 electrons
 * b) 2.925E+18 electrons
 * c) 3.217E+18 electrons
 * d) 3.539E+18 electrons
 * e) 3.893E+18 electrons

T6 G0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.8\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.1\text{ m}$$.


 * a) 7.517E+00 V/m2
 * b) 8.269E+00 V/m2
 * c) 9.096E+00 V/m2
 * d) 1.001E+01 V/m2
 * e) 1.101E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.988E+01 N&middot;m2/C
 * b) 5.487E+01 N&middot;m2/C
 * c) 6.035E+01 N&middot;m2/C
 * d) 6.639E+01 N&middot;m2/C
 * e) 7.303E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * a) 1.969E+02 V&middot;m
 * b) 2.166E+02 V&middot;m
 * c) 2.383E+02 V&middot;m
 * d) 2.621E+02 V&middot;m
 * e) 2.883E+02 V&middot;m

4) A 7 C charge is separated from a 15 C charge by distance of 14 cm.  What is the work done by increasing this separation to 20 cm?


 * a) 1.519E-06 J
 * b) 1.671E-06 J
 * c) 1.838E-06 J
 * d) 2.022E-06 J
 * e) 2.224E-06 J

5) Assume that a 16 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (6 cm, 0&deg;) and  P2 is at (14 cm, 27&deg;).


 * a) 9.354E+02 V
 * b) 1.029E+03 V
 * c) 1.132E+03 V
 * d) 1.245E+03 V
 * e) 1.370E+03 V

6) What is the net capacitance if C1=4.55 &mu;F, C2=4.39 &mu;F, and C3=3.32 &mu;F in the configuration shown?


 * a) 4.173E+00 &mu;F
 * b) 4.590E+00 &mu;F
 * c) 5.049E+00 &mu;F
 * d) 5.554E+00 &mu;F
 * e) 6.110E+00 &mu;F

7) A DC winch moter draws 25 amps at 128 volts as it lifts a 5.710E+03 N weight at a constant speed of 0.449 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 8.413E-01 &Omega;
 * b) 9.254E-01 &Omega;
 * c) 1.018E+00 &Omega;
 * d) 1.120E+00 &Omega;
 * e) 1.232E+00 &Omega;

8) Calculate the electric field in a 12-gauge copper wire that is 41 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 3.604E-04 V/m
 * b) 3.964E-04 V/m
 * c) 4.360E-04 V/m
 * d) 4.796E-04 V/m
 * e) 5.276E-04 V/m

9) In the circuit shown V=11.8 V, R1=2.38 &Omega;, R2=5.11 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * a) 8.489E+00 W
 * b) 9.338E+00 W
 * c) 1.027E+01 W
 * d) 1.130E+01 W
 * e) 1.243E+01 W

10) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=14.4 V are oriented as shownin the circuit. The resistances are R1=4.33 k&Omega; and  R2=1.65 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.59 mA and I4=1.07 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 9.142E+00 V
 * b) 1.006E+01 V
 * c) 1.106E+01 V
 * d) 1.217E+01 V
 * e) 1.338E+01 V

T6 G1
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.4\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=0.56\text{ m}$$.


 * a) 2.567E+01 V/m2
 * b) 2.824E+01 V/m2
 * c) 3.106E+01 V/m2
 * d) 3.417E+01 V/m2
 * e) 3.759E+01 V/m2

2) Assume that a 6 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (16 cm, 71&deg;).


 * a) 1.969E+02 V
 * b) 2.166E+02 V
 * c) 2.383E+02 V
 * d) 2.621E+02 V
 * e) 2.884E+02 V

3) Calculate the electric field in a 12-gauge copper wire that is 17 m long and carries a current of 56 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 1.941E-04 V/m
 * b) 2.135E-04 V/m
 * c) 2.349E-04 V/m
 * d) 2.584E-04 V/m
 * e) 2.842E-04 V/m

4) In the circuit shown V=16.1 V, R1=1.18 &Omega;, R2=5.28 &Omega;, and R3=14.8 &Omega;. What is the power dissipated by R2?


 * a) 2.172E+01 W
 * b) 2.389E+01 W
 * c) 2.628E+01 W
 * d) 2.891E+01 W
 * e) 3.180E+01 W

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.777E+01 N&middot;m2/C
 * b) 5.254E+01 N&middot;m2/C
 * c) 5.780E+01 N&middot;m2/C
 * d) 6.358E+01 N&middot;m2/C
 * e) 6.993E+01 N&middot;m2/C

6) A 5 C charge is separated from a 12 C charge by distance of 10 cm.  What is the work done by increasing this separation to 16 cm?


 * a) 1.381E-06 J
 * b) 1.519E-06 J
 * c) 1.671E-06 J
 * d) 1.838E-06 J
 * e) 2.022E-06 J

7) What is the net capacitance if C1=2.55 &mu;F, C2=4.13 &mu;F, and C3=2.5 &mu;F in the configuration shown?


 * a) 4.077E+00 &mu;F
 * b) 4.484E+00 &mu;F
 * c) 4.933E+00 &mu;F
 * d) 5.426E+00 &mu;F
 * e) 5.969E+00 &mu;F

8) A DC winch moter draws 26 amps at 177 volts as it lifts a 4.820E+03 N weight at a constant speed of 0.696 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.677E+00 &Omega;
 * b) 1.845E+00 &Omega;
 * c) 2.030E+00 &Omega;
 * d) 2.233E+00 &Omega;
 * e) 2.456E+00 &Omega;

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * a) 4.286E+03 V&middot;m
 * b) 4.714E+03 V&middot;m
 * c) 5.186E+03 V&middot;m
 * d) 5.704E+03 V&middot;m
 * e) 6.275E+03 V&middot;m

10) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.11 mA and I4=0.746 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 4.275E+00 V
 * b) 4.703E+00 V
 * c) 5.173E+00 V
 * d) 5.691E+00 V
 * e) 6.260E+00 V

T6 G2
1) What is the net capacitance if C1=3.97 &mu;F, C2=3.51 &mu;F, and C3=2.18 &mu;F in the configuration shown?


 * a) 3.038E+00 &mu;F
 * b) 3.341E+00 &mu;F
 * c) 3.675E+00 &mu;F
 * d) 4.043E+00 &mu;F
 * e) 4.447E+00 &mu;F

2) Calculate the electric field in a 12-gauge copper wire that is 26 m long and carries a current of 24 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 9.152E-05 V/m
 * b) 1.007E-04 V/m
 * c) 1.107E-04 V/m
 * d) 1.218E-04 V/m
 * e) 1.340E-04 V/m

3) Assume that a 5 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 31&deg;).


 * a) 1.397E+02 V
 * b) 1.536E+02 V
 * c) 1.690E+02 V
 * d) 1.859E+02 V
 * e) 2.045E+02 V

4) Two sources of emf &epsilon;1=21.0 V, and  &epsilon;2=8.72 V are oriented as shownin the circuit. The resistances are R1=3.12 k&Omega; and  R2=1.15 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.41 mA and I4=0.816 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 5.267E+00 V
 * b) 5.794E+00 V
 * c) 6.373E+00 V
 * d) 7.011E+00 V
 * e) 7.712E+00 V

5) In the circuit shown V=16.1 V, R1=1.18 &Omega;, R2=5.28 &Omega;, and R3=14.8 &Omega;. What is the power dissipated by R2?


 * a) 2.172E+01 W
 * b) 2.389E+01 W
 * c) 2.628E+01 W
 * d) 2.891E+01 W
 * e) 3.180E+01 W

6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.0}\hat i +2x^{2.1}\hat j +3y^{2.5}\hat k$$


 * a) 9.027E+03 V&middot;m
 * b) 9.930E+03 V&middot;m
 * c) 1.092E+04 V&middot;m
 * d) 1.202E+04 V&middot;m
 * e) 1.322E+04 V&middot;m

7) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=4.3\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.4\text{ m}$$.


 * a) 5.647E+00 V/m2
 * b) 6.212E+00 V/m2
 * c) 6.833E+00 V/m2
 * d) 7.517E+00 V/m2
 * e) 8.268E+00 V/m2

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 9.823E+00 N&middot;m2/C
 * b) 1.080E+01 N&middot;m2/C
 * c) 1.189E+01 N&middot;m2/C
 * d) 1.307E+01 N&middot;m2/C
 * e) 1.438E+01 N&middot;m2/C

9) A 2 C charge is separated from a 6 C charge by distance of 13 cm.  What is the work done by increasing this separation to 16 cm?


 * a) 1.556E-07 J
 * b) 1.711E-07 J
 * c) 1.882E-07 J
 * d) 2.070E-07 J
 * e) 2.277E-07 J

10) A DC winch moter draws 17 amps at 187 volts as it lifts a 5.600E+03 N weight at a constant speed of 0.381 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 2.471E+00 &Omega;
 * b) 2.718E+00 &Omega;
 * c) 2.990E+00 &Omega;
 * d) 3.288E+00 &Omega;
 * e) 3.617E+00 &Omega;

T6 H0
1) A large thin isolated square plate has an area of 6 m2. It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?


 * a) 3.214E+01 N/C
 * b) 3.536E+01 N/C
 * c) 3.889E+01 N/C
 * d) 4.278E+01 N/C
 * e) 4.706E+01 N/C

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.662E+01 N&middot;m2/C
 * b) 4.028E+01 N&middot;m2/C
 * c) 4.430E+01 N&middot;m2/C
 * d) 4.873E+01 N&middot;m2/C
 * e) 5.361E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.125E+01 N&middot;m2/C
 * b) 4.537E+01 N&middot;m2/C
 * c) 4.991E+01 N&middot;m2/C
 * d) 5.490E+01 N&middot;m2/C
 * e) 6.039E+01 N&middot;m2/C

4) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?


 * a) 1.439E+18 electrons
 * b) 1.582E+18 electrons
 * c) 1.741E+18 electrons
 * d) 1.915E+18 electrons
 * e) 2.106E+18 electrons

5) Two large parallel conducting plates are separated by 9.71 mm. Equal and opposite surface charges of 7.550E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?


 * a) 7.444E-01 mm
 * b) 8.561E-01 mm
 * c) 9.845E-01 mm
 * d) 1.132E+00 mm
 * e) 1.302E+00 mm

6) In the figure shown C1=19.9 &mu;F, C2=2.25 &mu;F, and C3=4.75 &mu;F. The voltage source provides &epsilon;=6.93 V. What is the charge on C1?


 * a) 2.451E+01 &mu;C
 * b) 2.696E+01 &mu;C
 * c) 2.966E+01 &mu;C
 * d) 3.262E+01 &mu;C
 * e) 3.589E+01 &mu;C

7) Calculate the resistance of a 12-gauge copper wire that is 86 m long and carries a current of 97 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 4.365E-01 &Omega;
 * b) 4.801E-01 &Omega;
 * c) 5.282E-01 &Omega;
 * d) 5.810E-01 &Omega;
 * e) 6.391E-01 &Omega;

8) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 2.292E+29 e&minus;/m3
 * b) 2.521E+29 e&minus;/m3
 * c) 2.773E+29 e&minus;/m3
 * d) 3.051E+29 e&minus;/m3
 * e) 3.356E+29 e&minus;/m3

9) Two sources of emf &epsilon;1=54.9 V, and  &epsilon;2=19.8 V are oriented as shownin the circuit. The resistances are R1=3.93 k&Omega; and  R2=1.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.18 mA and I4=1.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.779E+01 V
 * b) 1.957E+01 V
 * c) 2.153E+01 V
 * d) 2.368E+01 V
 * e) 2.605E+01 V

10) A battery with a terminal voltage of 13.2 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * a) 1.958E+00 V
 * b) 2.153E+00 V
 * c) 2.369E+00 V
 * d) 2.606E+00 V
 * e) 2.866E+00 V

T6 H1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.978E+01 N&middot;m2/C
 * b) 6.576E+01 N&middot;m2/C
 * c) 7.233E+01 N&middot;m2/C
 * d) 7.957E+01 N&middot;m2/C
 * e) 8.752E+01 N&middot;m2/C

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.737E+01 N&middot;m2/C
 * b) 1.910E+01 N&middot;m2/C
 * c) 2.101E+01 N&middot;m2/C
 * d) 2.311E+01 N&middot;m2/C
 * e) 2.543E+01 N&middot;m2/C

3) Calculate the resistance of a 12-gauge copper wire that is 42 m long and carries a current of 63 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 1.938E-01 &Omega;
 * b) 2.132E-01 &Omega;
 * c) 2.345E-01 &Omega;
 * d) 2.579E-01 &Omega;
 * e) 2.837E-01 &Omega;

4) Two sources of emf &epsilon;1=27.9 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=2.82 k&Omega; and  R2=2.25 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.1 mA and I4=0.676 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 8.334E+00 V
 * b) 9.167E+00 V
 * c) 1.008E+01 V
 * d) 1.109E+01 V
 * e) 1.220E+01 V

5) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 2.292E+29 e&minus;/m3
 * b) 2.521E+29 e&minus;/m3
 * c) 2.773E+29 e&minus;/m3
 * d) 3.051E+29 e&minus;/m3
 * e) 3.356E+29 e&minus;/m3

6) When a 4.91 V battery operates a 1.43 W bulb, how many electrons pass through it each second?


 * a) 1.242E+18 electrons
 * b) 1.366E+18 electrons
 * c) 1.502E+18 electrons
 * d) 1.653E+18 electrons
 * e) 1.818E+18 electrons

7) In the figure shown C1=19.0 &mu;F, C2=2.35 &mu;F, and C3=5.22 &mu;F. The voltage source provides &epsilon;=6.01 V. What is the charge on C1?


 * a) 2.444E+01 &mu;C
 * b) 2.689E+01 &mu;C
 * c) 2.958E+01 &mu;C
 * d) 3.253E+01 &mu;C
 * e) 3.579E+01 &mu;C

8) Two large parallel conducting plates are separated by 9.87 mm. Equal and opposite surface charges of 7.610E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 66 V?


 * a) 4.391E-01 mm
 * b) 5.049E-01 mm
 * c) 5.806E-01 mm
 * d) 6.677E-01 mm
 * e) 7.679E-01 mm

9) A large thin isolated square plate has an area of 5 m2. It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * a) 6.534E+01 N/C
 * b) 7.187E+01 N/C
 * c) 7.906E+01 N/C
 * d) 8.696E+01 N/C
 * e) 9.566E+01 N/C

10) A battery with a terminal voltage of 8.01 V is connected to a circuit consisting of 3 22.1 &Omega; resistors and one 14.5 &Omega; resistor. What is the voltage drop across the 14.5 &Omega; resistor?


 * a) 9.818E-01 V
 * b) 1.080E+00 V
 * c) 1.188E+00 V
 * d) 1.307E+00 V
 * e) 1.437E+00 V

T6 H2
1) A large thin isolated square plate has an area of 8 m2. It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * a) 2.652E+01 N/C
 * b) 2.917E+01 N/C
 * c) 3.209E+01 N/C
 * d) 3.529E+01 N/C
 * e) 3.882E+01 N/C

2) Two sources of emf &epsilon;1=17.3 V, and  &epsilon;2=6.46 V are oriented as shownin the circuit. The resistances are R1=2.54 k&Omega; and  R2=2.79 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.1 mA and I4=0.281 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 6.488E+00 V
 * b) 7.137E+00 V
 * c) 7.850E+00 V
 * d) 8.635E+00 V
 * e) 9.499E+00 V

3) Two large parallel conducting plates are separated by 9.6 mm. Equal and opposite surface charges of 7.610E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 71 V?


 * a) 4.723E-01 mm
 * b) 5.432E-01 mm
 * c) 6.246E-01 mm
 * d) 7.183E-01 mm
 * e) 8.261E-01 mm

4) Calculate the resistance of a 12-gauge copper wire that is 86 m long and carries a current of 97 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 4.365E-01 &Omega;
 * b) 4.801E-01 &Omega;
 * c) 5.282E-01 &Omega;
 * d) 5.810E-01 &Omega;
 * e) 6.391E-01 &Omega;

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.662E+01 N&middot;m2/C
 * b) 4.028E+01 N&middot;m2/C
 * c) 4.430E+01 N&middot;m2/C
 * d) 4.873E+01 N&middot;m2/C
 * e) 5.361E+01 N&middot;m2/C

6) A make-believe metal has a density of 3.470E+03 kg/m3 and an atomic mass of 33.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 6.180E+28 e&minus;/m3
 * b) 6.798E+28 e&minus;/m3
 * c) 7.478E+28 e&minus;/m3
 * d) 8.226E+28 e&minus;/m3
 * e) 9.049E+28 e&minus;/m3

7) When a 4.21 V battery operates a 2.17 W bulb, how many electrons pass through it each second?


 * a) 2.659E+18 electrons
 * b) 2.925E+18 electrons
 * c) 3.217E+18 electrons
 * d) 3.539E+18 electrons
 * e) 3.893E+18 electrons

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.978E+01 N&middot;m2/C
 * b) 6.576E+01 N&middot;m2/C
 * c) 7.233E+01 N&middot;m2/C
 * d) 7.957E+01 N&middot;m2/C
 * e) 8.752E+01 N&middot;m2/C

9) A battery with a terminal voltage of 14.1 V is connected to a circuit consisting of 2 20.3 &Omega; resistors and one 13.1 &Omega; resistor. What is the voltage drop across the 13.1 &Omega; resistor?


 * a) 2.843E+00 V
 * b) 3.127E+00 V
 * c) 3.440E+00 V
 * d) 3.784E+00 V
 * e) 4.162E+00 V

10) In the figure shown C1=19.2 &mu;F, C2=2.86 &mu;F, and C3=5.03 &mu;F. The voltage source provides &epsilon;=9.46 V. What is the charge on C1?


 * a) 4.809E+01 &mu;C
 * b) 5.290E+01 &mu;C
 * c) 5.819E+01 &mu;C
 * d) 6.401E+01 &mu;C
 * e) 7.041E+01 &mu;C

T6 I0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=3.0\text{ m}$$ and the surface charge density is $$\sigma=8\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.0\text{ m}$$.


 * a) 9.459E+00 V/m2
 * b) 1.040E+01 V/m2
 * c) 1.145E+01 V/m2
 * d) 1.259E+01 V/m2
 * e) 1.385E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.521E+01 N&middot;m2/C
 * b) 4.973E+01 N&middot;m2/C
 * c) 5.470E+01 N&middot;m2/C
 * d) 6.017E+01 N&middot;m2/C
 * e) 6.619E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is, $$\vec E=4y^{1.4}\hat i +2x^{2.3}\hat j +4y^{2.3}\hat k$$


 * a) 2.694E+03 V&middot;m
 * b) 2.963E+03 V&middot;m
 * c) 3.259E+03 V&middot;m
 * d) 3.585E+03 V&middot;m
 * e) 3.944E+03 V&middot;m

4) When a 6.03 V battery operates a 1.56 W bulb, how many electrons pass through it each second?


 * a) 1.615E+18 electrons
 * b) 1.776E+18 electrons
 * c) 1.954E+18 electrons
 * d) 2.149E+18 electrons
 * e) 2.364E+18 electrons

5) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.48 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.8 cm, y=2.24 cm)? Note that following the textbook's example, the y-value of the field point at 2.24 cm matches the disance of the positive charge above the x-axis.


 * a) 5.134E+02 V
 * b) 5.648E+02 V
 * c) 6.212E+02 V
 * d) 6.834E+02 V
 * e) 7.517E+02 V

6) In the figure shown C1=16.0 &mu;F, C2=2.27 &mu;F, and C3=4.4 &mu;F. The voltage source provides &epsilon;=7.11 V. What is the charge on C1?


 * a) 2.515E+01 &mu;C
 * b) 2.766E+01 &mu;C
 * c) 3.043E+01 &mu;C
 * d) 3.347E+01 &mu;C
 * e) 3.682E+01 &mu;C

7) Calculate the drift speed of electrons in a copper wire with a diameter of 5.33 mm carrying a 5.1 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.711E-05 m/s
 * b) 1.882E-05 m/s
 * c) 2.070E-05 m/s
 * d) 2.277E-05 m/s
 * e) 2.505E-05 m/s

8) Calculate the resistance of a 12-gauge copper wire that is 14 m long and carries a current of 38 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 5.873E-02 &Omega;
 * b) 6.460E-02 &Omega;
 * c) 7.106E-02 &Omega;
 * d) 7.816E-02 &Omega;
 * e) 8.598E-02 &Omega;

9) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.11 mA and I4=0.746 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 4.275E+00 V
 * b) 4.703E+00 V
 * c) 5.173E+00 V
 * d) 5.691E+00 V
 * e) 6.260E+00 V

10) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.440E+01 V
 * b) 1.584E+01 V
 * c) 1.742E+01 V
 * d) 1.916E+01 V
 * e) 2.108E+01 V

T6 I1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 5.3m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 7.793E+01 N&middot;m2/C
 * b) 8.572E+01 N&middot;m2/C
 * c) 9.429E+01 N&middot;m2/C
 * d) 1.037E+02 N&middot;m2/C
 * e) 1.141E+02 N&middot;m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * a) 4.286E+03 V&middot;m
 * b) 4.714E+03 V&middot;m
 * c) 5.186E+03 V&middot;m
 * d) 5.704E+03 V&middot;m
 * e) 6.275E+03 V&middot;m

3) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 k&Omega; and  R2=2.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.34 mA and I4=0.955 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 7.031E+00 V
 * b) 7.734E+00 V
 * c) 8.507E+00 V
 * d) 9.358E+00 V
 * e) 1.029E+01 V

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.


 * a) 5.134E-01 V/m2
 * b) 5.648E-01 V/m2
 * c) 6.212E-01 V/m2
 * d) 6.834E-01 V/m2
 * e) 7.517E-01 V/m2

5) Two sources of emf &epsilon;1=54.9 V, and  &epsilon;2=19.8 V are oriented as shownin the circuit. The resistances are R1=3.93 k&Omega; and  R2=1.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.18 mA and I4=1.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.779E+01 V
 * b) 1.957E+01 V
 * c) 2.153E+01 V
 * d) 2.368E+01 V
 * e) 2.605E+01 V

6) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.09 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.45 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * a) 3.814E+02 V
 * b) 4.195E+02 V
 * c) 4.615E+02 V
 * d) 5.077E+02 V
 * e) 5.584E+02 V

7) Calculate the drift speed of electrons in a copper wire with a diameter of 5.47 mm carrying a 3.48 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.008E-05 m/s
 * b) 1.108E-05 m/s
 * c) 1.219E-05 m/s
 * d) 1.341E-05 m/s
 * e) 1.475E-05 m/s

8) When a 8.6 V battery operates a 2.76 W bulb, how many electrons pass through it each second?


 * a) 1.655E+18 electrons
 * b) 1.821E+18 electrons
 * c) 2.003E+18 electrons
 * d) 2.203E+18 electrons
 * e) 2.424E+18 electrons

9) In the figure shown C1=17.5 &mu;F, C2=2.63 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=15.9 V. What is the charge on C1?


 * a) 8.197E+01 &mu;C
 * b) 9.017E+01 &mu;C
 * c) 9.919E+01 &mu;C
 * d) 1.091E+02 &mu;C
 * e) 1.200E+02 &mu;C

10) Calculate the resistance of a 12-gauge copper wire that is 30 m long and carries a current of 31 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 1.384E-01 &Omega;
 * b) 1.523E-01 &Omega;
 * c) 1.675E-01 &Omega;
 * d) 1.842E-01 &Omega;
 * e) 2.027E-01 &Omega;

T6 I2
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.698E+01 N&middot;m2/C
 * b) 1.868E+01 N&middot;m2/C
 * c) 2.055E+01 N&middot;m2/C
 * d) 2.260E+01 N&middot;m2/C
 * e) 2.486E+01 N&middot;m2/C

2) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.


 * a) 5.261E+02 V
 * b) 5.787E+02 V
 * c) 6.365E+02 V
 * d) 7.002E+02 V
 * e) 7.702E+02 V

3) Calculate the drift speed of electrons in a copper wire with a diameter of 3.53 mm carrying a 2.8 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.947E-05 m/s
 * b) 2.141E-05 m/s
 * c) 2.355E-05 m/s
 * d) 2.591E-05 m/s
 * e) 2.850E-05 m/s

4) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * a) 5.969E+01 &mu;C
 * b) 6.566E+01 &mu;C
 * c) 7.222E+01 &mu;C
 * d) 7.944E+01 &mu;C
 * e) 8.739E+01 &mu;C

5) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.3\text{ m}$$ and the surface charge density is $$\sigma=5\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.3\text{ m}$$.


 * a) 1.022E+00 V/m2
 * b) 1.125E+00 V/m2
 * c) 1.237E+00 V/m2
 * d) 1.361E+00 V/m2
 * e) 1.497E+00 V/m2

6) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.631E-01 &Omega;
 * b) 2.894E-01 &Omega;
 * c) 3.184E-01 &Omega;
 * d) 3.502E-01 &Omega;
 * e) 3.852E-01 &Omega;

7) Two sources of emf &epsilon;1=28.6 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=3.73 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.27 mA and I4=0.774 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 6.641E+00 V
 * b) 7.305E+00 V
 * c) 8.035E+00 V
 * d) 8.839E+00 V
 * e) 9.723E+00 V

8) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.440E+01 V
 * b) 1.584E+01 V
 * c) 1.742E+01 V
 * d) 1.916E+01 V
 * e) 2.108E+01 V

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is, $$\vec E=2y^{1.8}\hat i +3x^{1.9}\hat j +5y^{3.2}\hat k$$


 * a) 9.952E+03 V&middot;m
 * b) 1.095E+04 V&middot;m
 * c) 1.204E+04 V&middot;m
 * d) 1.325E+04 V&middot;m
 * e) 1.457E+04 V&middot;m

10) When a 7.78 V battery operates a 1.35 W bulb, how many electrons pass through it each second?


 * a) 7.397E+17 electrons
 * b) 8.137E+17 electrons
 * c) 8.951E+17 electrons
 * d) 9.846E+17 electrons
 * e) 1.083E+18 electrons

T6 J0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=4e$$?


 * a) 3.719E+01 degrees
 * b) 4.091E+01 degrees
 * c) 4.500E+01 degrees
 * d) 4.950E+01 degrees
 * e) 5.445E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.712E+01 N&middot;m2/C
 * b) 4.083E+01 N&middot;m2/C
 * c) 4.491E+01 N&middot;m2/C
 * d) 4.940E+01 N&middot;m2/C
 * e) 5.434E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.2}\hat i +1x^{3.3}\hat j +5y^{2.4}\hat k$$


 * a) 7.054E+03 V&middot;m
 * b) 7.759E+03 V&middot;m
 * c) 8.535E+03 V&middot;m
 * d) 9.388E+03 V&middot;m
 * e) 1.033E+04 V&middot;m

4) Two large parallel conducting plates are separated by 7.81 mm. Equal and opposite surface charges of 7.440E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 80 V?


 * a) 9.521E-01 mm
 * b) 1.095E+00 mm
 * c) 1.259E+00 mm
 * d) 1.448E+00 mm
 * e) 1.665E+00 mm

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 16 V.


 * a) 2.157E+06 m/s
 * b) 2.372E+06 m/s
 * c) 2.610E+06 m/s
 * d) 2.871E+06 m/s
 * e) 3.158E+06 m/s

6) In the figure shown C1=17.7 &mu;F, C2=2.5 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=12.8 V. What is the charge on C1?


 * a) 5.066E+01 &mu;C
 * b) 5.573E+01 &mu;C
 * c) 6.130E+01 &mu;C
 * d) 6.743E+01 &mu;C
 * e) 7.417E+01 &mu;C

7) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?


 * a) 2.240E+02 A
 * b) 2.464E+02 A
 * c) 2.711E+02 A
 * d) 2.982E+02 A
 * e) 3.280E+02 A

8) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * a) $2.791E+01
 * b) $3.071E+01
 * c) $3.378E+01
 * d) $3.715E+01
 * e) $4.087E+01

9) A battery with a terminal voltage of 6.49 V is connected to a circuit consisting of 3 18.0 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * a) 7.101E-01 V
 * b) 7.811E-01 V
 * c) 8.592E-01 V
 * d) 9.451E-01 V
 * e) 1.040E+00 V

10) A given battery has a 13 V emf and an internal resistance of 0.106 &Omega;. If it is connected to a 0.752 &Omega; resistor what is the power dissipated by that load?


 * a) 1.569E+02 W
 * b) 1.726E+02 W
 * c) 1.899E+02 W
 * d) 2.089E+02 W
 * e) 2.298E+02 W

T6 J1
1) What is consumer cost to operate one 74&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.119 per kilowatt-hour?


 * a) $1.976E+01
 * b) $2.173E+01
 * c) $2.391E+01
 * d) $2.630E+01
 * e) $2.893E+01

2) In the figure shown C1=15.4 &mu;F, C2=2.22 &mu;F, and C3=4.77 &mu;F. The voltage source provides &epsilon;=6.8 V. What is the charge on C1?


 * a) 2.702E+01 &mu;C
 * b) 2.972E+01 &mu;C
 * c) 3.269E+01 &mu;C
 * d) 3.596E+01 &mu;C
 * e) 3.956E+01 &mu;C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k$$


 * a) 8.731E+02 V&middot;m
 * b) 9.604E+02 V&middot;m
 * c) 1.056E+03 V&middot;m
 * d) 1.162E+03 V&middot;m
 * e) 1.278E+03 V&middot;m

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.898E+01 N&middot;m2/C
 * b) 7.588E+01 N&middot;m2/C
 * c) 8.347E+01 N&middot;m2/C
 * d) 9.181E+01 N&middot;m2/C
 * e) 1.010E+02 N&middot;m2/C

5) What is the average current involved when a truck battery sets in motion 779 C of charge in 3.96 s while starting an engine?


 * a) 1.626E+02 A
 * b) 1.788E+02 A
 * c) 1.967E+02 A
 * d) 2.164E+02 A
 * e) 2.380E+02 A

6) A battery with a terminal voltage of 8.41 V is connected to a circuit consisting of 3 16.1 &Omega; resistors and one 10.9 &Omega; resistor. What is the voltage drop across the 10.9 &Omega; resistor?


 * a) 1.058E+00 V
 * b) 1.163E+00 V
 * c) 1.280E+00 V
 * d) 1.408E+00 V
 * e) 1.548E+00 V

7) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * a) 4.766E+01 degrees
 * b) 5.243E+01 degrees
 * c) 5.767E+01 degrees
 * d) 6.343E+01 degrees
 * e) 6.978E+01 degrees

8) Two large parallel conducting plates are separated by 7.83 mm. Equal and opposite surface charges of 7.530E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 86 V?


 * a) 8.793E-01 mm
 * b) 1.011E+00 mm
 * c) 1.163E+00 mm
 * d) 1.337E+00 mm
 * e) 1.538E+00 mm

9) A given battery has a 11 V emf and an internal resistance of 0.0998 &Omega;. If it is connected to a 0.417 &Omega; resistor what is the power dissipated by that load?


 * a) 1.419E+02 W
 * b) 1.561E+02 W
 * c) 1.717E+02 W
 * d) 1.889E+02 W
 * e) 2.078E+02 W

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 6 V.


 * a) 1.091E+06 m/s
 * b) 1.201E+06 m/s
 * c) 1.321E+06 m/s
 * d) 1.453E+06 m/s
 * e) 1.598E+06 m/s

T6 J2
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.2}\hat i +1x^{3.0}\hat j +2y^{1.7}\hat k$$


 * a) 8.545E+01 V&middot;m
 * b) 9.400E+01 V&middot;m
 * c) 1.034E+02 V&middot;m
 * d) 1.137E+02 V&middot;m
 * e) 1.251E+02 V&middot;m

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.712E+01 N&middot;m2/C
 * b) 4.083E+01 N&middot;m2/C
 * c) 4.491E+01 N&middot;m2/C
 * d) 4.940E+01 N&middot;m2/C
 * e) 5.434E+01 N&middot;m2/C

3) What is consumer cost to operate one 73&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.113 per kilowatt-hour?


 * a) $3.312E+01
 * b) $3.643E+01
 * c) $4.007E+01
 * d) $4.408E+01
 * e) $4.849E+01

4) A given battery has a 15 V emf and an internal resistance of 0.0536 &Omega;. If it is connected to a 0.64 &Omega; resistor what is the power dissipated by that load?


 * a) 2.721E+02 W
 * b) 2.993E+02 W
 * c) 3.293E+02 W
 * d) 3.622E+02 W
 * e) 3.984E+02 W

5) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 &Omega; resistors and one 12.1 &Omega; resistor. What is the voltage drop across the 12.1 &Omega; resistor?


 * a) 1.333E+00 V
 * b) 1.466E+00 V
 * c) 1.612E+00 V
 * d) 1.774E+00 V
 * e) 1.951E+00 V

6) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * a) 5.969E+01 &mu;C
 * b) 6.566E+01 &mu;C
 * c) 7.222E+01 &mu;C
 * d) 7.944E+01 &mu;C
 * e) 8.739E+01 &mu;C

7) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?


 * a) 6.525E-01 mm
 * b) 7.504E-01 mm
 * c) 8.629E-01 mm
 * d) 9.923E-01 mm
 * e) 1.141E+00 mm

8) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=5e$$?


 * a) 5.272E+01 degrees
 * b) 5.799E+01 degrees
 * c) 6.379E+01 degrees
 * d) 7.017E+01 degrees
 * e) 7.719E+01 degrees

9) Calculate the final speed of a free electron accelerated from rest through a potential difference of 56 V.


 * a) 3.031E+06 m/s
 * b) 3.335E+06 m/s
 * c) 3.668E+06 m/s
 * d) 4.035E+06 m/s
 * e) 4.438E+06 m/s

10) What is the average current involved when a truck battery sets in motion 779 C of charge in 3.96 s while starting an engine?


 * a) 1.626E+02 A
 * b) 1.788E+02 A
 * c) 1.967E+02 A
 * d) 2.164E+02 A
 * e) 2.380E+02 A

T6 K0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * a) 8.690E+00 V/m2
 * b) 9.559E+00 V/m2
 * c) 1.051E+01 V/m2
 * d) 1.157E+01 V/m2
 * e) 1.272E+01 V/m2

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * a) 4.286E+03 V&middot;m
 * b) 4.714E+03 V&middot;m
 * c) 5.186E+03 V&middot;m
 * d) 5.704E+03 V&middot;m
 * e) 6.275E+03 V&middot;m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.740E+01 N&middot;m2/C
 * b) 1.914E+01 N&middot;m2/C
 * c) 2.106E+01 N&middot;m2/C
 * d) 2.316E+01 N&middot;m2/C
 * e) 2.548E+01 N&middot;m2/C

4) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 8.672E+02 V
 * b) 9.539E+02 V
 * c) 1.049E+03 V
 * d) 1.154E+03 V
 * e) 1.270E+03 V

5) A Van de Graff generator has a 141 cm diameter metal sphere that produces 280 kV near its surface. What  is the excess charge on the sphere?


 * a) 1.500E+01 &mu;C
 * b) 1.650E+01 &mu;C
 * c) 1.815E+01 &mu;C
 * d) 1.997E+01 &mu;C
 * e) 2.196E+01 &mu;C

6) In the figure shown C1=17.5 &mu;F, C2=2.63 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=15.9 V. What is the charge on C1?


 * a) 8.197E+01 &mu;C
 * b) 9.017E+01 &mu;C
 * c) 9.919E+01 &mu;C
 * d) 1.091E+02 &mu;C
 * e) 1.200E+02 &mu;C

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.58 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 5.520E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 349 &deg;C?


 * a) 9.526E+00 &Omega;
 * b) 1.000E+01 &Omega;
 * c) 1.050E+01 &Omega;
 * d) 1.103E+01 &Omega;
 * e) 1.158E+01 &Omega;

8) Calculate the drift speed of electrons in a copper wire with a diameter of 4.38 mm carrying a 5.79 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.615E-05 m/s
 * b) 2.876E-05 m/s
 * c) 3.164E-05 m/s
 * d) 3.480E-05 m/s
 * e) 3.828E-05 m/s

9) The resistances in the figure shown are R1= 1.18 &Omega;, R2= 0.878 &Omega;, and R2= 2.11 &Omega;. V1 and V3 are text 0.637 V and 3.51 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.547 V. What is the absolute value of the current through R1?


 * a) 1.701E-01 A
 * b) 1.871E-01 A
 * c) 2.058E-01 A
 * d) 2.264E-01 A
 * e) 2.490E-01 A

10) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 k&Omega; and  R2=2.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.34 mA and I4=0.955 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 7.031E+00 V
 * b) 7.734E+00 V
 * c) 8.507E+00 V
 * d) 9.358E+00 V
 * e) 1.029E+01 V

T6 K1
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.5 m if a=0.67 m, b=2.4 m.  The total charge on the rod is 9 nC.


 * a) 5.465E+00 V/m2
 * b) 6.012E+00 V/m2
 * c) 6.613E+00 V/m2
 * d) 7.274E+00 V/m2
 * e) 8.002E+00 V/m2

2) In the figure shown C1=18.0 &mu;F, C2=2.88 &mu;F, and C3=5.34 &mu;F. The voltage source provides &epsilon;=11.9 V. What is the charge on C1?


 * a) 5.045E+01 &mu;C
 * b) 5.550E+01 &mu;C
 * c) 6.105E+01 &mu;C
 * d) 6.715E+01 &mu;C
 * e) 7.387E+01 &mu;C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k$$


 * a) 1.997E+03 V&middot;m
 * b) 2.197E+03 V&middot;m
 * c) 2.417E+03 V&middot;m
 * d) 2.659E+03 V&middot;m
 * e) 2.924E+03 V&middot;m

4) Calculate the drift speed of electrons in a copper wire with a diameter of 5.46 mm carrying a 8.19 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.380E-05 m/s
 * b) 2.618E-05 m/s
 * c) 2.880E-05 m/s
 * d) 3.168E-05 m/s
 * e) 3.485E-05 m/s

5) Two sources of emf &epsilon;1=26.8 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.2 k&Omega; and  R2=2.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.29 mA and I4=0.464 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 3.436E+00 V
 * b) 3.779E+00 V
 * c) 4.157E+00 V
 * d) 4.573E+00 V
 * e) 5.030E+00 V

6) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.75 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 4.300E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 423 &deg;C?


 * a) 1.018E+01 &Omega;
 * b) 1.069E+01 &Omega;
 * c) 1.123E+01 &Omega;
 * d) 1.179E+01 &Omega;
 * e) 1.238E+01 &Omega;

7) The resistances in the figure shown are R1= 2.42 &Omega;, R2= 1.09 &Omega;, and R2= 3.89 &Omega;. V1 and V3 are text 0.677 V and 1.86 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.745 V. What is the absolute value of the current through R1?


 * a) 2.089E-01 A
 * b) 2.298E-01 A
 * c) 2.528E-01 A
 * d) 2.781E-01 A
 * e) 3.059E-01 A

8) A Van de Graff generator has a 149 cm diameter metal sphere that produces 172 kV near its surface. What  is the excess charge on the sphere?


 * a) 1.071E+01 &mu;C
 * b) 1.178E+01 &mu;C
 * c) 1.296E+01 &mu;C
 * d) 1.426E+01 &mu;C
 * e) 1.568E+01 &mu;C

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.740E+01 N&middot;m2/C
 * b) 1.914E+01 N&middot;m2/C
 * c) 2.106E+01 N&middot;m2/C
 * d) 2.316E+01 N&middot;m2/C
 * e) 2.548E+01 N&middot;m2/C

10) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.3 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.86 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 6.325E+02 V
 * b) 6.957E+02 V
 * c) 7.653E+02 V
 * d) 8.418E+02 V
 * e) 9.260E+02 V

T6 K2
1) A Van de Graff generator has a 76 cm diameter metal sphere that produces 193 kV near its surface. What  is the excess charge on the sphere?


 * a) 7.418E+00 &mu;C
 * b) 8.160E+00 &mu;C
 * c) 8.976E+00 &mu;C
 * d) 9.874E+00 &mu;C
 * e) 1.086E+01 &mu;C

2) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.48 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.69 cm, y=2.24 cm)? Note that following the textbook's example, the y-value of the field point at 2.24 cm matches the disance of the positive charge above the x-axis.


 * a) 5.645E+02 V
 * b) 6.210E+02 V
 * c) 6.831E+02 V
 * d) 7.514E+02 V
 * e) 8.266E+02 V

3) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=14.4 V are oriented as shownin the circuit. The resistances are R1=4.33 k&Omega; and  R2=1.65 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.59 mA and I4=1.07 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 9.142E+00 V
 * b) 1.006E+01 V
 * c) 1.106E+01 V
 * d) 1.217E+01 V
 * e) 1.338E+01 V

4) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * a) 5.969E+01 &mu;C
 * b) 6.566E+01 &mu;C
 * c) 7.222E+01 &mu;C
 * d) 7.944E+01 &mu;C
 * e) 8.739E+01 &mu;C

5) Calculate the drift speed of electrons in a copper wire with a diameter of 5.19 mm carrying a 18.2 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 5.321E-05 m/s
 * b) 5.853E-05 m/s
 * c) 6.439E-05 m/s
 * d) 7.083E-05 m/s
 * e) 7.791E-05 m/s

6) The resistances in the figure shown are R1= 2.04 &Omega;, R2= 1.19 &Omega;, and R2= 2.5 &Omega;. V1 and V3 are text 0.507 V and 3.07 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.602 V. What is the absolute value of the current through R1?


 * a) 1.401E-01 A
 * b) 1.542E-01 A
 * c) 1.696E-01 A
 * d) 1.865E-01 A
 * e) 2.052E-01 A

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.0}\hat i +3x^{2.0}\hat j +3y^{3.0}\hat k$$


 * a) 4.820E+03 V&middot;m
 * b) 5.302E+03 V&middot;m
 * c) 5.832E+03 V&middot;m
 * d) 6.415E+03 V&middot;m
 * e) 7.057E+03 V&middot;m

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.95 &Omega; at a temperature of 96&deg;C and that the temperature coefficient of expansion is 4.400E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 469 &deg;C?


 * a) 4.449E+00 &Omega;
 * b) 4.672E+00 &Omega;
 * c) 4.905E+00 &Omega;
 * d) 5.150E+00 &Omega;
 * e) 5.408E+00 &Omega;

9) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=1.0 m, b=2.0 m.  The total charge on the rod is 3 nC.


 * a) 1.665E+00 V/m2
 * b) 1.831E+00 V/m2
 * c) 2.014E+00 V/m2
 * d) 2.216E+00 V/m2
 * e) 2.437E+00 V/m2

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.192E+01 N&middot;m2/C
 * b) 6.811E+01 N&middot;m2/C
 * c) 7.492E+01 N&middot;m2/C
 * d) 8.242E+01 N&middot;m2/C
 * e) 9.066E+01 N&middot;m2/C

T6 L0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * a) 8.690E+00 V/m2
 * b) 9.559E+00 V/m2
 * c) 1.051E+01 V/m2
 * d) 1.157E+01 V/m2
 * e) 1.272E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.388E+01 N&middot;m2/C
 * b) 1.526E+01 N&middot;m2/C
 * c) 1.679E+01 N&middot;m2/C
 * d) 1.847E+01 N&middot;m2/C
 * e) 2.032E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * a) 3.429E+03 V&middot;m
 * b) 3.771E+03 V&middot;m
 * c) 4.149E+03 V&middot;m
 * d) 4.564E+03 V&middot;m
 * e) 5.020E+03 V&middot;m

4) If a 23 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=66 V is x2 + y2 + z2 = R2, where R=


 * a) 2.139E+00 m
 * b) 2.353E+00 m
 * c) 2.588E+00 m
 * d) 2.847E+00 m
 * e) 3.132E+00 m

5) A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.


 * a) 2.727E+02 V
 * b) 2.999E+02 V
 * c) 3.299E+02 V
 * d) 3.629E+02 V
 * e) 3.992E+02 V

6) In the figure shown C1=16.9 &mu;F, C2=2.3 &mu;F, and C3=4.67 &mu;F. The voltage source provides &epsilon;=13.4 V. What is the charge on C1?


 * a) 6.011E+01 &mu;C
 * b) 6.613E+01 &mu;C
 * c) 7.274E+01 &mu;C
 * d) 8.001E+01 &mu;C
 * e) 8.801E+01 &mu;C

7) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?


 * a) 2.240E+02 A
 * b) 2.464E+02 A
 * c) 2.711E+02 A
 * d) 2.982E+02 A
 * e) 3.280E+02 A

8) Calculate the drift speed of electrons in a copper wire with a diameter of 5.82 mm carrying a 9.11 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.926E-05 m/s
 * b) 2.118E-05 m/s
 * c) 2.330E-05 m/s
 * d) 2.563E-05 m/s
 * e) 2.819E-05 m/s

9) In the circuit shown V=17.8 V, R1=2.27 &Omega;, R2=6.79 &Omega;, and R3=15.1 &Omega;. What is the power dissipated by R2?


 * a) 1.446E+01 W
 * b) 1.591E+01 W
 * c) 1.750E+01 W
 * d) 1.925E+01 W
 * e) 2.117E+01 W

10) Two sources of emf &epsilon;1=30.5 V, and  &epsilon;2=12.0 V are oriented as shownin the circuit. The resistances are R1=3.79 k&Omega; and  R2=1.86 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.07 mA and I4=0.73 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.281E+00 mA
 * b) 2.509E+00 mA
 * c) 2.760E+00 mA
 * d) 3.036E+00 mA
 * e) 3.340E+00 mA

T6 L1
1) In the circuit shown V=15.4 V, R1=2.77 &Omega;, R2=6.07 &Omega;, and R3=14.5 &Omega;. What is the power dissipated by R2?


 * a) 1.190E+01 W
 * b) 1.309E+01 W
 * c) 1.440E+01 W
 * d) 1.584E+01 W
 * e) 1.742E+01 W

2) Calculate the drift speed of electrons in a copper wire with a diameter of 4.79 mm carrying a 10.9 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 3.401E-05 m/s
 * b) 3.741E-05 m/s
 * c) 4.116E-05 m/s
 * d) 4.527E-05 m/s
 * e) 4.980E-05 m/s

3) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 8.672E+02 V
 * b) 9.539E+02 V
 * c) 1.049E+03 V
 * d) 1.154E+03 V
 * e) 1.270E+03 V

4) If a 23 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=66 V is x2 + y2 + z2 = R2, where R=


 * a) 2.139E+00 m
 * b) 2.353E+00 m
 * c) 2.588E+00 m
 * d) 2.847E+00 m
 * e) 3.132E+00 m

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * a) 1.969E+02 V&middot;m
 * b) 2.166E+02 V&middot;m
 * c) 2.383E+02 V&middot;m
 * d) 2.621E+02 V&middot;m
 * e) 2.883E+02 V&middot;m

6) What is the average current involved when a truck battery sets in motion 682 C of charge in 5.29 s while starting an engine?


 * a) 1.065E+02 A
 * b) 1.172E+02 A
 * c) 1.289E+02 A
 * d) 1.418E+02 A
 * e) 1.560E+02 A

7) Two sources of emf &epsilon;1=44.4 V, and  &epsilon;2=16.8 V are oriented as shownin the circuit. The resistances are R1=4.58 k&Omega; and  R2=1.2 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=8.43 mA and I4=1.46 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 6.970E+00 mA
 * b) 7.667E+00 mA
 * c) 8.434E+00 mA
 * d) 9.277E+00 mA
 * e) 1.020E+01 mA

8) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=0.76 m, b=1.7 m.  The total charge on the rod is 8 nC.


 * a) 1.399E+01 V/m2
 * b) 1.539E+01 V/m2
 * c) 1.693E+01 V/m2
 * d) 1.862E+01 V/m2
 * e) 2.049E+01 V/m2

9) In the figure shown C1=17.1 &mu;F, C2=2.87 &mu;F, and C3=4.74 &mu;F. The voltage source provides &epsilon;=6.63 V. What is the charge on C1?


 * a) 2.385E+01 &mu;C
 * b) 2.623E+01 &mu;C
 * c) 2.886E+01 &mu;C
 * d) 3.174E+01 &mu;C
 * e) 3.492E+01 &mu;C

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.125E+01 N&middot;m2/C
 * b) 4.537E+01 N&middot;m2/C
 * c) 4.991E+01 N&middot;m2/C
 * d) 5.490E+01 N&middot;m2/C
 * e) 6.039E+01 N&middot;m2/C

T6 L2
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.901E+01 N&middot;m2/C
 * b) 3.192E+01 N&middot;m2/C
 * c) 3.511E+01 N&middot;m2/C
 * d) 3.862E+01 N&middot;m2/C
 * e) 4.248E+01 N&middot;m2/C

2) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.96 m if a=0.95 m, b=1.8 m.  The total charge on the rod is 7 nC.


 * a) 3.385E+00 V/m2
 * b) 3.724E+00 V/m2
 * c) 4.096E+00 V/m2
 * d) 4.506E+00 V/m2
 * e) 4.957E+00 V/m2

3) Calculate the drift speed of electrons in a copper wire with a diameter of 2.72 mm carrying a 16.2 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.087E-04 m/s
 * b) 2.295E-04 m/s
 * c) 2.525E-04 m/s
 * d) 2.777E-04 m/s
 * e) 3.055E-04 m/s

4) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 8.672E+02 V
 * b) 9.539E+02 V
 * c) 1.049E+03 V
 * d) 1.154E+03 V
 * e) 1.270E+03 V

5) Two sources of emf &epsilon;1=18.2 V, and  &epsilon;2=6.59 V are oriented as shownin the circuit. The resistances are R1=5.47 k&Omega; and  R2=2.81 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.64 mA and I4=0.341 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.299E+00 mA
 * b) 1.429E+00 mA
 * c) 1.572E+00 mA
 * d) 1.729E+00 mA
 * e) 1.902E+00 mA

6) What is the average current involved when a truck battery sets in motion 760 C of charge in 5.35 s while starting an engine?


 * a) 1.291E+02 A
 * b) 1.421E+02 A
 * c) 1.563E+02 A
 * d) 1.719E+02 A
 * e) 1.891E+02 A

7) In the circuit shown V=19.6 V, R1=1.45 &Omega;, R2=7.85 &Omega;, and R3=15.8 &Omega;. What is the power dissipated by R2?


 * a) 2.730E+01 W
 * b) 3.003E+01 W
 * c) 3.304E+01 W
 * d) 3.634E+01 W
 * e) 3.998E+01 W

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.7}\hat i +1x^{2.5}\hat j +3y^{3.3}\hat k$$


 * a) 1.128E+04 V&middot;m
 * b) 1.241E+04 V&middot;m
 * c) 1.365E+04 V&middot;m
 * d) 1.502E+04 V&middot;m
 * e) 1.652E+04 V&middot;m

9) In the figure shown C1=18.0 &mu;F, C2=2.88 &mu;F, and C3=5.34 &mu;F. The voltage source provides &epsilon;=11.9 V. What is the charge on C1?


 * a) 5.045E+01 &mu;C
 * b) 5.550E+01 &mu;C
 * c) 6.105E+01 &mu;C
 * d) 6.715E+01 &mu;C
 * e) 7.387E+01 &mu;C

10) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=76 V is x2 + y2 + z2 = R2, where R=


 * a) 1.422E+00 m
 * b) 1.564E+00 m
 * c) 1.720E+00 m
 * d) 1.892E+00 m
 * e) 2.081E+00 m

T6 M0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=4e$$?


 * a) 5.914E+01 degrees
 * b) 6.506E+01 degrees
 * c) 7.157E+01 degrees
 * d) 7.872E+01 degrees
 * e) 8.659E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.978E+01 N&middot;m2/C
 * b) 6.576E+01 N&middot;m2/C
 * c) 7.233E+01 N&middot;m2/C
 * d) 7.957E+01 N&middot;m2/C
 * e) 8.752E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.777E+01 N&middot;m2/C
 * b) 5.254E+01 N&middot;m2/C
 * c) 5.780E+01 N&middot;m2/C
 * d) 6.358E+01 N&middot;m2/C
 * e) 6.993E+01 N&middot;m2/C

4) Assume that a 26 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 42&deg;).


 * a) 7.263E+02 V
 * b) 7.989E+02 V
 * c) 8.788E+02 V
 * d) 9.667E+02 V
 * e) 1.063E+03 V

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 30 V.


 * a) 2.441E+06 m/s
 * b) 2.685E+06 m/s
 * c) 2.953E+06 m/s
 * d) 3.249E+06 m/s
 * e) 3.573E+06 m/s

6) An empty parallel-plate capacitor with metal plates has an area of 2.42 m2, separated by 1.33 mm. How much charge does it store if the voltage is 1.130E+03 V?


 * a) 1.368E+01 &mu;C
 * b) 1.505E+01 &mu;C
 * c) 1.655E+01 &mu;C
 * d) 1.820E+01 &mu;C
 * e) 2.003E+01 &mu;C

7) What is consumer cost to operate one 56&minus;W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.13 per kilowatt-hour?


 * a) $1.198E+01
 * b) $1.318E+01
 * c) $1.449E+01
 * d) $1.594E+01
 * e) $1.754E+01

8) What is the average current involved when a truck battery sets in motion 669 C of charge in 4.3 s while starting an engine?


 * a) 1.063E+02 A
 * b) 1.169E+02 A
 * c) 1.286E+02 A
 * d) 1.414E+02 A
 * e) 1.556E+02 A

9) The resistances in the figure shown are R1= 2.34 &Omega;, R2= 1.34 &Omega;, and R2= 2.94 &Omega;. V1 and V3 are text 0.609 V and 1.68 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.541 V. What is the absolute value of the current through R1?


 * a) 1.464E-01 A
 * b) 1.610E-01 A
 * c) 1.772E-01 A
 * d) 1.949E-01 A
 * e) 2.144E-01 A

10) Two sources of emf &epsilon;1=24.4 V, and  &epsilon;2=6.73 V are oriented as shownin the circuit. The resistances are R1=5.7 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.36 mA and I4=0.418 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 5.418E+00 V
 * b) 5.960E+00 V
 * c) 6.556E+00 V
 * d) 7.212E+00 V
 * e) 7.933E+00 V

T6 M1
1) Assume that a 3 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (6 cm, 0&deg;) and  P2 is at (12 cm, 32&deg;).


 * a) 1.857E+02 V
 * b) 2.043E+02 V
 * c) 2.247E+02 V
 * d) 2.472E+02 V
 * e) 2.719E+02 V

2) Two sources of emf &epsilon;1=14.3 V, and  &epsilon;2=5.6 V are oriented as shownin the circuit. The resistances are R1=5.31 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.12 mA and I4=0.284 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 3.416E+00 V
 * b) 3.757E+00 V
 * c) 4.133E+00 V
 * d) 4.546E+00 V
 * e) 5.001E+00 V

3) The resistances in the figure shown are R1= 2.41 &Omega;, R2= 1.74 &Omega;, and R2= 3.35 &Omega;. V1 and V3 are text 0.508 V and 1.36 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.595 V. What is the absolute value of the current through R1?


 * a) 1.203E-01 A
 * b) 1.324E-01 A
 * c) 1.456E-01 A
 * d) 1.602E-01 A
 * e) 1.762E-01 A

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * a) 5.569E+01 degrees
 * b) 6.125E+01 degrees
 * c) 6.738E+01 degrees
 * d) 7.412E+01 degrees
 * e) 8.153E+01 degrees

5) What is the average current involved when a truck battery sets in motion 728 C of charge in 3.94 s while starting an engine?


 * a) 1.848E+02 A
 * b) 2.032E+02 A
 * c) 2.236E+02 A
 * d) 2.459E+02 A
 * e) 2.705E+02 A

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.222E+01 N&middot;m2/C
 * b) 3.544E+01 N&middot;m2/C
 * c) 3.899E+01 N&middot;m2/C
 * d) 4.289E+01 N&middot;m2/C
 * e) 4.718E+01 N&middot;m2/C

7) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * a) $2.791E+01
 * b) $3.071E+01
 * c) $3.378E+01
 * d) $3.715E+01
 * e) $4.087E+01

8) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * a) 5.102E+06 m/s
 * b) 5.612E+06 m/s
 * c) 6.173E+06 m/s
 * d) 6.791E+06 m/s
 * e) 7.470E+06 m/s

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.730E+01 N&middot;m2/C
 * b) 5.203E+01 N&middot;m2/C
 * c) 5.723E+01 N&middot;m2/C
 * d) 6.295E+01 N&middot;m2/C
 * e) 6.925E+01 N&middot;m2/C

10) An empty parallel-plate capacitor with metal plates has an area of 1.81 m2, separated by 1.26 mm. How much charge does it store if the voltage is 4.610E+03 V?


 * a) 4.005E+01 &mu;C
 * b) 4.405E+01 &mu;C
 * c) 4.846E+01 &mu;C
 * d) 5.330E+01 &mu;C
 * e) 5.864E+01 &mu;C

T6 M2
1) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?


 * a) 2.240E+02 A
 * b) 2.464E+02 A
 * c) 2.711E+02 A
 * d) 2.982E+02 A
 * e) 3.280E+02 A

2) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * a) 4.638E+06 m/s
 * b) 5.102E+06 m/s
 * c) 5.612E+06 m/s
 * d) 6.173E+06 m/s
 * e) 6.791E+06 m/s

3) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * a) $2.791E+01
 * b) $3.071E+01
 * c) $3.378E+01
 * d) $3.715E+01
 * e) $4.087E+01

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.989E+01 N&middot;m2/C
 * b) 6.588E+01 N&middot;m2/C
 * c) 7.247E+01 N&middot;m2/C
 * d) 7.971E+01 N&middot;m2/C
 * e) 8.769E+01 N&middot;m2/C

5) Assume that a 26 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 42&deg;).


 * a) 7.263E+02 V
 * b) 7.989E+02 V
 * c) 8.788E+02 V
 * d) 9.667E+02 V
 * e) 1.063E+03 V

6) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * a) 5.569E+01 degrees
 * b) 6.125E+01 degrees
 * c) 6.738E+01 degrees
 * d) 7.412E+01 degrees
 * e) 8.153E+01 degrees

7) Two sources of emf &epsilon;1=34.7 V, and  &epsilon;2=13.9 V are oriented as shownin the circuit. The resistances are R1=3.68 k&Omega; and  R2=1.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.68 mA and I4=0.933 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 9.286E+00 V
 * b) 1.021E+01 V
 * c) 1.124E+01 V
 * d) 1.236E+01 V
 * e) 1.360E+01 V

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.614E+01 N&middot;m2/C
 * b) 7.275E+01 N&middot;m2/C
 * c) 8.003E+01 N&middot;m2/C
 * d) 8.803E+01 N&middot;m2/C
 * e) 9.683E+01 N&middot;m2/C

9) The resistances in the figure shown are R1= 2.04 &Omega;, R2= 1.19 &Omega;, and R2= 2.5 &Omega;. V1 and V3 are text 0.507 V and 3.07 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.602 V. What is the absolute value of the current through R1?


 * a) 1.401E-01 A
 * b) 1.542E-01 A
 * c) 1.696E-01 A
 * d) 1.865E-01 A
 * e) 2.052E-01 A

10) An empty parallel-plate capacitor with metal plates has an area of 1.94 m2, separated by 1.27 mm. How much charge does it store if the voltage is 8.780E+03 V?


 * a) 1.080E+02 &mu;C
 * b) 1.188E+02 &mu;C
 * c) 1.306E+02 &mu;C
 * d) 1.437E+02 &mu;C
 * e) 1.581E+02 &mu;C

T6 N0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=5e$$?


 * a) 2.248E-14 N
 * b) 2.473E-14 N
 * c) 2.721E-14 N
 * d) 2.993E-14 N
 * e) 3.292E-14 N

2) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?


 * a) 2.274E+02 N/C
 * b) 2.501E+02 N/C
 * c) 2.751E+02 N/C
 * d) 3.026E+02 N/C
 * e) 3.329E+02 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.186E+01 N&middot;m2/C
 * b) 2.404E+01 N&middot;m2/C
 * c) 2.645E+01 N&middot;m2/C
 * d) 2.909E+01 N&middot;m2/C
 * e) 3.200E+01 N&middot;m2/C

4) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=7 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 3.116E+01 J
 * b) 3.427E+01 J
 * c) 3.770E+01 J
 * d) 4.147E+01 J
 * e) 4.562E+01 J

5) An electron gun has parallel plates separated by 2.68 cm and gives electrons 29 keV of energy. What force would the field between the plates exert on a 0.496 &mu;C charge that gets between the plates?


 * a) 5.367E-01 N
 * b) 5.904E-01 N
 * c) 6.494E-01 N
 * d) 7.144E-01 N
 * e) 7.858E-01 N

6) An empty parallel-plate capacitor with metal plates has an area of 2.1 m2, separated by 1.13 mm. How much charge does it store if the voltage is 1.680E+03 V?


 * a) 2.764E+01 &mu;C
 * b) 3.041E+01 &mu;C
 * c) 3.345E+01 &mu;C
 * d) 3.679E+01 &mu;C
 * e) 4.047E+01 &mu;C

7) What is consumer cost to operate one 79&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.142 per kilowatt-hour?


 * a) $2.517E+01
 * b) $2.769E+01
 * c) $3.046E+01
 * d) $3.350E+01
 * e) $3.685E+01

8) Calculate the resistance of a 12-gauge copper wire that is 42 m long and carries a current of 63 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 1.938E-01 &Omega;
 * b) 2.132E-01 &Omega;
 * c) 2.345E-01 &Omega;
 * d) 2.579E-01 &Omega;
 * e) 2.837E-01 &Omega;

9) A battery with a terminal voltage of 13.2 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * a) 1.958E+00 V
 * b) 2.153E+00 V
 * c) 2.369E+00 V
 * d) 2.606E+00 V
 * e) 2.866E+00 V

10) Three resistors, R1 = 1.82 &Omega;, and R2 = R2 = 4.14 &Omega;, are connected in parallel to a 5.65 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 1.754E+01 W
 * b) 1.929E+01 W
 * c) 2.122E+01 W
 * d) 2.335E+01 W
 * e) 2.568E+01 W

T6 N1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.924E+01 N&middot;m2/C
 * b) 4.316E+01 N&middot;m2/C
 * c) 4.748E+01 N&middot;m2/C
 * d) 5.222E+01 N&middot;m2/C
 * e) 5.745E+01 N&middot;m2/C

2) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=3 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?


 * a) 1.457E+02 N/C
 * b) 1.603E+02 N/C
 * c) 1.763E+02 N/C
 * d) 1.939E+02 N/C
 * e) 2.133E+02 N/C

3) An electron gun has parallel plates separated by 5.31 cm and gives electrons 41 keV of energy. What force would the field between the plates exert on a 0.368 &mu;C charge that gets between the plates?


 * a) 2.348E-01 N
 * b) 2.583E-01 N
 * c) 2.841E-01 N
 * d) 3.126E-01 N
 * e) 3.438E-01 N

4) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * a) 1.677E+00 V
 * b) 1.844E+00 V
 * c) 2.029E+00 V
 * d) 2.231E+00 V
 * e) 2.455E+00 V

5) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?


 * a) 5.243E-14 N
 * b) 5.768E-14 N
 * c) 6.344E-14 N
 * d) 6.979E-14 N
 * e) 7.677E-14 N

6) An empty parallel-plate capacitor with metal plates has an area of 2.02 m2, separated by 1.44 mm. How much charge does it store if the voltage is 2.170E+03 V?


 * a) 2.450E+01 &mu;C
 * b) 2.695E+01 &mu;C
 * c) 2.965E+01 &mu;C
 * d) 3.261E+01 &mu;C
 * e) 3.587E+01 &mu;C

7) Three resistors, R1 = 1.43 &Omega;, and R2 = R2 = 3.25 &Omega;, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 5.184E+01 W
 * b) 5.702E+01 W
 * c) 6.272E+01 W
 * d) 6.900E+01 W
 * e) 7.590E+01 W

8) What is consumer cost to operate one 76&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.144 per kilowatt-hour?


 * a) $3.595E+01
 * b) $3.955E+01
 * c) $4.350E+01
 * d) $4.785E+01
 * e) $5.264E+01

9) Calculate the resistance of a 12-gauge copper wire that is 19 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 7.970E-02 &Omega;
 * b) 8.767E-02 &Omega;
 * c) 9.644E-02 &Omega;
 * d) 1.061E-01 &Omega;
 * e) 1.167E-01 &Omega;

10) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=6 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 2.343E+01 J
 * b) 2.577E+01 J
 * c) 2.835E+01 J
 * d) 3.118E+01 J
 * e) 3.430E+01 J

T6 N2
1) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?


 * a) 2.285E+01 N/C
 * b) 2.514E+01 N/C
 * c) 2.765E+01 N/C
 * d) 3.042E+01 N/C
 * e) 3.346E+01 N/C

2) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?


 * a) 3.876E-14 N
 * b) 4.263E-14 N
 * c) 4.690E-14 N
 * d) 5.159E-14 N
 * e) 5.675E-14 N

3) An empty parallel-plate capacitor with metal plates has an area of 2.51 m2, separated by 1.44 mm. How much charge does it store if the voltage is 2.230E+03 V?


 * a) 2.351E+01 &mu;C
 * b) 2.586E+01 &mu;C
 * c) 2.844E+01 &mu;C
 * d) 3.129E+01 &mu;C
 * e) 3.442E+01 &mu;C

4) An electron gun has parallel plates separated by 4.36 cm and gives electrons 13 keV of energy. What force would the field between the plates exert on a 0.816 &mu;C charge that gets between the plates?


 * a) 2.212E-01 N
 * b) 2.433E-01 N
 * c) 2.676E-01 N
 * d) 2.944E-01 N
 * e) 3.238E-01 N

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=8 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 3.444E+01 J
 * b) 3.789E+01 J
 * c) 4.168E+01 J
 * d) 4.585E+01 J
 * e) 5.043E+01 J

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.385E+01 N&middot;m2/C
 * b) 5.923E+01 N&middot;m2/C
 * c) 6.516E+01 N&middot;m2/C
 * d) 7.167E+01 N&middot;m2/C
 * e) 7.884E+01 N&middot;m2/C

7) Calculate the resistance of a 12-gauge copper wire that is 15 m long and carries a current of 27 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 5.200E-02 &Omega;
 * b) 5.720E-02 &Omega;
 * c) 6.292E-02 &Omega;
 * d) 6.921E-02 &Omega;
 * e) 7.613E-02 &Omega;

8) Three resistors, R1 = 0.906 &Omega;, and R2 = R2 = 2.02 &Omega;, are connected in parallel to a 5.98 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 3.262E+01 W
 * b) 3.588E+01 W
 * c) 3.947E+01 W
 * d) 4.342E+01 W
 * e) 4.776E+01 W

9) What is consumer cost to operate one 104&minus;W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.136 per kilowatt-hour?


 * a) $2.116E+01
 * b) $2.327E+01
 * c) $2.560E+01
 * d) $2.816E+01
 * e) $3.098E+01

10) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * a) 1.677E+00 V
 * b) 1.844E+00 V
 * c) 2.029E+00 V
 * d) 2.231E+00 V
 * e) 2.455E+00 V

T6 O0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.


 * a) 5.134E-01 V/m2
 * b) 5.648E-01 V/m2
 * c) 6.212E-01 V/m2
 * d) 6.834E-01 V/m2
 * e) 7.517E-01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.9 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 8.1m2. An electric field has the xyz components (0, 8.1, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.529E+01 N&middot;m2/C
 * b) 7.181E+01 N&middot;m2/C
 * c) 7.900E+01 N&middot;m2/C
 * d) 8.690E+01 N&middot;m2/C
 * e) 9.559E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.992E+01 N&middot;m2/C
 * b) 2.192E+01 N&middot;m2/C
 * c) 2.411E+01 N&middot;m2/C
 * d) 2.652E+01 N&middot;m2/C
 * e) 2.917E+01 N&middot;m2/C

4) A 3 C charge is separated from a 9 C charge by distance of 13 cm.  What is the work done by increasing this separation to 21 cm?


 * a) 6.465E-07 J
 * b) 7.111E-07 J
 * c) 7.822E-07 J
 * d) 8.604E-07 J
 * e) 9.465E-07 J

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 4.235E+01 J
 * b) 4.659E+01 J
 * c) 5.125E+01 J
 * d) 5.637E+01 J
 * e) 6.201E+01 J

6) What is the net capacitance if C1=4.75 &mu;F, C2=2.77 &mu;F, and C3=2.47 &mu;F in the configuration shown?


 * a) 4.220E+00 &mu;F
 * b) 4.642E+00 &mu;F
 * c) 5.106E+00 &mu;F
 * d) 5.616E+00 &mu;F
 * e) 6.178E+00 &mu;F

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.75 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 4.300E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 423 &deg;C?


 * a) 1.018E+01 &Omega;
 * b) 1.069E+01 &Omega;
 * c) 1.123E+01 &Omega;
 * d) 1.179E+01 &Omega;
 * e) 1.238E+01 &Omega;

8) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=27 C  and $$\tau=$$0.0154 s. What is the current at $$t=$$0.0177 s?


 * a) 4.591E+02 A
 * b) 5.050E+02 A
 * c) 5.555E+02 A
 * d) 6.111E+02 A
 * e) 6.722E+02 A

9) Two sources of emf &epsilon;1=40.3 V, and  &epsilon;2=16.8 V are oriented as shownin the circuit. The resistances are R1=2.57 k&Omega; and  R2=2.25 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.96 mA and I4=0.752 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.825E+00 mA
 * b) 2.007E+00 mA
 * c) 2.208E+00 mA
 * d) 2.429E+00 mA
 * e) 2.672E+00 mA

10) Three resistors, R1 = 0.61 &Omega;, and R2 = R2 = 1.35 &Omega;, are connected in parallel to a 7.04 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 7.386E+01 W
 * b) 8.125E+01 W
 * c) 8.937E+01 W
 * d) 9.831E+01 W
 * e) 1.081E+02 W

T6 O1
1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.73 &Omega; at a temperature of 99&deg;C and that the temperature coefficient of expansion is 5.260E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 420 &deg;C?


 * a) 1.267E+01 &Omega;
 * b) 1.331E+01 &Omega;
 * c) 1.397E+01 &Omega;
 * d) 1.467E+01 &Omega;
 * e) 1.540E+01 &Omega;

2) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=63 C  and $$\tau=$$0.0149 s. What is the current at $$t=$$0.0172 s?


 * a) 1.212E+03 A
 * b) 1.333E+03 A
 * c) 1.466E+03 A
 * d) 1.613E+03 A
 * e) 1.774E+03 A

3) A 2 C charge is separated from a 10 C charge by distance of 8 cm.  What is the work done by increasing this separation to 14 cm?


 * a) 8.754E-07 J
 * b) 9.630E-07 J
 * c) 1.059E-06 J
 * d) 1.165E-06 J
 * e) 1.282E-06 J

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.9\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.1\text{ m}$$.


 * a) 8.253E-01 V/m2
 * b) 9.079E-01 V/m2
 * c) 9.987E-01 V/m2
 * d) 1.099E+00 V/m2
 * e) 1.208E+00 V/m2

5) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=6 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 2.617E+01 J
 * b) 2.879E+01 J
 * c) 3.167E+01 J
 * d) 3.484E+01 J
 * e) 3.832E+01 J

6) Three resistors, R1 = 0.548 &Omega;, and R2 = R2 = 1.24 &Omega;, are connected in parallel to a 7.16 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 7.029E+01 W
 * b) 7.731E+01 W
 * c) 8.505E+01 W
 * d) 9.355E+01 W
 * e) 1.029E+02 W

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.385E+01 N&middot;m2/C
 * b) 5.923E+01 N&middot;m2/C
 * c) 6.516E+01 N&middot;m2/C
 * d) 7.167E+01 N&middot;m2/C
 * e) 7.884E+01 N&middot;m2/C

8) Two sources of emf &epsilon;1=39.0 V, and  &epsilon;2=15.9 V are oriented as shownin the circuit. The resistances are R1=3.4 k&Omega; and  R2=2.12 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.58 mA and I4=0.978 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.150E+00 mA
 * b) 2.365E+00 mA
 * c) 2.602E+00 mA
 * d) 2.862E+00 mA
 * e) 3.148E+00 mA

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.192E+01 N&middot;m2/C
 * b) 6.811E+01 N&middot;m2/C
 * c) 7.492E+01 N&middot;m2/C
 * d) 8.242E+01 N&middot;m2/C
 * e) 9.066E+01 N&middot;m2/C

10) What is the net capacitance if C1=4.13 &mu;F, C2=3.56 &mu;F, and C3=3.57 &mu;F in the configuration shown?


 * a) 5.482E+00 &mu;F
 * b) 6.030E+00 &mu;F
 * c) 6.633E+00 &mu;F
 * d) 7.296E+00 &mu;F
 * e) 8.026E+00 &mu;F

T6 O2
1) Three resistors, R1 = 1.2 &Omega;, and R2 = R2 = 2.75 &Omega;, are connected in parallel to a 6.42 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * a) 2.581E+01 W
 * b) 2.839E+01 W
 * c) 3.122E+01 W
 * d) 3.435E+01 W
 * e) 3.778E+01 W

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.698E+01 N&middot;m2/C
 * b) 1.868E+01 N&middot;m2/C
 * c) 2.055E+01 N&middot;m2/C
 * d) 2.260E+01 N&middot;m2/C
 * e) 2.486E+01 N&middot;m2/C

3) Two sources of emf &epsilon;1=49.6 V, and  &epsilon;2=19.3 V are oriented as shownin the circuit. The resistances are R1=4.87 k&Omega; and  R2=2.81 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.37 mA and I4=1.01 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 3.055E+00 mA
 * b) 3.360E+00 mA
 * c) 3.696E+00 mA
 * d) 4.066E+00 mA
 * e) 4.472E+00 mA

4) Imagine a substance could be made into a very hot filament. Suppose the resitance is 4.08 &Omega; at a temperature of 26&deg;C and that the temperature coefficient of expansion is 4.800E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 388 &deg;C?


 * a) 1.064E+01 &Omega;
 * b) 1.117E+01 &Omega;
 * c) 1.173E+01 &Omega;
 * d) 1.231E+01 &Omega;
 * e) 1.293E+01 &Omega;

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.074E+01 N&middot;m2/C
 * b) 3.382E+01 N&middot;m2/C
 * c) 3.720E+01 N&middot;m2/C
 * d) 4.092E+01 N&middot;m2/C
 * e) 4.501E+01 N&middot;m2/C

6) What is the net capacitance if C1=3.06 &mu;F, C2=3.09 &mu;F, and C3=2.48 &mu;F in the configuration shown?


 * a) 3.018E+00 &mu;F
 * b) 3.320E+00 &mu;F
 * c) 3.652E+00 &mu;F
 * d) 4.017E+00 &mu;F
 * e) 4.419E+00 &mu;F

7) A 9 C charge is separated from a 16 C charge by distance of 10 cm.  What is the work done by increasing this separation to 16 cm?


 * a) 4.853E-06 J
 * b) 5.339E-06 J
 * c) 5.872E-06 J
 * d) 6.460E-06 J
 * e) 7.106E-06 J

8) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.8\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.1\text{ m}$$.


 * a) 7.517E+00 V/m2
 * b) 8.269E+00 V/m2
 * c) 9.096E+00 V/m2
 * d) 1.001E+01 V/m2
 * e) 1.101E+01 V/m2

9) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=38 C  and $$\tau=$$0.0167 s. What is the current at $$t=$$0.0183 s?


 * a) 5.715E+02 A
 * b) 6.286E+02 A
 * c) 6.915E+02 A
 * d) 7.606E+02 A
 * e) 8.367E+02 A

10) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 4.235E+01 J
 * b) 4.659E+01 J
 * c) 5.125E+01 J
 * d) 5.637E+01 J
 * e) 6.201E+01 J

T6 P0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.4\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=0.56\text{ m}$$.


 * a) 2.567E+01 V/m2
 * b) 2.824E+01 V/m2
 * c) 3.106E+01 V/m2
 * d) 3.417E+01 V/m2
 * e) 3.759E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.898E+01 N&middot;m2/C
 * b) 7.588E+01 N&middot;m2/C
 * c) 8.347E+01 N&middot;m2/C
 * d) 9.181E+01 N&middot;m2/C
 * e) 1.010E+02 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 8.314E+01 N&middot;m2/C
 * b) 9.146E+01 N&middot;m2/C
 * c) 1.006E+02 N&middot;m2/C
 * d) 1.107E+02 N&middot;m2/C
 * e) 1.217E+02 N&middot;m2/C

4) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * a) 7.017E+02 V
 * b) 7.718E+02 V
 * c) 8.490E+02 V
 * d) 9.339E+02 V
 * e) 1.027E+03 V

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=6 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 2.343E+01 J
 * b) 2.577E+01 J
 * c) 2.835E+01 J
 * d) 3.118E+01 J
 * e) 3.430E+01 J

6) In the figure shown C1=18.2 &mu;F, C2=2.44 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=7.78 V. What is the energy stored in C2?


 * a) 1.225E+01 &mu;J
 * b) 1.347E+01 &mu;J
 * c) 1.482E+01 &mu;J
 * d) 1.630E+01 &mu;J
 * e) 1.793E+01 &mu;J

7) Calculate the electric field in a 12-gauge copper wire that is 41 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 3.604E-04 V/m
 * b) 3.964E-04 V/m
 * c) 4.360E-04 V/m
 * d) 4.796E-04 V/m
 * e) 5.276E-04 V/m

8) What is consumer cost to operate one 59&minus;W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.132 per kilowatt-hour?


 * a) $2.584E+01
 * b) $2.843E+01
 * c) $3.127E+01
 * d) $3.440E+01
 * e) $3.784E+01

9) Two sources of emf &epsilon;1=34.7 V, and  &epsilon;2=13.9 V are oriented as shownin the circuit. The resistances are R1=3.68 k&Omega; and  R2=1.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.68 mA and I4=0.933 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 9.286E+00 V
 * b) 1.021E+01 V
 * c) 1.124E+01 V
 * d) 1.236E+01 V
 * e) 1.360E+01 V

10) In the circuit shown V=19.6 V, R1=1.45 &Omega;, R2=7.85 &Omega;, and R3=15.8 &Omega;. What is the power dissipated by R2?


 * a) 2.730E+01 W
 * b) 3.003E+01 W
 * c) 3.304E+01 W
 * d) 3.634E+01 W
 * e) 3.998E+01 W

T6 P1
1) In the figure shown C1=15.4 &mu;F, C2=2.6 &mu;F, and C3=5.17 &mu;F. The voltage source provides &epsilon;=9.6 V. What is the energy stored in C2?


 * a) 1.508E+01 &mu;J
 * b) 1.659E+01 &mu;J
 * c) 1.825E+01 &mu;J
 * d) 2.007E+01 &mu;J
 * e) 2.208E+01 &mu;J

2) What is consumer cost to operate one 79&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.142 per kilowatt-hour?


 * a) $2.517E+01
 * b) $2.769E+01
 * c) $3.046E+01
 * d) $3.350E+01
 * e) $3.685E+01

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.186E+01 N&middot;m2/C
 * b) 2.404E+01 N&middot;m2/C
 * c) 2.645E+01 N&middot;m2/C
 * d) 2.909E+01 N&middot;m2/C
 * e) 3.200E+01 N&middot;m2/C

4) Calculate the electric field in a 12-gauge copper wire that is 23 m long and carries a current of 64 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.953E-04 V/m
 * b) 3.248E-04 V/m
 * c) 3.573E-04 V/m
 * d) 3.930E-04 V/m
 * e) 4.324E-04 V/m

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.012E+01 N&middot;m2/C
 * b) 2.213E+01 N&middot;m2/C
 * c) 2.435E+01 N&middot;m2/C
 * d) 2.678E+01 N&middot;m2/C
 * e) 2.946E+01 N&middot;m2/C

6) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=8 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 3.444E+01 J
 * b) 3.789E+01 J
 * c) 4.168E+01 J
 * d) 4.585E+01 J
 * e) 5.043E+01 J

7) In the circuit shown V=16.2 V, R1=2.84 &Omega;, R2=7.06 &Omega;, and R3=13.1 &Omega;. What is the power dissipated by R2?


 * a) 1.418E+01 W
 * b) 1.560E+01 W
 * c) 1.716E+01 W
 * d) 1.887E+01 W
 * e) 2.076E+01 W

8) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=4.3\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.4\text{ m}$$.


 * a) 5.647E+00 V/m2
 * b) 6.212E+00 V/m2
 * c) 6.833E+00 V/m2
 * d) 7.517E+00 V/m2
 * e) 8.268E+00 V/m2

9) Two sources of emf &epsilon;1=67.2 V, and  &epsilon;2=18.7 V are oriented as shownin the circuit. The resistances are R1=3.45 k&Omega; and  R2=1.2 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.49 mA and I4=1.81 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.906E+01 V
 * b) 2.097E+01 V
 * c) 2.306E+01 V
 * d) 2.537E+01 V
 * e) 2.790E+01 V

10) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * a) 7.017E+02 V
 * b) 7.718E+02 V
 * c) 8.490E+02 V
 * d) 9.339E+02 V
 * e) 1.027E+03 V

T6 P2
1) A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.


 * a) 2.727E+02 V
 * b) 2.999E+02 V
 * c) 3.299E+02 V
 * d) 3.629E+02 V
 * e) 3.992E+02 V

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.695E+01 N&middot;m2/C
 * b) 4.065E+01 N&middot;m2/C
 * c) 4.472E+01 N&middot;m2/C
 * d) 4.919E+01 N&middot;m2/C
 * e) 5.411E+01 N&middot;m2/C

3) In the circuit shown V=15.8 V, R1=1.86 &Omega;, R2=7.66 &Omega;, and R3=12.9 &Omega;. What is the power dissipated by R2?


 * a) 1.157E+01 W
 * b) 1.273E+01 W
 * c) 1.400E+01 W
 * d) 1.540E+01 W
 * e) 1.694E+01 W

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.2\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.6\text{ m}$$.


 * a) 1.606E+00 V/m2
 * b) 1.767E+00 V/m2
 * c) 1.943E+00 V/m2
 * d) 2.138E+00 V/m2
 * e) 2.351E+00 V/m2

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.662E+01 N&middot;m2/C
 * b) 4.028E+01 N&middot;m2/C
 * c) 4.430E+01 N&middot;m2/C
 * d) 4.873E+01 N&middot;m2/C
 * e) 5.361E+01 N&middot;m2/C

6) Two sources of emf &epsilon;1=17.3 V, and  &epsilon;2=6.46 V are oriented as shownin the circuit. The resistances are R1=2.54 k&Omega; and  R2=2.79 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.1 mA and I4=0.281 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 6.488E+00 V
 * b) 7.137E+00 V
 * c) 7.850E+00 V
 * d) 8.635E+00 V
 * e) 9.499E+00 V

7) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 7.789E+01 J
 * b) 8.568E+01 J
 * c) 9.425E+01 J
 * d) 1.037E+02 J
 * e) 1.140E+02 J

8) Calculate the electric field in a 12-gauge copper wire that is 13 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.250E-04 V/m
 * b) 2.475E-04 V/m
 * c) 2.722E-04 V/m
 * d) 2.995E-04 V/m
 * e) 3.294E-04 V/m

9) In the figure shown C1=16.3 &mu;F, C2=2.17 &mu;F, and C3=4.67 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * a) 8.718E+00 &mu;J
 * b) 9.589E+00 &mu;J
 * c) 1.055E+01 &mu;J
 * d) 1.160E+01 &mu;J
 * e) 1.276E+01 &mu;J

10) What is consumer cost to operate one 102&minus;W incandescent bulb for 5 hours per day for 1 year (365 days) if the cost of electricity is $0.149 per kilowatt-hour?


 * a) $2.292E+01
 * b) $2.521E+01
 * c) $2.774E+01
 * d) $3.051E+01
 * e) $3.356E+01

T6 Q0
1) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?


 * a) 6.925E+09 N/C2
 * b) 7.617E+09 N/C2
 * c) 8.379E+09 N/C2
 * d) 9.217E+09 N/C2
 * e) 1.014E+10 N/C2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 8.457E+01 N&middot;m2/C
 * b) 9.303E+01 N&middot;m2/C
 * c) 1.023E+02 N&middot;m2/C
 * d) 1.126E+02 N&middot;m2/C
 * e) 1.238E+02 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k$$


 * a) 8.731E+02 V&middot;m
 * b) 9.604E+02 V&middot;m
 * c) 1.056E+03 V&middot;m
 * d) 1.162E+03 V&middot;m
 * e) 1.278E+03 V&middot;m

4) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=52 V is x2 + y2 + z2 = R2, where R=


 * a) 2.420E+00 m
 * b) 2.662E+00 m
 * c) 2.928E+00 m
 * d) 3.221E+00 m
 * e) 3.543E+00 m

5) Two large parallel conducting plates are separated by 9.58 mm. Equal and opposite surface charges of 7.360E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 84 V?


 * a) 6.644E-01 mm
 * b) 7.641E-01 mm
 * c) 8.787E-01 mm
 * d) 1.011E+00 mm
 * e) 1.162E+00 mm

6) An empty parallel-plate capacitor with metal plates has an area of 2.21 m2, separated by 1.25 mm. How much charge does it store if the voltage is 1.580E+03 V?


 * a) 2.249E+01 &mu;C
 * b) 2.473E+01 &mu;C
 * c) 2.721E+01 &mu;C
 * d) 2.993E+01 &mu;C
 * e) 3.292E+01 &mu;C

7) A DC winch moter draws 27 amps at 190 volts as it lifts a 4.910E+03 N weight at a constant speed of 0.769 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.396E+00 &Omega;
 * b) 1.535E+00 &Omega;
 * c) 1.689E+00 &Omega;
 * d) 1.858E+00 &Omega;
 * e) 2.043E+00 &Omega;

8) What is the average current involved when a truck battery sets in motion 821 C of charge in 5.51 s while starting an engine?


 * a) 1.231E+02 A
 * b) 1.355E+02 A
 * c) 1.490E+02 A
 * d) 1.639E+02 A
 * e) 1.803E+02 A

9) In the circuit shown V=11.8 V, R1=2.38 &Omega;, R2=5.11 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * a) 8.489E+00 W
 * b) 9.338E+00 W
 * c) 1.027E+01 W
 * d) 1.130E+01 W
 * e) 1.243E+01 W

10) Two sources of emf &epsilon;1=40.6 V, and  &epsilon;2=13.5 V are oriented as shownin the circuit. The resistances are R1=4.35 k&Omega; and  R2=2.44 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.73 mA and I4=0.78 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.332E+00 mA
 * b) 1.465E+00 mA
 * c) 1.612E+00 mA
 * d) 1.773E+00 mA
 * e) 1.950E+00 mA

T6 Q1
1) Two sources of emf &epsilon;1=43.0 V, and  &epsilon;2=13.8 V are oriented as shownin the circuit. The resistances are R1=3.97 k&Omega; and  R2=1.12 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=6.25 mA and I4=1.82 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 3.661E+00 mA
 * b) 4.027E+00 mA
 * c) 4.430E+00 mA
 * d) 4.873E+00 mA
 * e) 5.360E+00 mA

2) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?


 * a) 4.142E+09 N/C2
 * b) 4.556E+09 N/C2
 * c) 5.012E+09 N/C2
 * d) 5.513E+09 N/C2
 * e) 6.064E+09 N/C2

3) What is the average current involved when a truck battery sets in motion 537 C of charge in 5.08 s while starting an engine?


 * a) 8.736E+01 A
 * b) 9.610E+01 A
 * c) 1.057E+02 A
 * d) 1.163E+02 A
 * e) 1.279E+02 A

4) In the circuit shown V=13.5 V, R1=2.66 &Omega;, R2=7.29 &Omega;, and R3=14.5 &Omega;. What is the power dissipated by R2?


 * a) 7.123E+00 W
 * b) 7.835E+00 W
 * c) 8.618E+00 W
 * d) 9.480E+00 W
 * e) 1.043E+01 W

5) Two large parallel conducting plates are separated by 7.14 mm. Equal and opposite surface charges of 7.660E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?


 * a) 4.031E-01 mm
 * b) 4.636E-01 mm
 * c) 5.332E-01 mm
 * d) 6.131E-01 mm
 * e) 7.051E-01 mm

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 8.457E+01 N&middot;m2/C
 * b) 9.303E+01 N&middot;m2/C
 * c) 1.023E+02 N&middot;m2/C
 * d) 1.126E+02 N&middot;m2/C
 * e) 1.238E+02 N&middot;m2/C

7) An empty parallel-plate capacitor with metal plates has an area of 2.83 m2, separated by 1.14 mm. How much charge does it store if the voltage is 4.180E+03 V?


 * a) 6.275E+01 &mu;C
 * b) 6.903E+01 &mu;C
 * c) 7.593E+01 &mu;C
 * d) 8.352E+01 &mu;C
 * e) 9.188E+01 &mu;C

8) If a 21 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=94 V is x2 + y2 + z2 = R2, where R=


 * a) 1.371E+00 m
 * b) 1.509E+00 m
 * c) 1.659E+00 m
 * d) 1.825E+00 m
 * e) 2.008E+00 m

9) A DC winch moter draws 18 amps at 126 volts as it lifts a 5.830E+03 N weight at a constant speed of 0.26 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.919E+00 &Omega;
 * b) 2.111E+00 &Omega;
 * c) 2.322E+00 &Omega;
 * d) 2.554E+00 &Omega;
 * e) 2.809E+00 &Omega;

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * a) 4.286E+03 V&middot;m
 * b) 4.714E+03 V&middot;m
 * c) 5.186E+03 V&middot;m
 * d) 5.704E+03 V&middot;m
 * e) 6.275E+03 V&middot;m

T6 Q2
1) Two sources of emf &epsilon;1=44.4 V, and  &epsilon;2=16.8 V are oriented as shownin the circuit. The resistances are R1=4.58 k&Omega; and  R2=1.2 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=8.43 mA and I4=1.46 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 6.970E+00 mA
 * b) 7.667E+00 mA
 * c) 8.434E+00 mA
 * d) 9.277E+00 mA
 * e) 1.020E+01 mA

2) What is the average current involved when a truck battery sets in motion 889 C of charge in 3.64 s while starting an engine?


 * a) 2.442E+02 A
 * b) 2.687E+02 A
 * c) 2.955E+02 A
 * d) 3.251E+02 A
 * e) 3.576E+02 A

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.920E+01 N&middot;m2/C
 * b) 7.612E+01 N&middot;m2/C
 * c) 8.373E+01 N&middot;m2/C
 * d) 9.210E+01 N&middot;m2/C
 * e) 1.013E+02 N&middot;m2/C

4) In the circuit shown V=18.4 V, R1=1.64 &Omega;, R2=6.56 &Omega;, and R3=12.8 &Omega;. What is the power dissipated by R2?


 * a) 2.470E+01 W
 * b) 2.717E+01 W
 * c) 2.989E+01 W
 * d) 3.288E+01 W
 * e) 3.617E+01 W

5) An empty parallel-plate capacitor with metal plates has an area of 1.81 m2, separated by 1.26 mm. How much charge does it store if the voltage is 4.610E+03 V?


 * a) 4.005E+01 &mu;C
 * b) 4.405E+01 &mu;C
 * c) 4.846E+01 &mu;C
 * d) 5.330E+01 &mu;C
 * e) 5.864E+01 &mu;C

6) A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?


 * a) 5.402E+09 N/C2
 * b) 5.943E+09 N/C2
 * c) 6.537E+09 N/C2
 * d) 7.191E+09 N/C2
 * e) 7.910E+09 N/C2

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is, $$\vec E=2y^{1.8}\hat i +3x^{1.9}\hat j +5y^{3.2}\hat k$$


 * a) 9.952E+03 V&middot;m
 * b) 1.095E+04 V&middot;m
 * c) 1.204E+04 V&middot;m
 * d) 1.325E+04 V&middot;m
 * e) 1.457E+04 V&middot;m

8) Two large parallel conducting plates are separated by 7.01 mm. Equal and opposite surface charges of 7.330E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 55 V?


 * a) 3.799E-01 mm
 * b) 4.368E-01 mm
 * c) 5.024E-01 mm
 * d) 5.777E-01 mm
 * e) 6.644E-01 mm

9) If a 21 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=94 V is x2 + y2 + z2 = R2, where R=


 * a) 1.371E+00 m
 * b) 1.509E+00 m
 * c) 1.659E+00 m
 * d) 1.825E+00 m
 * e) 2.008E+00 m

10) A DC winch moter draws 24 amps at 159 volts as it lifts a 4.120E+03 N weight at a constant speed of 0.657 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.447E+00 &Omega;
 * b) 1.591E+00 &Omega;
 * c) 1.751E+00 &Omega;
 * d) 1.926E+00 &Omega;
 * e) 2.118E+00 &Omega;

T6 R0
1) A large thin isolated square plate has an area of 9 m2. It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * a) 2.571E+01 N/C
 * b) 2.828E+01 N/C
 * c) 3.111E+01 N/C
 * d) 3.422E+01 N/C
 * e) 3.765E+01 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?


 * a) 9.144E+00 N/C
 * b) 1.006E+01 N/C
 * c) 1.106E+01 N/C
 * d) 1.217E+01 N/C
 * e) 1.339E+01 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.978E+01 N&middot;m2/C
 * b) 6.576E+01 N&middot;m2/C
 * c) 7.233E+01 N&middot;m2/C
 * d) 7.957E+01 N&middot;m2/C
 * e) 8.752E+01 N&middot;m2/C

4) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 8.672E+02 V
 * b) 9.539E+02 V
 * c) 1.049E+03 V
 * d) 1.154E+03 V
 * e) 1.270E+03 V

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * a) 4.638E+06 m/s
 * b) 5.102E+06 m/s
 * c) 5.612E+06 m/s
 * d) 6.173E+06 m/s
 * e) 6.791E+06 m/s

6) An empty parallel-plate capacitor with metal plates has an area of 2.04 m2, separated by 1.21 mm. How much charge does it store if the voltage is 7.730E+03 V?


 * a) 1.049E+02 &mu;C
 * b) 1.154E+02 &mu;C
 * c) 1.269E+02 &mu;C
 * d) 1.396E+02 &mu;C
 * e) 1.536E+02 &mu;C

7) Calculate the drift speed of electrons in a copper wire with a diameter of 4.49 mm carrying a 11.6 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 4.120E-05 m/s
 * b) 4.532E-05 m/s
 * c) 4.985E-05 m/s
 * d) 5.483E-05 m/s
 * e) 6.032E-05 m/s

8) A make-believe metal has a density of 1.180E+04 kg/m3 and an atomic mass of 121.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 4.010E+28 e&minus;/m3
 * b) 4.411E+28 e&minus;/m3
 * c) 4.852E+28 e&minus;/m3
 * d) 5.337E+28 e&minus;/m3
 * e) 5.871E+28 e&minus;/m3

9) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.945E+00 V
 * b) 9.840E+00 V
 * c) 1.082E+01 V
 * d) 1.191E+01 V
 * e) 1.310E+01 V

10) A battery with a terminal voltage of 9.88 V is connected to a circuit consisting of 3 15.9 &Omega; resistors and one 10.8 &Omega; resistor. What is the voltage drop across the 10.8 &Omega; resistor?


 * a) 1.370E+00 V
 * b) 1.507E+00 V
 * c) 1.658E+00 V
 * d) 1.824E+00 V
 * e) 2.006E+00 V

T6 R1
1) A make-believe metal has a density of 2.670E+03 kg/m3 and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 3.930E+28 e&minus;/m3
 * b) 4.323E+28 e&minus;/m3
 * c) 4.755E+28 e&minus;/m3
 * d) 5.231E+28 e&minus;/m3
 * e) 5.754E+28 e&minus;/m3

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.978E+01 N&middot;m2/C
 * b) 6.576E+01 N&middot;m2/C
 * c) 7.233E+01 N&middot;m2/C
 * d) 7.957E+01 N&middot;m2/C
 * e) 8.752E+01 N&middot;m2/C

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 27 V.


 * a) 2.802E+06 m/s
 * b) 3.082E+06 m/s
 * c) 3.390E+06 m/s
 * d) 3.729E+06 m/s
 * e) 4.102E+06 m/s

4) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.472E-04 m/s
 * b) 1.619E-04 m/s
 * c) 1.781E-04 m/s
 * d) 1.959E-04 m/s
 * e) 2.155E-04 m/s

5) A battery with a terminal voltage of 14.9 V is connected to a circuit consisting of 2 16.3 &Omega; resistors and one 9.8 &Omega; resistor. What is the voltage drop across the 9.8 &Omega; resistor?


 * a) 2.352E+00 V
 * b) 2.587E+00 V
 * c) 2.846E+00 V
 * d) 3.131E+00 V
 * e) 3.444E+00 V

6) Two sources of emf &epsilon;1=57.0 V, and  &epsilon;2=18.1 V are oriented as shownin the circuit. The resistances are R1=4.95 k&Omega; and  R2=2.09 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.23 mA and I4=1.04 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 1.921E+01 V
 * b) 2.114E+01 V
 * c) 2.325E+01 V
 * d) 2.557E+01 V
 * e) 2.813E+01 V

7) A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.


 * a) 2.727E+02 V
 * b) 2.999E+02 V
 * c) 3.299E+02 V
 * d) 3.629E+02 V
 * e) 3.992E+02 V

8) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?


 * a) 2.837E+01 N/C
 * b) 3.121E+01 N/C
 * c) 3.433E+01 N/C
 * d) 3.776E+01 N/C
 * e) 4.154E+01 N/C

9) A large thin isolated square plate has an area of 6 m2. It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?


 * a) 8.471E+01 N/C
 * b) 9.318E+01 N/C
 * c) 1.025E+02 N/C
 * d) 1.127E+02 N/C
 * e) 1.240E+02 N/C

10) An empty parallel-plate capacitor with metal plates has an area of 2.78 m2, separated by 1.16 mm. How much charge does it store if the voltage is 8.980E+03 V?


 * a) 1.432E+02 &mu;C
 * b) 1.575E+02 &mu;C
 * c) 1.732E+02 &mu;C
 * d) 1.906E+02 &mu;C
 * e) 2.096E+02 &mu;C

T6 R2
1) A battery with a terminal voltage of 7.63 V is connected to a circuit consisting of 2 15.9 &Omega; resistors and one 10.4 &Omega; resistor. What is the voltage drop across the 10.4 &Omega; resistor?


 * a) 1.709E+00 V
 * b) 1.880E+00 V
 * c) 2.068E+00 V
 * d) 2.275E+00 V
 * e) 2.503E+00 V

2) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 2.292E+29 e&minus;/m3
 * b) 2.521E+29 e&minus;/m3
 * c) 2.773E+29 e&minus;/m3
 * d) 3.051E+29 e&minus;/m3
 * e) 3.356E+29 e&minus;/m3

3) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.09 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.45 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * a) 3.814E+02 V
 * b) 4.195E+02 V
 * c) 4.615E+02 V
 * d) 5.077E+02 V
 * e) 5.584E+02 V

4) Two sources of emf &epsilon;1=27.1 V, and  &epsilon;2=8.04 V are oriented as shownin the circuit. The resistances are R1=2.94 k&Omega; and  R2=1.61 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.87 mA and I4=0.57 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.482E+00 V
 * b) 9.330E+00 V
 * c) 1.026E+01 V
 * d) 1.129E+01 V
 * e) 1.242E+01 V

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.3 m, z=z0=1.3 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 5.7m2. An electric field has the xyz components (0, 5.7, 7.5) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.249E+01 N&middot;m2/C
 * b) 3.574E+01 N&middot;m2/C
 * c) 3.931E+01 N&middot;m2/C
 * d) 4.324E+01 N&middot;m2/C
 * e) 4.757E+01 N&middot;m2/C

6) A large thin isolated square plate has an area of 4 m2. It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?


 * a) 9.546E+01 N/C
 * b) 1.050E+02 N/C
 * c) 1.155E+02 N/C
 * d) 1.271E+02 N/C
 * e) 1.398E+02 N/C

7) Calculate the final speed of a free electron accelerated from rest through a potential difference of 19 V.


 * a) 1.942E+06 m/s
 * b) 2.137E+06 m/s
 * c) 2.350E+06 m/s
 * d) 2.585E+06 m/s
 * e) 2.844E+06 m/s

8) An empty parallel-plate capacitor with metal plates has an area of 2.78 m2, separated by 1.16 mm. How much charge does it store if the voltage is 8.980E+03 V?


 * a) 1.432E+02 &mu;C
 * b) 1.575E+02 &mu;C
 * c) 1.732E+02 &mu;C
 * d) 1.906E+02 &mu;C
 * e) 2.096E+02 &mu;C

9) Calculate the drift speed of electrons in a copper wire with a diameter of 3.33 mm carrying a 13.8 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 8.910E-05 m/s
 * b) 9.801E-05 m/s
 * c) 1.078E-04 m/s
 * d) 1.186E-04 m/s
 * e) 1.305E-04 m/s

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?


 * a) 1.017E+01 N/C
 * b) 1.118E+01 N/C
 * c) 1.230E+01 N/C
 * d) 1.353E+01 N/C
 * e) 1.488E+01 N/C

T6 S0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=6e$$?


 * a) 5.767E+01 degrees
 * b) 6.343E+01 degrees
 * c) 6.978E+01 degrees
 * d) 7.676E+01 degrees
 * e) 8.443E+01 degrees

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?


 * a) 5.297E+00 N/C
 * b) 5.827E+00 N/C
 * c) 6.409E+00 N/C
 * d) 7.050E+00 N/C
 * e) 7.755E+00 N/C

3) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=3 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?


 * a) 2.039E+01 N/C
 * b) 2.243E+01 N/C
 * c) 2.467E+01 N/C
 * d) 2.714E+01 N/C
 * e) 2.985E+01 N/C

4) When a 8.6 V battery operates a 2.76 W bulb, how many electrons pass through it each second?


 * a) 1.655E+18 electrons
 * b) 1.821E+18 electrons
 * c) 2.003E+18 electrons
 * d) 2.203E+18 electrons
 * e) 2.424E+18 electrons

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=7 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 2.300E+01 J
 * b) 2.530E+01 J
 * c) 2.783E+01 J
 * d) 3.061E+01 J
 * e) 3.367E+01 J

6) In the figure shown C1=16.1 &mu;F, C2=2.14 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * a) 1.199E+01 &mu;J
 * b) 1.319E+01 &mu;J
 * c) 1.450E+01 &mu;J
 * d) 1.595E+01 &mu;J
 * e) 1.755E+01 &mu;J

7) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.631E-01 &Omega;
 * b) 2.894E-01 &Omega;
 * c) 3.184E-01 &Omega;
 * d) 3.502E-01 &Omega;
 * e) 3.852E-01 &Omega;

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.98 &Omega; at a temperature of 92&deg;C and that the temperature coefficient of expansion is 5.080E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 455 &deg;C?


 * a) 5.363E+00 &Omega;
 * b) 5.631E+00 &Omega;
 * c) 5.913E+00 &Omega;
 * d) 6.208E+00 &Omega;
 * e) 6.519E+00 &Omega;

9) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.945E+00 V
 * b) 9.840E+00 V
 * c) 1.082E+01 V
 * d) 1.191E+01 V
 * e) 1.310E+01 V

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 301 V.  If the combined external and internal resistance is 245 &Omega and the capacitance is  63 mF, how long will it take for the capacitor's voltage to reach 192.0 V?


 * a) 1.296E+01 s
 * b) 1.425E+01 s
 * c) 1.568E+01 s
 * d) 1.725E+01 s
 * e) 1.897E+01 s

T6 S1
1) Calculate the resistance of a 12-gauge copper wire that is 59 m long and carries a current of 26 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.995E-01 &Omega;
 * b) 3.294E-01 &Omega;
 * c) 3.623E-01 &Omega;
 * d) 3.986E-01 &Omega;
 * e) 4.384E-01 &Omega;

2) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 190 V.  If the combined external and internal resistance is 255 &Omega and the capacitance is  54 mF, how long will it take for the capacitor's voltage to reach 101.0 V?


 * a) 1.044E+01 s
 * b) 1.149E+01 s
 * c) 1.264E+01 s
 * d) 1.390E+01 s
 * e) 1.529E+01 s

3) In the figure shown C1=16.9 &mu;F, C2=2.86 &mu;F, and C3=5.1 &mu;F. The voltage source provides &epsilon;=9.98 V. What is the energy stored in C2?


 * a) 1.764E+01 &mu;J
 * b) 1.940E+01 &mu;J
 * c) 2.134E+01 &mu;J
 * d) 2.348E+01 &mu;J
 * e) 2.583E+01 &mu;J

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * a) 5.243E+01 degrees
 * b) 5.767E+01 degrees
 * c) 6.343E+01 degrees
 * d) 6.978E+01 degrees
 * e) 7.676E+01 degrees

5) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=3 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?


 * a) 1.457E+02 N/C
 * b) 1.603E+02 N/C
 * c) 1.763E+02 N/C
 * d) 1.939E+02 N/C
 * e) 2.133E+02 N/C

6) Two sources of emf &epsilon;1=57.0 V, and  &epsilon;2=18.1 V are oriented as shownin the circuit. The resistances are R1=4.95 k&Omega; and  R2=2.09 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.23 mA and I4=1.04 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 1.921E+01 V
 * b) 2.114E+01 V
 * c) 2.325E+01 V
 * d) 2.557E+01 V
 * e) 2.813E+01 V

7) When a 8.6 V battery operates a 2.76 W bulb, how many electrons pass through it each second?


 * a) 1.655E+18 electrons
 * b) 1.821E+18 electrons
 * c) 2.003E+18 electrons
 * d) 2.203E+18 electrons
 * e) 2.424E+18 electrons

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.74 &Omega; at a temperature of 89&deg;C and that the temperature coefficient of expansion is 4.990E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 366 &deg;C?


 * a) 1.529E+01 &Omega;
 * b) 1.606E+01 &Omega;
 * c) 1.686E+01 &Omega;
 * d) 1.770E+01 &Omega;
 * e) 1.859E+01 &Omega;

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?


 * a) 2.837E+01 N/C
 * b) 3.121E+01 N/C
 * c) 3.433E+01 N/C
 * d) 3.776E+01 N/C
 * e) 4.154E+01 N/C

10) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 1.241E+02 J
 * b) 1.365E+02 J
 * c) 1.501E+02 J
 * d) 1.652E+02 J
 * e) 1.817E+02 J

T6 S2
1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.58 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 5.520E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 349 &deg;C?


 * a) 9.526E+00 &Omega;
 * b) 1.000E+01 &Omega;
 * c) 1.050E+01 &Omega;
 * d) 1.103E+01 &Omega;
 * e) 1.158E+01 &Omega;

2) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?


 * a) 4.743E+01 degrees
 * b) 5.217E+01 degrees
 * c) 5.739E+01 degrees
 * d) 6.313E+01 degrees
 * e) 6.944E+01 degrees

3) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.631E-01 &Omega;
 * b) 2.894E-01 &Omega;
 * c) 3.184E-01 &Omega;
 * d) 3.502E-01 &Omega;
 * e) 3.852E-01 &Omega;

4) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 554 V.  If the combined external and internal resistance is 228 &Omega and the capacitance is  93 mF, how long will it take for the capacitor's voltage to reach 450.0 V?


 * a) 3.224E+01 s
 * b) 3.547E+01 s
 * c) 3.902E+01 s
 * d) 4.292E+01 s
 * e) 4.721E+01 s

5) When a 2.59 V battery operates a 2.89 W bulb, how many electrons pass through it each second?


 * a) 5.756E+18 electrons
 * b) 6.331E+18 electrons
 * c) 6.964E+18 electrons
 * d) 7.661E+18 electrons
 * e) 8.427E+18 electrons

6) In the figure shown C1=17.6 &mu;F, C2=2.12 &mu;F, and C3=4.72 &mu;F. The voltage source provides &epsilon;=5.35 V. What is the energy stored in C2?


 * a) 6.750E+00 &mu;J
 * b) 7.425E+00 &mu;J
 * c) 8.168E+00 &mu;J
 * d) 8.984E+00 &mu;J
 * e) 9.883E+00 &mu;J

7) Two sources of emf &epsilon;1=39.2 V, and  &epsilon;2=12.6 V are oriented as shownin the circuit. The resistances are R1=3.86 k&Omega; and  R2=1.89 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.05 mA and I4=0.701 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.687E+00 V
 * b) 9.555E+00 V
 * c) 1.051E+01 V
 * d) 1.156E+01 V
 * e) 1.272E+01 V

8) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 5.178E+01 J
 * b) 5.696E+01 J
 * c) 6.266E+01 J
 * d) 6.892E+01 J
 * e) 7.582E+01 J

9) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?


 * a) 2.285E+01 N/C
 * b) 2.514E+01 N/C
 * c) 2.765E+01 N/C
 * d) 3.042E+01 N/C
 * e) 3.346E+01 N/C

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?


 * a) 3.251E+01 N/C
 * b) 3.577E+01 N/C
 * c) 3.934E+01 N/C
 * d) 4.328E+01 N/C
 * e) 4.760E+01 N/C

T6 T0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * a) 9.958E-15 N
 * b) 1.095E-14 N
 * c) 1.205E-14 N
 * d) 1.325E-14 N
 * e) 1.458E-14 N

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.901E+01 N&middot;m2/C
 * b) 3.192E+01 N&middot;m2/C
 * c) 3.511E+01 N&middot;m2/C
 * d) 3.862E+01 N&middot;m2/C
 * e) 4.248E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 8.415E+01 N&middot;m2/C
 * b) 9.256E+01 N&middot;m2/C
 * c) 1.018E+02 N&middot;m2/C
 * d) 1.120E+02 N&middot;m2/C
 * e) 1.232E+02 N&middot;m2/C

4) Calculate the final speed of a free electron accelerated from rest through a potential difference of 6 V.


 * a) 1.091E+06 m/s
 * b) 1.201E+06 m/s
 * c) 1.321E+06 m/s
 * d) 1.453E+06 m/s
 * e) 1.598E+06 m/s

5) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 7.789E+01 J
 * b) 8.568E+01 J
 * c) 9.425E+01 J
 * d) 1.037E+02 J
 * e) 1.140E+02 J

6) What is the net capacitance if C1=3.25 &mu;F, C2=4.87 &mu;F, and C3=2.19 &mu;F in the configuration shown?


 * a) 4.139E+00 &mu;F
 * b) 4.553E+00 &mu;F
 * c) 5.008E+00 &mu;F
 * d) 5.509E+00 &mu;F
 * e) 6.060E+00 &mu;F

7) Calculate the drift speed of electrons in a copper wire with a diameter of 4.38 mm carrying a 5.79 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.615E-05 m/s
 * b) 2.876E-05 m/s
 * c) 3.164E-05 m/s
 * d) 3.480E-05 m/s
 * e) 3.828E-05 m/s

8) A DC winch moter draws 12 amps at 129 volts as it lifts a 4.210E+03 N weight at a constant speed of 0.318 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 9.924E-01 &Omega;
 * b) 1.092E+00 &Omega;
 * c) 1.201E+00 &Omega;
 * d) 1.321E+00 &Omega;
 * e) 1.453E+00 &Omega;

9) Two sources of emf &epsilon;1=24.4 V, and  &epsilon;2=6.73 V are oriented as shownin the circuit. The resistances are R1=5.7 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.36 mA and I4=0.418 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 5.418E+00 V
 * b) 5.960E+00 V
 * c) 6.556E+00 V
 * d) 7.212E+00 V
 * e) 7.933E+00 V

10) The resistances in the figure shown are R1= 2.74 &Omega;, R2= 1.63 &Omega;, and R2= 2.75 &Omega;. V1 and V3 are text 0.485 V and 2.01 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.555 V. What is the absolute value of the current through R1?


 * a) 1.114E-01 A
 * b) 1.225E-01 A
 * c) 1.348E-01 A
 * d) 1.483E-01 A
 * e) 1.631E-01 A

T6 T1
1) Calculate the final speed of a free electron accelerated from rest through a potential difference of 69 V.


 * a) 3.365E+06 m/s
 * b) 3.701E+06 m/s
 * c) 4.072E+06 m/s
 * d) 4.479E+06 m/s
 * e) 4.927E+06 m/s

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.756E+01 N&middot;m2/C
 * b) 3.032E+01 N&middot;m2/C
 * c) 3.335E+01 N&middot;m2/C
 * d) 3.668E+01 N&middot;m2/C
 * e) 4.035E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.901E+01 N&middot;m2/C
 * b) 3.192E+01 N&middot;m2/C
 * c) 3.511E+01 N&middot;m2/C
 * d) 3.862E+01 N&middot;m2/C
 * e) 4.248E+01 N&middot;m2/C

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?


 * a) 5.732E-15 N
 * b) 6.305E-15 N
 * c) 6.936E-15 N
 * d) 7.629E-15 N
 * e) 8.392E-15 N

5) What is the net capacitance if C1=3.54 &mu;F, C2=3.53 &mu;F, and C3=3.65 &mu;F in the configuration shown?


 * a) 3.700E+00 &mu;F
 * b) 4.070E+00 &mu;F
 * c) 4.477E+00 &mu;F
 * d) 4.925E+00 &mu;F
 * e) 5.417E+00 &mu;F

6) The resistances in the figure shown are R1= 2.42 &Omega;, R2= 1.09 &Omega;, and R2= 3.89 &Omega;. V1 and V3 are text 0.677 V and 1.86 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.745 V. What is the absolute value of the current through R1?


 * a) 2.089E-01 A
 * b) 2.298E-01 A
 * c) 2.528E-01 A
 * d) 2.781E-01 A
 * e) 3.059E-01 A

7) A DC winch moter draws 24 amps at 159 volts as it lifts a 4.120E+03 N weight at a constant speed of 0.657 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.447E+00 &Omega;
 * b) 1.591E+00 &Omega;
 * c) 1.751E+00 &Omega;
 * d) 1.926E+00 &Omega;
 * e) 2.118E+00 &Omega;

8) Two sources of emf &epsilon;1=54.9 V, and  &epsilon;2=19.8 V are oriented as shownin the circuit. The resistances are R1=3.93 k&Omega; and  R2=1.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.18 mA and I4=1.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.779E+01 V
 * b) 1.957E+01 V
 * c) 2.153E+01 V
 * d) 2.368E+01 V
 * e) 2.605E+01 V

9) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 1.241E+02 J
 * b) 1.365E+02 J
 * c) 1.501E+02 J
 * d) 1.652E+02 J
 * e) 1.817E+02 J

10) Calculate the drift speed of electrons in a copper wire with a diameter of 3.53 mm carrying a 2.8 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.947E-05 m/s
 * b) 2.141E-05 m/s
 * c) 2.355E-05 m/s
 * d) 2.591E-05 m/s
 * e) 2.850E-05 m/s

T6 T2
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=5e$$?


 * a) 8.259E-15 N
 * b) 9.085E-15 N
 * c) 9.993E-15 N
 * d) 1.099E-14 N
 * e) 1.209E-14 N

2) Two sources of emf &epsilon;1=36.7 V, and  &epsilon;2=12.1 V are oriented as shownin the circuit. The resistances are R1=2.52 k&Omega; and  R2=1.22 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.14 mA and I4=1.19 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 7.805E+00 V
 * b) 8.586E+00 V
 * c) 9.444E+00 V
 * d) 1.039E+01 V
 * e) 1.143E+01 V

3) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=7 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 5.998E+01 J
 * b) 6.598E+01 J
 * c) 7.257E+01 J
 * d) 7.983E+01 J
 * e) 8.781E+01 J

4) Calculate the drift speed of electrons in a copper wire with a diameter of 2.17 mm carrying a 19.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 3.569E-04 m/s
 * b) 3.926E-04 m/s
 * c) 4.319E-04 m/s
 * d) 4.750E-04 m/s
 * e) 5.226E-04 m/s

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.777E+01 N&middot;m2/C
 * b) 5.254E+01 N&middot;m2/C
 * c) 5.780E+01 N&middot;m2/C
 * d) 6.358E+01 N&middot;m2/C
 * e) 6.993E+01 N&middot;m2/C

6) What is the net capacitance if C1=2.49 &mu;F, C2=4.24 &mu;F, and C3=2.96 &mu;F in the configuration shown?


 * a) 4.117E+00 &mu;F
 * b) 4.529E+00 &mu;F
 * c) 4.982E+00 &mu;F
 * d) 5.480E+00 &mu;F
 * e) 6.028E+00 &mu;F

7) Calculate the final speed of a free electron accelerated from rest through a potential difference of 16 V.


 * a) 2.157E+06 m/s
 * b) 2.372E+06 m/s
 * c) 2.610E+06 m/s
 * d) 2.871E+06 m/s
 * e) 3.158E+06 m/s

8) The resistances in the figure shown are R1= 1.33 &Omega;, R2= 1.72 &Omega;, and R2= 3.69 &Omega;. V1 and V3 are text 0.606 V and 3.31 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.608 V. What is the absolute value of the current through R1?


 * a) 1.137E-01 A
 * b) 1.251E-01 A
 * c) 1.376E-01 A
 * d) 1.514E-01 A
 * e) 1.665E-01 A

9) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 3.551E+00 &Omega;
 * b) 3.906E+00 &Omega;
 * c) 4.297E+00 &Omega;
 * d) 4.726E+00 &Omega;
 * e) 5.199E+00 &Omega;

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.388E+01 N&middot;m2/C
 * b) 1.526E+01 N&middot;m2/C
 * c) 1.679E+01 N&middot;m2/C
 * d) 1.847E+01 N&middot;m2/C
 * e) 2.032E+01 N&middot;m2/C

T6 U0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * a) 5.014E-14 N
 * b) 5.515E-14 N
 * c) 6.067E-14 N
 * d) 6.674E-14 N
 * e) 7.341E-14 N

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.8 (r&le;R) where a=2 nC&middot;m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?


 * a) 2.079E+02 N/C
 * b) 2.287E+02 N/C
 * c) 2.516E+02 N/C
 * d) 2.767E+02 N/C
 * e) 3.044E+02 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.420E+01 N&middot;m2/C
 * b) 4.862E+01 N&middot;m2/C
 * c) 5.348E+01 N&middot;m2/C
 * d) 5.882E+01 N&middot;m2/C
 * e) 6.471E+01 N&middot;m2/C

4) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=19 V is x2 + y2 + z2 = R2, where R=


 * a) 5.169E+00 m
 * b) 5.686E+00 m
 * c) 6.255E+00 m
 * d) 6.880E+00 m
 * e) 7.568E+00 m

5) A 12.0 V battery can move 26,000 C of charge. How many Joules does it deliver?


 * a) 2.836E+05 J
 * b) 3.120E+05 J
 * c) 3.432E+05 J
 * d) 3.775E+05 J
 * e) 4.153E+05 J

6) In the figure shown C1=15.7 &mu;F, C2=2.87 &mu;F, and C3=5.46 &mu;F. The voltage source provides &epsilon;=5.38 V. What is the energy stored in C2?


 * a) 6.890E+00 &mu;J
 * b) 7.579E+00 &mu;J
 * c) 8.337E+00 &mu;J
 * d) 9.171E+00 &mu;J
 * e) 1.009E+01 &mu;J

7) A make-believe metal has a density of 3.530E+03 kg/m3 and an atomic mass of 10.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 1.673E+29 e&minus;/m3
 * b) 1.840E+29 e&minus;/m3
 * c) 2.024E+29 e&minus;/m3
 * d) 2.226E+29 e&minus;/m3
 * e) 2.449E+29 e&minus;/m3

8) Calculate the drift speed of electrons in a copper wire with a diameter of 3.17 mm carrying a 12.0 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.138E-04 m/s
 * b) 1.252E-04 m/s
 * c) 1.377E-04 m/s
 * d) 1.515E-04 m/s
 * e) 1.666E-04 m/s

9) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 1.440E+01 V
 * b) 1.584E+01 V
 * c) 1.742E+01 V
 * d) 1.916E+01 V
 * e) 2.108E+01 V

10) The resistances in the figure shown are R1= 1.57 &Omega;, R2= 1.25 &Omega;, and R2= 3.38 &Omega;. V1 and V3 are text 0.585 V and 2.91 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.55 V. What is the absolute value of the current through R1?


 * a) 1.427E-01 A
 * b) 1.569E-01 A
 * c) 1.726E-01 A
 * d) 1.899E-01 A
 * e) 2.089E-01 A

T6 U1
1) A make-believe metal has a density of 2.670E+03 kg/m3 and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 3.930E+28 e&minus;/m3
 * b) 4.323E+28 e&minus;/m3
 * c) 4.755E+28 e&minus;/m3
 * d) 5.231E+28 e&minus;/m3
 * e) 5.754E+28 e&minus;/m3

2) If a 24 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=97 V is x2 + y2 + z2 = R2, where R=


 * a) 1.838E+00 m
 * b) 2.022E+00 m
 * c) 2.224E+00 m
 * d) 2.446E+00 m
 * e) 2.691E+00 m

3) Calculate the drift speed of electrons in a copper wire with a diameter of 5.47 mm carrying a 3.48 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 1.008E-05 m/s
 * b) 1.108E-05 m/s
 * c) 1.219E-05 m/s
 * d) 1.341E-05 m/s
 * e) 1.475E-05 m/s

4) Two sources of emf &epsilon;1=36.7 V, and  &epsilon;2=12.1 V are oriented as shownin the circuit. The resistances are R1=2.52 k&Omega; and  R2=1.22 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.14 mA and I4=1.19 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 7.805E+00 V
 * b) 8.586E+00 V
 * c) 9.444E+00 V
 * d) 1.039E+01 V
 * e) 1.143E+01 V

5) The resistances in the figure shown are R1= 2.49 &Omega;, R2= 1.72 &Omega;, and R2= 3.58 &Omega;. V1 and V3 are text 0.417 V and 1.83 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.53 V. What is the absolute value of the current through R1?


 * a) 8.220E-02 A
 * b) 9.042E-02 A
 * c) 9.946E-02 A
 * d) 1.094E-01 A
 * e) 1.203E-01 A

6) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?


 * a) 4.782E+02 N/C
 * b) 5.260E+02 N/C
 * c) 5.787E+02 N/C
 * d) 6.365E+02 N/C
 * e) 7.002E+02 N/C

7) A 12.0 V battery can move 30,000 C of charge. How many Joules does it deliver?


 * a) 3.273E+05 J
 * b) 3.600E+05 J
 * c) 3.960E+05 J
 * d) 4.356E+05 J
 * e) 4.792E+05 J

8) In the figure shown C1=16.7 &mu;F, C2=2.26 &mu;F, and C3=4.53 &mu;F. The voltage source provides &epsilon;=10.7 V. What is the energy stored in C2?


 * a) 1.292E+01 &mu;J
 * b) 1.421E+01 &mu;J
 * c) 1.563E+01 &mu;J
 * d) 1.719E+01 &mu;J
 * e) 1.891E+01 &mu;J

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.214E+01 N&middot;m2/C
 * b) 2.436E+01 N&middot;m2/C
 * c) 2.679E+01 N&middot;m2/C
 * d) 2.947E+01 N&middot;m2/C
 * e) 3.242E+01 N&middot;m2/C

10) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=2e$$?


 * a) 3.391E-14 N
 * b) 3.731E-14 N
 * c) 4.104E-14 N
 * d) 4.514E-14 N
 * e) 4.965E-14 N

T6 U2
1) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=3 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?


 * a) 4.874E+01 N/C
 * b) 5.362E+01 N/C
 * c) 5.898E+01 N/C
 * d) 6.488E+01 N/C
 * e) 7.137E+01 N/C

2) A make-believe metal has a density of 5.880E+03 kg/m3 and an atomic mass of 87.4 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 3.347E+28 e&minus;/m3
 * b) 3.682E+28 e&minus;/m3
 * c) 4.050E+28 e&minus;/m3
 * d) 4.455E+28 e&minus;/m3
 * e) 4.901E+28 e&minus;/m3

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.695E+01 N&middot;m2/C
 * b) 4.065E+01 N&middot;m2/C
 * c) 4.472E+01 N&middot;m2/C
 * d) 4.919E+01 N&middot;m2/C
 * e) 5.411E+01 N&middot;m2/C

4) The resistances in the figure shown are R1= 1.81 &Omega;, R2= 1.18 &Omega;, and R2= 2.62 &Omega;. V1 and V3 are text 0.628 V and 2.54 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.748 V. What is the absolute value of the current through R1?


 * a) 1.552E-01 A
 * b) 1.707E-01 A
 * c) 1.878E-01 A
 * d) 2.065E-01 A
 * e) 2.272E-01 A

5) In the figure shown C1=18.2 &mu;F, C2=2.44 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=7.78 V. What is the energy stored in C2?


 * a) 1.225E+01 &mu;J
 * b) 1.347E+01 &mu;J
 * c) 1.482E+01 &mu;J
 * d) 1.630E+01 &mu;J
 * e) 1.793E+01 &mu;J

6) Calculate the drift speed of electrons in a copper wire with a diameter of 5.46 mm carrying a 8.19 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * a) 2.380E-05 m/s
 * b) 2.618E-05 m/s
 * c) 2.880E-05 m/s
 * d) 3.168E-05 m/s
 * e) 3.485E-05 m/s

7) Two sources of emf &epsilon;1=34.7 V, and  &epsilon;2=13.9 V are oriented as shownin the circuit. The resistances are R1=3.68 k&Omega; and  R2=1.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.68 mA and I4=0.933 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * a) 9.286E+00 V
 * b) 1.021E+01 V
 * c) 1.124E+01 V
 * d) 1.236E+01 V
 * e) 1.360E+01 V

8) If a 28 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=77 V is x2 + y2 + z2 = R2, where R=


 * a) 2.701E+00 m
 * b) 2.971E+00 m
 * c) 3.268E+00 m
 * d) 3.595E+00 m
 * e) 3.955E+00 m

9) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=4e$$?


 * a) 8.613E-15 N
 * b) 9.474E-15 N
 * c) 1.042E-14 N
 * d) 1.146E-14 N
 * e) 1.261E-14 N

10) A 12.0 V battery can move 29,000 C of charge. How many Joules does it deliver?


 * a) 2.615E+05 J
 * b) 2.876E+05 J
 * c) 3.164E+05 J
 * d) 3.480E+05 J
 * e) 3.828E+05 J

T6 V0
1) A large thin isolated square plate has an area of 5 m2. It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * a) 6.534E+01 N/C
 * b) 7.187E+01 N/C
 * c) 7.906E+01 N/C
 * d) 8.696E+01 N/C
 * e) 9.566E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k$$


 * a) 1.997E+03 V&middot;m
 * b) 2.197E+03 V&middot;m
 * c) 2.417E+03 V&middot;m
 * d) 2.659E+03 V&middot;m
 * e) 2.924E+03 V&middot;m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.420E+01 N&middot;m2/C
 * b) 4.862E+01 N&middot;m2/C
 * c) 5.348E+01 N&middot;m2/C
 * d) 5.882E+01 N&middot;m2/C
 * e) 6.471E+01 N&middot;m2/C

4) When a 6.24 V battery operates a 2.1 W bulb, how many electrons pass through it each second?


 * a) 1.435E+18 electrons
 * b) 1.578E+18 electrons
 * c) 1.736E+18 electrons
 * d) 1.910E+18 electrons
 * e) 2.101E+18 electrons

5) Two large parallel conducting plates are separated by 9.58 mm. Equal and opposite surface charges of 7.360E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 84 V?


 * a) 6.644E-01 mm
 * b) 7.641E-01 mm
 * c) 8.787E-01 mm
 * d) 1.011E+00 mm
 * e) 1.162E+00 mm

6) In the figure shown C1=17.7 &mu;F, C2=2.48 &mu;F, and C3=4.68 &mu;F. The voltage source provides &epsilon;=12.7 V. What is the energy stored in C2?


 * a) 2.242E+01 &mu;J
 * b) 2.467E+01 &mu;J
 * c) 2.713E+01 &mu;J
 * d) 2.985E+01 &mu;J
 * e) 3.283E+01 &mu;J

7) A make-believe metal has a density of 8.060E+03 kg/m3 and an atomic mass of 19.7 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 1.850E+29 e&minus;/m3
 * b) 2.036E+29 e&minus;/m3
 * c) 2.239E+29 e&minus;/m3
 * d) 2.463E+29 e&minus;/m3
 * e) 2.709E+29 e&minus;/m3

8) What is consumer cost to operate one 79&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.142 per kilowatt-hour?


 * a) $2.517E+01
 * b) $2.769E+01
 * c) $3.046E+01
 * d) $3.350E+01
 * e) $3.685E+01

9) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 301 V.  If the combined external and internal resistance is 245 &Omega and the capacitance is  63 mF, how long will it take for the capacitor's voltage to reach 192.0 V?


 * a) 1.296E+01 s
 * b) 1.425E+01 s
 * c) 1.568E+01 s
 * d) 1.725E+01 s
 * e) 1.897E+01 s

10) A battery with a terminal voltage of 14.6 V is connected to a circuit consisting of 2 21.7 &Omega; resistors and one 14.4 &Omega; resistor. What is the voltage drop across the 14.4 &Omega; resistor?


 * a) 3.637E+00 V
 * b) 4.001E+00 V
 * c) 4.401E+00 V
 * d) 4.841E+00 V
 * e) 5.325E+00 V

T6 V1
1) A battery with a terminal voltage of 8.14 V is connected to a circuit consisting of 2 21.5 &Omega; resistors and one 13.1 &Omega; resistor. What is the voltage drop across the 13.1 &Omega; resistor?


 * a) 1.298E+00 V
 * b) 1.428E+00 V
 * c) 1.571E+00 V
 * d) 1.728E+00 V
 * e) 1.901E+00 V

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.8}\hat i +1x^{2.3}\hat j +2y^{2.9}\hat k$$


 * a) 2.210E+04 V&middot;m
 * b) 2.431E+04 V&middot;m
 * c) 2.674E+04 V&middot;m
 * d) 2.941E+04 V&middot;m
 * e) 3.235E+04 V&middot;m

3) A make-believe metal has a density of 1.050E+04 kg/m3 and an atomic mass of 58.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 1.075E+29 e&minus;/m3
 * b) 1.183E+29 e&minus;/m3
 * c) 1.301E+29 e&minus;/m3
 * d) 1.431E+29 e&minus;/m3
 * e) 1.574E+29 e&minus;/m3

4) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?


 * a) 6.525E-01 mm
 * b) 7.504E-01 mm
 * c) 8.629E-01 mm
 * d) 9.923E-01 mm
 * e) 1.141E+00 mm

5) In the figure shown C1=16.7 &mu;F, C2=2.26 &mu;F, and C3=4.53 &mu;F. The voltage source provides &epsilon;=10.7 V. What is the energy stored in C2?


 * a) 1.292E+01 &mu;J
 * b) 1.421E+01 &mu;J
 * c) 1.563E+01 &mu;J
 * d) 1.719E+01 &mu;J
 * e) 1.891E+01 &mu;J

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.698E+01 N&middot;m2/C
 * b) 1.868E+01 N&middot;m2/C
 * c) 2.055E+01 N&middot;m2/C
 * d) 2.260E+01 N&middot;m2/C
 * e) 2.486E+01 N&middot;m2/C

7) A large thin isolated square plate has an area of 4 m2. It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?


 * a) 9.546E+01 N/C
 * b) 1.050E+02 N/C
 * c) 1.155E+02 N/C
 * d) 1.271E+02 N/C
 * e) 1.398E+02 N/C

8) What is consumer cost to operate one 89&minus;W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.141 per kilowatt-hour?


 * a) $3.785E+01
 * b) $4.164E+01
 * c) $4.580E+01
 * d) $5.038E+01
 * e) $5.542E+01

9) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?


 * a) 1.439E+18 electrons
 * b) 1.582E+18 electrons
 * c) 1.741E+18 electrons
 * d) 1.915E+18 electrons
 * e) 2.106E+18 electrons

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 327 V.  If the combined external and internal resistance is 204 &Omega and the capacitance is  68 mF, how long will it take for the capacitor's voltage to reach 218.0 V?


 * a) 1.385E+01 s
 * b) 1.524E+01 s
 * c) 1.676E+01 s
 * d) 1.844E+01 s
 * e) 2.028E+01 s

T6 V2
1) In the figure shown C1=16.5 &mu;F, C2=2.7 &mu;F, and C3=4.82 &mu;F. The voltage source provides &epsilon;=15.7 V. What is the energy stored in C2?


 * a) 2.188E+01 &mu;J
 * b) 2.407E+01 &mu;J
 * c) 2.647E+01 &mu;J
 * d) 2.912E+01 &mu;J
 * e) 3.203E+01 &mu;J

2) What is consumer cost to operate one 73&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.113 per kilowatt-hour?


 * a) $3.312E+01
 * b) $3.643E+01
 * c) $4.007E+01
 * d) $4.408E+01
 * e) $4.849E+01

3) A large thin isolated square plate has an area of 8 m2. It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?


 * a) 4.492E+01 N/C
 * b) 4.941E+01 N/C
 * c) 5.435E+01 N/C
 * d) 5.979E+01 N/C
 * e) 6.577E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k$$


 * a) 8.731E+02 V&middot;m
 * b) 9.604E+02 V&middot;m
 * c) 1.056E+03 V&middot;m
 * d) 1.162E+03 V&middot;m
 * e) 1.278E+03 V&middot;m

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 8.457E+01 N&middot;m2/C
 * b) 9.303E+01 N&middot;m2/C
 * c) 1.023E+02 N&middot;m2/C
 * d) 1.126E+02 N&middot;m2/C
 * e) 1.238E+02 N&middot;m2/C

6) A make-believe metal has a density of 7.000E+03 kg/m3 and an atomic mass of 89.4 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * a) 3.219E+28 e&minus;/m3
 * b) 3.541E+28 e&minus;/m3
 * c) 3.896E+28 e&minus;/m3
 * d) 4.285E+28 e&minus;/m3
 * e) 4.714E+28 e&minus;/m3

7) A battery with a terminal voltage of 14.1 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.2 &Omega; resistor. What is the voltage drop across the 10.2 &Omega; resistor?


 * a) 2.074E+00 V
 * b) 2.282E+00 V
 * c) 2.510E+00 V
 * d) 2.761E+00 V
 * e) 3.037E+00 V

8) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?


 * a) 1.439E+18 electrons
 * b) 1.582E+18 electrons
 * c) 1.741E+18 electrons
 * d) 1.915E+18 electrons
 * e) 2.106E+18 electrons

9) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?


 * a) 6.525E-01 mm
 * b) 7.504E-01 mm
 * c) 8.629E-01 mm
 * d) 9.923E-01 mm
 * e) 1.141E+00 mm

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 467 V.  If the combined external and internal resistance is 172 &Omega and the capacitance is  74 mF, how long will it take for the capacitor's voltage to reach 258.0 V?


 * a) 7.688E+00 s
 * b) 8.457E+00 s
 * c) 9.303E+00 s
 * d) 1.023E+01 s
 * e) 1.126E+01 s

T6 W0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-8e$$, and $$q_3=6e$$?


 * a) 5.243E+01 degrees
 * b) 5.767E+01 degrees
 * c) 6.343E+01 degrees
 * d) 6.978E+01 degrees
 * e) 7.676E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.134E+01 N&middot;m2/C
 * b) 2.347E+01 N&middot;m2/C
 * c) 2.582E+01 N&middot;m2/C
 * d) 2.840E+01 N&middot;m2/C
 * e) 3.124E+01 N&middot;m2/C

3) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=3 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?


 * a) 4.874E+01 N/C
 * b) 5.362E+01 N/C
 * c) 5.898E+01 N/C
 * d) 6.488E+01 N/C
 * e) 7.137E+01 N/C

4) Two large parallel conducting plates are separated by 7.14 mm. Equal and opposite surface charges of 7.660E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?


 * a) 4.031E-01 mm
 * b) 4.636E-01 mm
 * c) 5.332E-01 mm
 * d) 6.131E-01 mm
 * e) 7.051E-01 mm

5) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=61 V is x2 + y2 + z2 = R2, where R=


 * a) 1.107E+00 m
 * b) 1.218E+00 m
 * c) 1.339E+00 m
 * d) 1.473E+00 m
 * e) 1.621E+00 m

6) An empty parallel-plate capacitor with metal plates has an area of 2.16 m2, separated by 1.12 mm. How much charge does it store if the voltage is 1.530E+03 V?


 * a) 2.375E+01 &mu;C
 * b) 2.613E+01 &mu;C
 * c) 2.874E+01 &mu;C
 * d) 3.161E+01 &mu;C
 * e) 3.477E+01 &mu;C

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.06 &Omega; at a temperature of 80&deg;C and that the temperature coefficient of expansion is 4.290E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 330 &deg;C?


 * a) 1.196E+01 &Omega;
 * b) 1.256E+01 &Omega;
 * c) 1.319E+01 &Omega;
 * d) 1.385E+01 &Omega;
 * e) 1.454E+01 &Omega;

8) A DC winch moter draws 18 amps at 126 volts as it lifts a 5.830E+03 N weight at a constant speed of 0.26 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.919E+00 &Omega;
 * b) 2.111E+00 &Omega;
 * c) 2.322E+00 &Omega;
 * d) 2.554E+00 &Omega;
 * e) 2.809E+00 &Omega;

9) Two sources of emf &epsilon;1=28.6 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=3.73 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.27 mA and I4=0.774 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 6.641E+00 V
 * b) 7.305E+00 V
 * c) 8.035E+00 V
 * d) 8.839E+00 V
 * e) 9.723E+00 V

10) A given battery has a 11 V emf and an internal resistance of 0.0998 &Omega;. If it is connected to a 0.417 &Omega; resistor what is the power dissipated by that load?


 * a) 1.419E+02 W
 * b) 1.561E+02 W
 * c) 1.717E+02 W
 * d) 1.889E+02 W
 * e) 2.078E+02 W

T6 W1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 3.750E+01 N&middot;m2/C
 * b) 4.125E+01 N&middot;m2/C
 * c) 4.537E+01 N&middot;m2/C
 * d) 4.991E+01 N&middot;m2/C
 * e) 5.490E+01 N&middot;m2/C

2) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=61 V is x2 + y2 + z2 = R2, where R=


 * a) 1.107E+00 m
 * b) 1.218E+00 m
 * c) 1.339E+00 m
 * d) 1.473E+00 m
 * e) 1.621E+00 m

3) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 &Omega; at a temperature of 82&deg;C and that the temperature coefficient of expansion is 4.530E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 390 &deg;C?


 * a) 7.532E+00 &Omega;
 * b) 7.908E+00 &Omega;
 * c) 8.303E+00 &Omega;
 * d) 8.719E+00 &Omega;
 * e) 9.155E+00 &Omega;

4) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=8.29 V are oriented as shownin the circuit. The resistances are R1=3.43 k&Omega; and  R2=1.16 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.09 mA and I4=1.06 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 6.720E+00 V
 * b) 7.392E+00 V
 * c) 8.131E+00 V
 * d) 8.944E+00 V
 * e) 9.838E+00 V

5) A given battery has a 15 V emf and an internal resistance of 0.177 &Omega;. If it is connected to a 0.824 &Omega; resistor what is the power dissipated by that load?


 * a) 1.682E+02 W
 * b) 1.850E+02 W
 * c) 2.035E+02 W
 * d) 2.239E+02 W
 * e) 2.463E+02 W

6) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-8e$$, and $$q_3=6e$$?


 * a) 5.243E+01 degrees
 * b) 5.767E+01 degrees
 * c) 6.343E+01 degrees
 * d) 6.978E+01 degrees
 * e) 7.676E+01 degrees

7) A DC winch moter draws 20 amps at 175 volts as it lifts a 5.180E+03 N weight at a constant speed of 0.541 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 1.744E+00 &Omega;
 * b) 1.918E+00 &Omega;
 * c) 2.110E+00 &Omega;
 * d) 2.321E+00 &Omega;
 * e) 2.553E+00 &Omega;

8) Two large parallel conducting plates are separated by 8.7 mm. Equal and opposite surface charges of 7.220E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 67 V?


 * a) 4.698E-01 mm
 * b) 5.402E-01 mm
 * c) 6.213E-01 mm
 * d) 7.145E-01 mm
 * e) 8.216E-01 mm

9) An empty parallel-plate capacitor with metal plates has an area of 2.51 m2, separated by 1.44 mm. How much charge does it store if the voltage is 2.230E+03 V?


 * a) 2.351E+01 &mu;C
 * b) 2.586E+01 &mu;C
 * c) 2.844E+01 &mu;C
 * d) 3.129E+01 &mu;C
 * e) 3.442E+01 &mu;C

10) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?


 * a) 4.782E+02 N/C
 * b) 5.260E+02 N/C
 * c) 5.787E+02 N/C
 * d) 6.365E+02 N/C
 * e) 7.002E+02 N/C

T6 W2
1) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * a) 3.551E+00 &Omega;
 * b) 3.906E+00 &Omega;
 * c) 4.297E+00 &Omega;
 * d) 4.726E+00 &Omega;
 * e) 5.199E+00 &Omega;

2) A given battery has a 14 V emf and an internal resistance of 0.132 &Omega;. If it is connected to a 0.689 &Omega; resistor what is the power dissipated by that load?


 * a) 1.656E+02 W
 * b) 1.821E+02 W
 * c) 2.003E+02 W
 * d) 2.204E+02 W
 * e) 2.424E+02 W

3) Two large parallel conducting plates are separated by 6.86 mm. Equal and opposite surface charges of 7.540E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 79 V?


 * a) 6.100E-01 mm
 * b) 7.015E-01 mm
 * c) 8.067E-01 mm
 * d) 9.277E-01 mm
 * e) 1.067E+00 mm

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=5e$$?


 * a) 3.961E+01 degrees
 * b) 4.357E+01 degrees
 * c) 4.793E+01 degrees
 * d) 5.272E+01 degrees
 * e) 5.799E+01 degrees

5) Two sources of emf &epsilon;1=26.8 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.2 k&Omega; and  R2=2.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.29 mA and I4=0.464 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 3.436E+00 V
 * b) 3.779E+00 V
 * c) 4.157E+00 V
 * d) 4.573E+00 V
 * e) 5.030E+00 V

6) An empty parallel-plate capacitor with metal plates has an area of 2.21 m2, separated by 1.25 mm. How much charge does it store if the voltage is 1.580E+03 V?


 * a) 2.249E+01 &mu;C
 * b) 2.473E+01 &mu;C
 * c) 2.721E+01 &mu;C
 * d) 2.993E+01 &mu;C
 * e) 3.292E+01 &mu;C

7) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=43 V is x2 + y2 + z2 = R2, where R=


 * a) 2.299E+00 m
 * b) 2.529E+00 m
 * c) 2.782E+00 m
 * d) 3.060E+00 m
 * e) 3.366E+00 m

8) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=2 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?


 * a) 3.821E+02 N/C
 * b) 4.203E+02 N/C
 * c) 4.624E+02 N/C
 * d) 5.086E+02 N/C
 * e) 5.594E+02 N/C

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.777E+01 N&middot;m2/C
 * b) 5.254E+01 N&middot;m2/C
 * c) 5.780E+01 N&middot;m2/C
 * d) 6.358E+01 N&middot;m2/C
 * e) 6.993E+01 N&middot;m2/C

10) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.95 &Omega; at a temperature of 96&deg;C and that the temperature coefficient of expansion is 4.400E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 469 &deg;C?


 * a) 4.449E+00 &Omega;
 * b) 4.672E+00 &Omega;
 * c) 4.905E+00 &Omega;
 * d) 5.150E+00 &Omega;
 * e) 5.408E+00 &Omega;

T6 X0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=0.76 m, b=1.7 m.  The total charge on the rod is 8 nC.


 * a) 1.399E+01 V/m2
 * b) 1.539E+01 V/m2
 * c) 1.693E+01 V/m2
 * d) 1.862E+01 V/m2
 * e) 2.049E+01 V/m2

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * a) 1.969E+02 V&middot;m
 * b) 2.166E+02 V&middot;m
 * c) 2.383E+02 V&middot;m
 * d) 2.621E+02 V&middot;m
 * e) 2.883E+02 V&middot;m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?


 * a) 3.251E+01 N/C
 * b) 3.577E+01 N/C
 * c) 3.934E+01 N/C
 * d) 4.328E+01 N/C
 * e) 4.760E+01 N/C

4) If a 23 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=62 V is x2 + y2 + z2 = R2, where R=


 * a) 2.277E+00 m
 * b) 2.505E+00 m
 * c) 2.755E+00 m
 * d) 3.031E+00 m
 * e) 3.334E+00 m

5) A diploe has a charge magnitude of q=4 nC and a separation distance of d=4.07 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.88 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * a) 2.164E+02 V
 * b) 2.381E+02 V
 * c) 2.619E+02 V
 * d) 2.880E+02 V
 * e) 3.168E+02 V

6) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * a) 5.969E+01 &mu;C
 * b) 6.566E+01 &mu;C
 * c) 7.222E+01 &mu;C
 * d) 7.944E+01 &mu;C
 * e) 8.739E+01 &mu;C

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 &Omega; at a temperature of 82&deg;C and that the temperature coefficient of expansion is 4.530E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 390 &deg;C?


 * a) 7.532E+00 &Omega;
 * b) 7.908E+00 &Omega;
 * c) 8.303E+00 &Omega;
 * d) 8.719E+00 &Omega;
 * e) 9.155E+00 &Omega;

8) Calculate the electric field in a 12-gauge copper wire that is 16 m long and carries a current of 58 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.212E-04 V/m
 * b) 2.433E-04 V/m
 * c) 2.676E-04 V/m
 * d) 2.944E-04 V/m
 * e) 3.238E-04 V/m

9) Two sources of emf &epsilon;1=38.8 V, and  &epsilon;2=14.9 V are oriented as shownin the circuit. The resistances are R1=5.83 k&Omega; and  R2=1.77 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.57 mA and I4=1.19 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 1.013E+01 V
 * b) 1.115E+01 V
 * c) 1.226E+01 V
 * d) 1.349E+01 V
 * e) 1.484E+01 V

10) A given battery has a 13 V emf and an internal resistance of 0.159 &Omega;. If it is connected to a 0.617 &Omega; resistor what is the power dissipated by that load?


 * a) 1.301E+02 W
 * b) 1.431E+02 W
 * c) 1.574E+02 W
 * d) 1.732E+02 W
 * e) 1.905E+02 W

T6 X1
1) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * a) 7.017E+02 V
 * b) 7.718E+02 V
 * c) 8.490E+02 V
 * d) 9.339E+02 V
 * e) 1.027E+03 V

2) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.73 m if a=0.52 m, b=1.6 m.  The total charge on the rod is 7 nC.


 * a) 9.655E+00 V/m2
 * b) 1.062E+01 V/m2
 * c) 1.168E+01 V/m2
 * d) 1.285E+01 V/m2
 * e) 1.414E+01 V/m2

3) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.11 mA and I4=0.746 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 4.275E+00 V
 * b) 4.703E+00 V
 * c) 5.173E+00 V
 * d) 5.691E+00 V
 * e) 6.260E+00 V

4) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.52 &Omega; at a temperature of 45&deg;C and that the temperature coefficient of expansion is 4.330E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 479 &deg;C?


 * a) 3.970E+00 &Omega;
 * b) 4.168E+00 &Omega;
 * c) 4.376E+00 &Omega;
 * d) 4.595E+00 &Omega;
 * e) 4.825E+00 &Omega;

5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?


 * a) 1.096E+00 N/C
 * b) 1.206E+00 N/C
 * c) 1.327E+00 N/C
 * d) 1.459E+00 N/C
 * e) 1.605E+00 N/C

6) In the figure shown C1=19.0 &mu;F, C2=2.35 &mu;F, and C3=5.22 &mu;F. The voltage source provides &epsilon;=6.01 V. What is the charge on C1?


 * a) 2.444E+01 &mu;C
 * b) 2.689E+01 &mu;C
 * c) 2.958E+01 &mu;C
 * d) 3.253E+01 &mu;C
 * e) 3.579E+01 &mu;C

7) A given battery has a 15 V emf and an internal resistance of 0.0536 &Omega;. If it is connected to a 0.64 &Omega; resistor what is the power dissipated by that load?


 * a) 2.721E+02 W
 * b) 2.993E+02 W
 * c) 3.293E+02 W
 * d) 3.622E+02 W
 * e) 3.984E+02 W

8) Calculate the electric field in a 12-gauge copper wire that is 99 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 3.604E-04 V/m
 * b) 3.964E-04 V/m
 * c) 4.360E-04 V/m
 * d) 4.796E-04 V/m
 * e) 5.276E-04 V/m

9) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=19 V is x2 + y2 + z2 = R2, where R=


 * a) 5.169E+00 m
 * b) 5.686E+00 m
 * c) 6.255E+00 m
 * d) 6.880E+00 m
 * e) 7.568E+00 m

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * a) 3.429E+03 V&middot;m
 * b) 3.771E+03 V&middot;m
 * c) 4.149E+03 V&middot;m
 * d) 4.564E+03 V&middot;m
 * e) 5.020E+03 V&middot;m

T6 X2
1) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * a) 4.324E+02 V
 * b) 4.757E+02 V
 * c) 5.232E+02 V
 * d) 5.755E+02 V
 * e) 6.331E+02 V

2) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.61 m, b=1.7 m.  The total charge on the rod is 8 nC.


 * a) 5.995E+00 V/m2
 * b) 6.595E+00 V/m2
 * c) 7.254E+00 V/m2
 * d) 7.980E+00 V/m2
 * e) 8.778E+00 V/m2

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?


 * a) 3.251E+01 N/C
 * b) 3.577E+01 N/C
 * c) 3.934E+01 N/C
 * d) 4.328E+01 N/C
 * e) 4.760E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k$$


 * a) 1.997E+03 V&middot;m
 * b) 2.197E+03 V&middot;m
 * c) 2.417E+03 V&middot;m
 * d) 2.659E+03 V&middot;m
 * e) 2.924E+03 V&middot;m

5) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * a) 5.969E+01 &mu;C
 * b) 6.566E+01 &mu;C
 * c) 7.222E+01 &mu;C
 * d) 7.944E+01 &mu;C
 * e) 8.739E+01 &mu;C

6) Calculate the electric field in a 12-gauge copper wire that is 41 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 3.604E-04 V/m
 * b) 3.964E-04 V/m
 * c) 4.360E-04 V/m
 * d) 4.796E-04 V/m
 * e) 5.276E-04 V/m

7) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=76 V is x2 + y2 + z2 = R2, where R=


 * a) 1.422E+00 m
 * b) 1.564E+00 m
 * c) 1.720E+00 m
 * d) 1.892E+00 m
 * e) 2.081E+00 m

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.74 &Omega; at a temperature of 89&deg;C and that the temperature coefficient of expansion is 4.990E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 366 &deg;C?


 * a) 1.529E+01 &Omega;
 * b) 1.606E+01 &Omega;
 * c) 1.686E+01 &Omega;
 * d) 1.770E+01 &Omega;
 * e) 1.859E+01 &Omega;

9) A given battery has a 10 V emf and an internal resistance of 0.119 &Omega;. If it is connected to a 0.445 &Omega; resistor what is the power dissipated by that load?


 * a) 1.272E+02 W
 * b) 1.399E+02 W
 * c) 1.539E+02 W
 * d) 1.693E+02 W
 * e) 1.862E+02 W

10) Two sources of emf &epsilon;1=52.7 V, and  &epsilon;2=17.5 V are oriented as shownin the circuit. The resistances are R1=5.86 k&Omega; and  R2=2.08 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.48 mA and I4=0.988 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 2.064E+01 V
 * b) 2.270E+01 V
 * c) 2.497E+01 V
 * d) 2.747E+01 V
 * e) 3.021E+01 V

T6 Y0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?


 * a) 3.629E+01 degrees
 * b) 3.992E+01 degrees
 * c) 4.391E+01 degrees
 * d) 4.830E+01 degrees
 * e) 5.313E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 13.0m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.953E+01 N&middot;m2/C
 * b) 5.449E+01 N&middot;m2/C
 * c) 5.993E+01 N&middot;m2/C
 * d) 6.593E+01 N&middot;m2/C
 * e) 7.252E+01 N&middot;m2/C

3) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?


 * a) 2.285E+01 N/C
 * b) 2.514E+01 N/C
 * c) 2.765E+01 N/C
 * d) 3.042E+01 N/C
 * e) 3.346E+01 N/C

4) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 4.554E+01 J
 * b) 5.009E+01 J
 * c) 5.510E+01 J
 * d) 6.061E+01 J
 * e) 6.667E+01 J

5) When a 6.24 V battery operates a 2.1 W bulb, how many electrons pass through it each second?


 * a) 1.435E+18 electrons
 * b) 1.578E+18 electrons
 * c) 1.736E+18 electrons
 * d) 1.910E+18 electrons
 * e) 2.101E+18 electrons

6) In the figure shown C1=17.7 &mu;F, C2=2.48 &mu;F, and C3=4.68 &mu;F. The voltage source provides &epsilon;=12.7 V. What is the energy stored in C2?


 * a) 2.242E+01 &mu;J
 * b) 2.467E+01 &mu;J
 * c) 2.713E+01 &mu;J
 * d) 2.985E+01 &mu;J
 * e) 3.283E+01 &mu;J

7) A device requires consumes 196 W of power and requires 2.4 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * a) 4.563E+05 A/m2
 * b) 5.019E+05 A/m2
 * c) 5.521E+05 A/m2
 * d) 6.073E+05 A/m2
 * e) 6.680E+05 A/m2

8) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 4.957E-02 &Omega;
 * b) 5.453E-02 &Omega;
 * c) 5.998E-02 &Omega;
 * d) 6.598E-02 &Omega;
 * e) 7.258E-02 &Omega;

9) Two sources of emf &epsilon;1=27.1 V, and  &epsilon;2=8.04 V are oriented as shownin the circuit. The resistances are R1=2.94 k&Omega; and  R2=1.61 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.87 mA and I4=0.57 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.482E+00 V
 * b) 9.330E+00 V
 * c) 1.026E+01 V
 * d) 1.129E+01 V
 * e) 1.242E+01 V

10) Two sources of emf &epsilon;1=29.5 V, and  &epsilon;2=11.0 V are oriented as shownin the circuit. The resistances are R1=2.45 k&Omega; and  R2=1.96 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.03 mA and I4=0.783 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.247E+00 mA
 * b) 2.472E+00 mA
 * c) 2.719E+00 mA
 * d) 2.991E+00 mA
 * e) 3.290E+00 mA

T6 Y1
1) A device requires consumes 72 W of power and requires 11.7 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * a) 1.519E+06 A/m2
 * b) 1.671E+06 A/m2
 * c) 1.838E+06 A/m2
 * d) 2.022E+06 A/m2
 * e) 2.224E+06 A/m2

2) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=2 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?


 * a) 2.406E+01 N/C
 * b) 2.646E+01 N/C
 * c) 2.911E+01 N/C
 * d) 3.202E+01 N/C
 * e) 3.522E+01 N/C

3) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 4.957E-02 &Omega;
 * b) 5.453E-02 &Omega;
 * c) 5.998E-02 &Omega;
 * d) 6.598E-02 &Omega;
 * e) 7.258E-02 &Omega;

4) Two sources of emf &epsilon;1=16.8 V, and  &epsilon;2=7.15 V are oriented as shownin the circuit. The resistances are R1=3.12 k&Omega; and  R2=1.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.95 mA and I4=0.603 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 4.108E+00 V
 * b) 4.519E+00 V
 * c) 4.970E+00 V
 * d) 5.468E+00 V
 * e) 6.014E+00 V

5) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * a) 4.766E+01 degrees
 * b) 5.243E+01 degrees
 * c) 5.767E+01 degrees
 * d) 6.343E+01 degrees
 * e) 6.978E+01 degrees

6) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=7 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 4.438E+01 J
 * b) 4.882E+01 J
 * c) 5.370E+01 J
 * d) 5.907E+01 J
 * e) 6.498E+01 J

7) When a 2.76 V battery operates a 2.71 W bulb, how many electrons pass through it each second?


 * a) 5.571E+18 electrons
 * b) 6.128E+18 electrons
 * c) 6.741E+18 electrons
 * d) 7.415E+18 electrons
 * e) 8.157E+18 electrons

8) Two sources of emf &epsilon;1=24.9 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 k&Omega; and  R2=2.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.74 mA and I4=0.444 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.725E+00 mA
 * b) 1.898E+00 mA
 * c) 2.087E+00 mA
 * d) 2.296E+00 mA
 * e) 2.526E+00 mA

9) In the figure shown C1=15.4 &mu;F, C2=2.6 &mu;F, and C3=5.17 &mu;F. The voltage source provides &epsilon;=9.6 V. What is the energy stored in C2?


 * a) 1.508E+01 &mu;J
 * b) 1.659E+01 &mu;J
 * c) 1.825E+01 &mu;J
 * d) 2.007E+01 &mu;J
 * e) 2.208E+01 &mu;J

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 6.192E+01 N&middot;m2/C
 * b) 6.811E+01 N&middot;m2/C
 * c) 7.492E+01 N&middot;m2/C
 * d) 8.242E+01 N&middot;m2/C
 * e) 9.066E+01 N&middot;m2/C

T6 Y2
1) When a 6.32 V battery operates a 1.94 W bulb, how many electrons pass through it each second?


 * a) 1.439E+18 electrons
 * b) 1.583E+18 electrons
 * c) 1.742E+18 electrons
 * d) 1.916E+18 electrons
 * e) 2.107E+18 electrons

2) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=3 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?


 * a) 4.874E+01 N/C
 * b) 5.362E+01 N/C
 * c) 5.898E+01 N/C
 * d) 6.488E+01 N/C
 * e) 7.137E+01 N/C

3) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=4 &mu;C, q2=5 &mu;C, q3=7 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?


 * a) 3.910E+01 J
 * b) 4.301E+01 J
 * c) 4.731E+01 J
 * d) 5.204E+01 J
 * e) 5.725E+01 J

4) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * a) 2.631E-01 &Omega;
 * b) 2.894E-01 &Omega;
 * c) 3.184E-01 &Omega;
 * d) 3.502E-01 &Omega;
 * e) 3.852E-01 &Omega;

5) A device requires consumes 177 W of power and requires 6.82 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * a) 9.741E+05 A/m2
 * b) 1.072E+06 A/m2
 * c) 1.179E+06 A/m2
 * d) 1.297E+06 A/m2
 * e) 1.426E+06 A/m2

6) Two sources of emf &epsilon;1=43.7 V, and  &epsilon;2=13.1 V are oriented as shownin the circuit. The resistances are R1=5.21 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.86 mA and I4=0.9 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.691E+00 mA
 * b) 2.960E+00 mA
 * c) 3.256E+00 mA
 * d) 3.582E+00 mA
 * e) 3.940E+00 mA

7) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * a) 4.357E+01 degrees
 * b) 4.793E+01 degrees
 * c) 5.272E+01 degrees
 * d) 5.799E+01 degrees
 * e) 6.379E+01 degrees

8) In the figure shown C1=16.1 &mu;F, C2=2.14 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * a) 1.199E+01 &mu;J
 * b) 1.319E+01 &mu;J
 * c) 1.450E+01 &mu;J
 * d) 1.595E+01 &mu;J
 * e) 1.755E+01 &mu;J

9) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * a) 8.945E+00 V
 * b) 9.840E+00 V
 * c) 1.082E+01 V
 * d) 1.191E+01 V
 * e) 1.310E+01 V

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 8.5m2. Those in the xy plane have area 2.8m2 ,and those in the zx plane have area 3.7m2. An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 2.079E+01 N&middot;m2/C
 * b) 2.287E+01 N&middot;m2/C
 * c) 2.516E+01 N&middot;m2/C
 * d) 2.768E+01 N&middot;m2/C
 * e) 3.044E+01 N&middot;m2/C

T6 Z0
1) A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?


 * a) 1.202E+09 N/C2
 * b) 1.322E+09 N/C2
 * c) 1.454E+09 N/C2
 * d) 1.599E+09 N/C2
 * e) 1.759E+09 N/C2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 4.730E+01 N&middot;m2/C
 * b) 5.203E+01 N&middot;m2/C
 * c) 5.723E+01 N&middot;m2/C
 * d) 6.295E+01 N&middot;m2/C
 * e) 6.925E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.0}\hat i +2x^{2.1}\hat j +3y^{2.5}\hat k$$


 * a) 9.027E+03 V&middot;m
 * b) 9.930E+03 V&middot;m
 * c) 1.092E+04 V&middot;m
 * d) 1.202E+04 V&middot;m
 * e) 1.322E+04 V&middot;m

4) An electron gun has parallel plates separated by 3.39 cm and gives electrons 57 keV of energy. What force would the field between the plates exert on a 0.218 &mu;C charge that gets between the plates?


 * a) 3.029E-01 N
 * b) 3.332E-01 N
 * c) 3.665E-01 N
 * d) 4.032E-01 N
 * e) 4.435E-01 N

5) A 7 C charge is separated from a 15 C charge by distance of 14 cm.  What is the work done by increasing this separation to 20 cm?


 * a) 1.519E-06 J
 * b) 1.671E-06 J
 * c) 1.838E-06 J
 * d) 2.022E-06 J
 * e) 2.224E-06 J

6) In the figure shown C1=16.7 &mu;F, C2=2.26 &mu;F, and C3=4.53 &mu;F. The voltage source provides &epsilon;=10.7 V. What is the energy stored in C2?


 * a) 1.292E+01 &mu;J
 * b) 1.421E+01 &mu;J
 * c) 1.563E+01 &mu;J
 * d) 1.719E+01 &mu;J
 * e) 1.891E+01 &mu;J

7) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=16 C  and $$\tau=$$0.0214 s. What is the current at $$t=$$0.0207 s?


 * a) 2.135E+02 A
 * b) 2.349E+02 A
 * c) 2.584E+02 A
 * d) 2.842E+02 A
 * e) 3.126E+02 A

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 &Omega; at a temperature of 82&deg;C and that the temperature coefficient of expansion is 4.530E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 390 &deg;C?


 * a) 7.532E+00 &Omega;
 * b) 7.908E+00 &Omega;
 * c) 8.303E+00 &Omega;
 * d) 8.719E+00 &Omega;
 * e) 9.155E+00 &Omega;

9) In the circuit shown V=11.9 V, R1=2.75 &Omega;, R2=7.19 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * a) 7.982E+00 W
 * b) 8.780E+00 W
 * c) 9.658E+00 W
 * d) 1.062E+01 W
 * e) 1.169E+01 W

10) Two sources of emf &epsilon;1=31.0 V, and  &epsilon;2=10.0 V are oriented as shownin the circuit. The resistances are R1=4.22 k&Omega; and  R2=1.37 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.32 mA and I4=1.03 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 2.290E+00 mA
 * b) 2.519E+00 mA
 * c) 2.771E+00 mA
 * d) 3.048E+00 mA
 * e) 3.353E+00 mA

T6 Z1
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.7}\hat i +2x^{2.9}\hat j +2y^{2.0}\hat k$$


 * a) 7.200E+01 V&middot;m
 * b) 7.920E+01 V&middot;m
 * c) 8.712E+01 V&middot;m
 * d) 9.583E+01 V&middot;m
 * e) 1.054E+02 V&middot;m

2) A 3 C charge is separated from a 7 C charge by distance of 10 cm.  What is the work done by increasing this separation to 15 cm?


 * a) 5.199E-07 J
 * b) 5.719E-07 J
 * c) 6.291E-07 J
 * d) 6.920E-07 J
 * e) 7.612E-07 J

3) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.74 &Omega; at a temperature of 89&deg;C and that the temperature coefficient of expansion is 4.990E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 366 &deg;C?


 * a) 1.529E+01 &Omega;
 * b) 1.606E+01 &Omega;
 * c) 1.686E+01 &Omega;
 * d) 1.770E+01 &Omega;
 * e) 1.859E+01 &Omega;

4) In the circuit shown V=11.8 V, R1=2.38 &Omega;, R2=5.11 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * a) 8.489E+00 W
 * b) 9.338E+00 W
 * c) 1.027E+01 W
 * d) 1.130E+01 W
 * e) 1.243E+01 W

5) Two sources of emf &epsilon;1=18.2 V, and  &epsilon;2=6.59 V are oriented as shownin the circuit. The resistances are R1=5.47 k&Omega; and  R2=2.81 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.64 mA and I4=0.341 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.299E+00 mA
 * b) 1.429E+00 mA
 * c) 1.572E+00 mA
 * d) 1.729E+00 mA
 * e) 1.902E+00 mA

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 1.891E+01 N&middot;m2/C
 * b) 2.080E+01 N&middot;m2/C
 * c) 2.288E+01 N&middot;m2/C
 * d) 2.517E+01 N&middot;m2/C
 * e) 2.768E+01 N&middot;m2/C

7) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=27 C  and $$\tau=$$0.0154 s. What is the current at $$t=$$0.0177 s?


 * a) 4.591E+02 A
 * b) 5.050E+02 A
 * c) 5.555E+02 A
 * d) 6.111E+02 A
 * e) 6.722E+02 A

8) In the figure shown C1=18.1 &mu;F, C2=2.13 &mu;F, and C3=5.48 &mu;F. The voltage source provides &epsilon;=14.6 V. What is the energy stored in C2?


 * a) 1.645E+01 &mu;J
 * b) 1.809E+01 &mu;J
 * c) 1.990E+01 &mu;J
 * d) 2.189E+01 &mu;J
 * e) 2.408E+01 &mu;J

9) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?


 * a) 6.925E+09 N/C2
 * b) 7.617E+09 N/C2
 * c) 8.379E+09 N/C2
 * d) 9.217E+09 N/C2
 * e) 1.014E+10 N/C2

10) An electron gun has parallel plates separated by 5.38 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.427 &mu;C charge that gets between the plates?


 * a) 3.542E-01 N
 * b) 3.896E-01 N
 * c) 4.286E-01 N
 * d) 4.714E-01 N
 * e) 5.186E-01 N

T6 Z2
1) An electron gun has parallel plates separated by 3.02 cm and gives electrons 39 keV of energy. What force would the field between the plates exert on a 0.699 &mu;C charge that gets between the plates?


 * a) 8.206E-01 N
 * b) 9.027E-01 N
 * c) 9.930E-01 N
 * d) 1.092E+00 N
 * e) 1.201E+00 N

2) In the figure shown C1=20.7 &mu;F, C2=2.79 &mu;F, and C3=5.18 &mu;F. The voltage source provides &epsilon;=15.0 V. What is the energy stored in C2?


 * a) 2.064E+01 &mu;J
 * b) 2.270E+01 &mu;J
 * c) 2.497E+01 &mu;J
 * d) 2.747E+01 &mu;J
 * e) 3.022E+01 &mu;J

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * a) 1.969E+02 V&middot;m
 * b) 2.166E+02 V&middot;m
 * c) 2.383E+02 V&middot;m
 * d) 2.621E+02 V&middot;m
 * e) 2.883E+02 V&middot;m

4) In the circuit shown V=11.9 V, R1=2.75 &Omega;, R2=7.19 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * a) 7.982E+00 W
 * b) 8.780E+00 W
 * c) 9.658E+00 W
 * d) 1.062E+01 W
 * e) 1.169E+01 W

5) Two sources of emf &epsilon;1=24.8 V, and  &epsilon;2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 k&Omega; and  R2=1.6 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.49 mA and I4=0.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * a) 1.660E+00 mA
 * b) 1.826E+00 mA
 * c) 2.009E+00 mA
 * d) 2.209E+00 mA
 * e) 2.430E+00 mA

6) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.95 &Omega; at a temperature of 96&deg;C and that the temperature coefficient of expansion is 4.400E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 469 &deg;C?


 * a) 4.449E+00 &Omega;
 * b) 4.672E+00 &Omega;
 * c) 4.905E+00 &Omega;
 * d) 5.150E+00 &Omega;
 * e) 5.408E+00 &Omega;

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * a) 5.978E+01 N&middot;m2/C
 * b) 6.576E+01 N&middot;m2/C
 * c) 7.233E+01 N&middot;m2/C
 * d) 7.957E+01 N&middot;m2/C
 * e) 8.752E+01 N&middot;m2/C

8) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=23 C  and $$\tau=$$0.0204 s. What is the current at $$t=$$0.0106 s?


 * a) 6.096E+02 A
 * b) 6.706E+02 A
 * c) 7.376E+02 A
 * d) 8.114E+02 A
 * e) 8.925E+02 A

9) A 8 C charge is separated from a 13 C charge by distance of 7 cm.  What is the work done by increasing this separation to 13 cm?


 * a) 4.209E-06 J
 * b) 4.630E-06 J
 * c) 5.093E-06 J
 * d) 5.603E-06 J
 * e) 6.163E-06 J

10) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?


 * a) 6.925E+09 N/C2
 * b) 7.617E+09 N/C2
 * c) 8.379E+09 N/C2
 * d) 9.217E+09 N/C2
 * e) 1.014E+10 N/C2


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Key: A0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?


 * -a) 1.028E-14 N
 * -b) 1.130E-14 N
 * -c) 1.244E-14 N
 * -d) 1.368E-14 N
 * +e) 1.505E-14 N

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is, $$\vec E=4y^{1.4}\hat i +2x^{2.3}\hat j +4y^{2.3}\hat k$$


 * -a) 2.694E+03 V&middot;m
 * -b) 2.963E+03 V&middot;m
 * -c) 3.259E+03 V&middot;m
 * +d) 3.585E+03 V&middot;m
 * -e) 3.944E+03 V&middot;m

3) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?


 * +a) 7.825E+02 N/C
 * -b) 8.607E+02 N/C
 * -c) 9.468E+02 N/C
 * -d) 1.041E+03 N/C
 * -e) 1.146E+03 N/C

4) Assume that a 11 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (12 cm, 14&deg;).


 * -a) 1.876E+02 V
 * -b) 2.063E+02 V
 * -c) 2.270E+02 V
 * -d) 2.497E+02 V
 * +e) 2.746E+02 V

5) A 3 C charge is separated from a 11 C charge by distance of 12 cm.  What is the work done by increasing this separation to 19 cm?


 * -a) 8.278E-07 J
 * +b) 9.106E-07 J
 * -c) 1.002E-06 J
 * -d) 1.102E-06 J
 * -e) 1.212E-06 J

6) What is the net capacitance if C1=2.25 &mu;F, C2=4.16 &mu;F, and C3=2.49 &mu;F in the configuration shown?


 * -a) 2.698E+00 &mu;F
 * -b) 2.968E+00 &mu;F
 * -c) 3.265E+00 &mu;F
 * -d) 3.591E+00 &mu;F
 * +e) 3.950E+00 &mu;F

7) A device requires consumes 81 W of power and requires 2.34 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * -a) 3.342E+05 A/m2
 * -b) 3.677E+05 A/m2
 * -c) 4.044E+05 A/m2
 * +d) 4.449E+05 A/m2
 * -e) 4.894E+05 A/m2

8) What is the average current involved when a truck battery sets in motion 775 C of charge in 2.9 s while starting an engine?


 * -a) 2.209E+02 A
 * -b) 2.429E+02 A
 * +c) 2.672E+02 A
 * -d) 2.940E+02 A
 * -e) 3.234E+02 A

9) A given battery has a 13 V emf and an internal resistance of 0.113 &Omega;. If it is connected to a 0.686 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.501E+02 W
 * -b) 1.651E+02 W
 * +c) 1.816E+02 W
 * -d) 1.998E+02 W
 * -e) 2.197E+02 W

10) The resistances in the figure shown are R1= 1.54 &Omega;, R2= 0.927 &Omega;, and R2= 2.46 &Omega;. V1 and V3 are text 0.632 V and 2.12 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.586 V. What is the absolute value of the current through R1?


 * -a) 1.770E-01 A
 * -b) 1.947E-01 A
 * +c) 2.141E-01 A
 * -d) 2.355E-01 A
 * -e) 2.591E-01 A

Key: A1
1) Assume that a 24 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 27&deg;).


 * -a) 5.540E+02 V
 * -b) 6.095E+02 V
 * -c) 6.704E+02 V
 * +d) 7.374E+02 V
 * -e) 8.112E+02 V

2) What is the net capacitance if C1=3.25 &mu;F, C2=4.87 &mu;F, and C3=2.19 &mu;F in the configuration shown?


 * +a) 4.139E+00 &mu;F
 * -b) 4.553E+00 &mu;F
 * -c) 5.008E+00 &mu;F
 * -d) 5.509E+00 &mu;F
 * -e) 6.060E+00 &mu;F

3) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=2 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?


 * -a) 1.123E+02 N/C
 * -b) 1.235E+02 N/C
 * +c) 1.358E+02 N/C
 * -d) 1.494E+02 N/C
 * -e) 1.644E+02 N/C

4) A device requires consumes 185 W of power and requires 10.1 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * +a) 1.920E+06 A/m2
 * -b) 2.112E+06 A/m2
 * -c) 2.323E+06 A/m2
 * -d) 2.556E+06 A/m2
 * -e) 2.811E+06 A/m2

5) The resistances in the figure shown are R1= 1.6 &Omega;, R2= 1.3 &Omega;, and R2= 2.22 &Omega;. V1 and V3 are text 0.55 V and 3.18 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.743 V. What is the absolute value of the current through R1?


 * +a) 1.721E-01 A
 * -b) 1.893E-01 A
 * -c) 2.082E-01 A
 * -d) 2.291E-01 A
 * -e) 2.520E-01 A

6) What is the average current involved when a truck battery sets in motion 622 C of charge in 5.69 s while starting an engine?


 * -a) 9.034E+01 A
 * -b) 9.938E+01 A
 * +c) 1.093E+02 A
 * -d) 1.202E+02 A
 * -e) 1.323E+02 A

7) A given battery has a 11 V emf and an internal resistance of 0.0998 &Omega;. If it is connected to a 0.417 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.419E+02 W
 * -b) 1.561E+02 W
 * -c) 1.717E+02 W
 * +d) 1.889E+02 W
 * -e) 2.078E+02 W

8) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=3e$$?


 * -a) 4.171E-14 N
 * -b) 4.588E-14 N
 * +c) 5.047E-14 N
 * -d) 5.551E-14 N
 * -e) 6.107E-14 N

9) A 7 C charge is separated from a 12 C charge by distance of 11 cm.  What is the work done by increasing this separation to 19 cm?


 * +a) 2.890E-06 J
 * -b) 3.179E-06 J
 * -c) 3.497E-06 J
 * -d) 3.846E-06 J
 * -e) 4.231E-06 J

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.2}\hat i +3x^{2.1}\hat j +5y^{3.3}\hat k$$


 * -a) 2.610E+03 V&middot;m
 * -b) 2.871E+03 V&middot;m
 * +c) 3.158E+03 V&middot;m
 * -d) 3.474E+03 V&middot;m
 * -e) 3.822E+03 V&middot;m

Key: A2
1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?


 * -a) 2.777E+02 N/C
 * -b) 3.055E+02 N/C
 * +c) 3.361E+02 N/C
 * -d) 3.697E+02 N/C
 * -e) 4.066E+02 N/C

2) A 2 C charge is separated from a 10 C charge by distance of 10 cm.  What is the work done by increasing this separation to 16 cm?


 * -a) 6.128E-07 J
 * +b) 6.741E-07 J
 * -c) 7.415E-07 J
 * -d) 8.156E-07 J
 * -e) 8.972E-07 J

3) The resistances in the figure shown are R1= 1.1 &Omega;, R2= 1.55 &Omega;, and R2= 2.11 &Omega;. V1 and V3 are text 0.545 V and 3.22 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.744 V. What is the absolute value of the current through R1?


 * -a) 1.886E-01 A
 * +b) 2.075E-01 A
 * -c) 2.282E-01 A
 * -d) 2.510E-01 A
 * -e) 2.761E-01 A

4) A device requires consumes 126 W of power and requires 1.11 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * +a) 2.110E+05 A/m2
 * -b) 2.321E+05 A/m2
 * -c) 2.553E+05 A/m2
 * -d) 2.809E+05 A/m2
 * -e) 3.090E+05 A/m2

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * +a) 3.429E+03 V&middot;m
 * -b) 3.771E+03 V&middot;m
 * -c) 4.149E+03 V&middot;m
 * -d) 4.564E+03 V&middot;m
 * -e) 5.020E+03 V&middot;m

6) A given battery has a 12 V emf and an internal resistance of 0.107 &Omega;. If it is connected to a 0.814 &Omega; resistor what is the power dissipated by that load?


 * +a) 1.382E+02 W
 * -b) 1.520E+02 W
 * -c) 1.672E+02 W
 * -d) 1.839E+02 W
 * -e) 2.023E+02 W

7) What is the net capacitance if C1=3.27 &mu;F, C2=2.87 &mu;F, and C3=3.23 &mu;F in the configuration shown?


 * -a) 3.250E+00 &mu;F
 * -b) 3.575E+00 &mu;F
 * -c) 3.933E+00 &mu;F
 * -d) 4.326E+00 &mu;F
 * +e) 4.758E+00 &mu;F

8) What is the average current involved when a truck battery sets in motion 821 C of charge in 5.51 s while starting an engine?


 * -a) 1.231E+02 A
 * -b) 1.355E+02 A
 * +c) 1.490E+02 A
 * -d) 1.639E+02 A
 * -e) 1.803E+02 A

9) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?


 * -a) 1.028E-14 N
 * -b) 1.130E-14 N
 * -c) 1.244E-14 N
 * -d) 1.368E-14 N
 * +e) 1.505E-14 N

10) Assume that a 6 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (8 cm, 0&deg;) and  P2 is at (14 cm, 34&deg;).


 * -a) 2.626E+02 V
 * +b) 2.889E+02 V
 * -c) 3.178E+02 V
 * -d) 3.496E+02 V
 * -e) 3.845E+02 V

Key: B0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.


 * +a) 5.825E+00 V/m2
 * -b) 6.407E+00 V/m2
 * -c) 7.048E+00 V/m2
 * -d) 7.753E+00 V/m2
 * -e) 8.528E+00 V/m2

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?


 * -a) 2.964E+00 N/C
 * -b) 3.260E+00 N/C
 * -c) 3.586E+00 N/C
 * +d) 3.944E+00 N/C
 * -e) 4.339E+00 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.924E+01 N&middot;m2/C
 * -b) 4.316E+01 N&middot;m2/C
 * -c) 4.748E+01 N&middot;m2/C
 * +d) 5.222E+01 N&middot;m2/C
 * -e) 5.745E+01 N&middot;m2/C

4) A Van de Graff generator has a 149 cm diameter metal sphere that produces 172 kV near its surface. What  is the excess charge on the sphere?


 * -a) 1.071E+01 &mu;C
 * -b) 1.178E+01 &mu;C
 * -c) 1.296E+01 &mu;C
 * +d) 1.426E+01 &mu;C
 * -e) 1.568E+01 &mu;C

5) When a 5.65 V battery operates a 2.73 W bulb, how many electrons pass through it each second?


 * +a) 3.016E+18 electrons
 * -b) 3.317E+18 electrons
 * -c) 3.649E+18 electrons
 * -d) 4.014E+18 electrons
 * -e) 4.415E+18 electrons

6) What is the net capacitance if C1=3.54 &mu;F, C2=3.53 &mu;F, and C3=3.65 &mu;F in the configuration shown?


 * -a) 3.700E+00 &mu;F
 * -b) 4.070E+00 &mu;F
 * -c) 4.477E+00 &mu;F
 * -d) 4.925E+00 &mu;F
 * +e) 5.417E+00 &mu;F

7) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 2.292E+29 e&minus;/m3
 * -b) 2.521E+29 e&minus;/m3
 * -c) 2.773E+29 e&minus;/m3
 * -d) 3.051E+29 e&minus;/m3
 * -e) 3.356E+29 e&minus;/m3

8) What is the average current involved when a truck battery sets in motion 775 C of charge in 2.9 s while starting an engine?


 * -a) 2.209E+02 A
 * -b) 2.429E+02 A
 * +c) 2.672E+02 A
 * -d) 2.940E+02 A
 * -e) 3.234E+02 A

9) A battery with a terminal voltage of 8.01 V is connected to a circuit consisting of 3 22.1 &Omega; resistors and one 14.5 &Omega; resistor. What is the voltage drop across the 14.5 &Omega; resistor?


 * -a) 9.818E-01 V
 * -b) 1.080E+00 V
 * -c) 1.188E+00 V
 * -d) 1.307E+00 V
 * +e) 1.437E+00 V

10) Two sources of emf &epsilon;1=58.5 V, and  &epsilon;2=17.3 V are oriented as shownin the circuit. The resistances are R1=3.06 k&Omega; and  R2=1.88 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.25 mA and I4=1.25 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 1.981E+01 V
 * +b) 2.179E+01 V
 * -c) 2.397E+01 V
 * -d) 2.637E+01 V
 * -e) 2.901E+01 V

Key: B1
1) A make-believe metal has a density of 2.670E+03 kg/m3 and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 3.930E+28 e&minus;/m3
 * -b) 4.323E+28 e&minus;/m3
 * -c) 4.755E+28 e&minus;/m3
 * -d) 5.231E+28 e&minus;/m3
 * -e) 5.754E+28 e&minus;/m3

2) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.440E+01 V
 * -b) 1.584E+01 V
 * -c) 1.742E+01 V
 * -d) 1.916E+01 V
 * -e) 2.108E+01 V

3) A Van de Graff generator has a 76 cm diameter metal sphere that produces 193 kV near its surface. What  is the excess charge on the sphere?


 * -a) 7.418E+00 &mu;C
 * +b) 8.160E+00 &mu;C
 * -c) 8.976E+00 &mu;C
 * -d) 9.874E+00 &mu;C
 * -e) 1.086E+01 &mu;C

4) When a 7.78 V battery operates a 1.35 W bulb, how many electrons pass through it each second?


 * -a) 7.397E+17 electrons
 * -b) 8.137E+17 electrons
 * -c) 8.951E+17 electrons
 * -d) 9.846E+17 electrons
 * +e) 1.083E+18 electrons

5) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * -a) 1.677E+00 V
 * -b) 1.844E+00 V
 * +c) 2.029E+00 V
 * -d) 2.231E+00 V
 * -e) 2.455E+00 V

6) What is the net capacitance if C1=4.7 &mu;F, C2=4.82 &mu;F, and C3=3.61 &mu;F in the configuration shown?


 * -a) 5.445E+00 &mu;F
 * +b) 5.990E+00 &mu;F
 * -c) 6.589E+00 &mu;F
 * -d) 7.247E+00 &mu;F
 * -e) 7.972E+00 &mu;F

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.698E+01 N&middot;m2/C
 * -b) 1.868E+01 N&middot;m2/C
 * -c) 2.055E+01 N&middot;m2/C
 * -d) 2.260E+01 N&middot;m2/C
 * +e) 2.486E+01 N&middot;m2/C

8) What is the average current involved when a truck battery sets in motion 728 C of charge in 3.94 s while starting an engine?


 * +a) 1.848E+02 A
 * -b) 2.032E+02 A
 * -c) 2.236E+02 A
 * -d) 2.459E+02 A
 * -e) 2.705E+02 A

9) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.1 m, b=1.4 m.  The total charge on the rod is 5 nC.


 * +a) 4.602E+00 V/m2
 * -b) 5.062E+00 V/m2
 * -c) 5.568E+00 V/m2
 * -d) 6.125E+00 V/m2
 * -e) 6.738E+00 V/m2

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?


 * -a) 2.601E+01 N/C
 * -b) 2.861E+01 N/C
 * -c) 3.147E+01 N/C
 * +d) 3.462E+01 N/C
 * -e) 3.808E+01 N/C

Key: B2
1) A Van de Graff generator has a 141 cm diameter metal sphere that produces 280 kV near its surface. What  is the excess charge on the sphere?


 * -a) 1.500E+01 &mu;C
 * -b) 1.650E+01 &mu;C
 * -c) 1.815E+01 &mu;C
 * -d) 1.997E+01 &mu;C
 * +e) 2.196E+01 &mu;C

2) When a 6.24 V battery operates a 2.1 W bulb, how many electrons pass through it each second?


 * -a) 1.435E+18 electrons
 * -b) 1.578E+18 electrons
 * -c) 1.736E+18 electrons
 * -d) 1.910E+18 electrons
 * +e) 2.101E+18 electrons

3) What is the average current involved when a truck battery sets in motion 821 C of charge in 5.51 s while starting an engine?


 * -a) 1.231E+02 A
 * -b) 1.355E+02 A
 * +c) 1.490E+02 A
 * -d) 1.639E+02 A
 * -e) 1.803E+02 A

4) A battery with a terminal voltage of 8.41 V is connected to a circuit consisting of 3 16.1 &Omega; resistors and one 10.9 &Omega; resistor. What is the voltage drop across the 10.9 &Omega; resistor?


 * -a) 1.058E+00 V
 * -b) 1.163E+00 V
 * -c) 1.280E+00 V
 * -d) 1.408E+00 V
 * +e) 1.548E+00 V

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.385E+01 N&middot;m2/C
 * -b) 5.923E+01 N&middot;m2/C
 * -c) 6.516E+01 N&middot;m2/C
 * -d) 7.167E+01 N&middot;m2/C
 * -e) 7.884E+01 N&middot;m2/C

6) What is the net capacitance if C1=4.75 &mu;F, C2=2.77 &mu;F, and C3=2.47 &mu;F in the configuration shown?


 * +a) 4.220E+00 &mu;F
 * -b) 4.642E+00 &mu;F
 * -c) 5.106E+00 &mu;F
 * -d) 5.616E+00 &mu;F
 * -e) 6.178E+00 &mu;F

7) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.1 m, b=1.4 m.  The total charge on the rod is 5 nC.


 * +a) 4.602E+00 V/m2
 * -b) 5.062E+00 V/m2
 * -c) 5.568E+00 V/m2
 * -d) 6.125E+00 V/m2
 * -e) 6.738E+00 V/m2

8) Two sources of emf &epsilon;1=27.9 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=2.82 k&Omega; and  R2=2.25 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.1 mA and I4=0.676 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 8.334E+00 V
 * -b) 9.167E+00 V
 * +c) 1.008E+01 V
 * -d) 1.109E+01 V
 * -e) 1.220E+01 V

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?


 * -a) 6.641E+00 N/C
 * -b) 7.305E+00 N/C
 * +c) 8.036E+00 N/C
 * -d) 8.839E+00 N/C
 * -e) 9.723E+00 N/C

10) A make-believe metal has a density of 1.300E+04 kg/m3 and an atomic mass of 75.7 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 9.398E+28 e&minus;/m3
 * +b) 1.034E+29 e&minus;/m3
 * -c) 1.137E+29 e&minus;/m3
 * -d) 1.251E+29 e&minus;/m3
 * -e) 1.376E+29 e&minus;/m3

Key: C0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.


 * +a) 5.825E+00 V/m2
 * -b) 6.407E+00 V/m2
 * -c) 7.048E+00 V/m2
 * -d) 7.753E+00 V/m2
 * -e) 8.528E+00 V/m2

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?


 * +a) 9.592E+00 N/C
 * -b) 1.055E+01 N/C
 * -c) 1.161E+01 N/C
 * -d) 1.277E+01 N/C
 * -e) 1.404E+01 N/C

3) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?


 * +a) 7.825E+02 N/C
 * -b) 8.607E+02 N/C
 * -c) 9.468E+02 N/C
 * -d) 1.041E+03 N/C
 * -e) 1.146E+03 N/C

4) Calculate the final speed of a free electron accelerated from rest through a potential difference of 19 V.


 * -a) 1.942E+06 m/s
 * -b) 2.137E+06 m/s
 * -c) 2.350E+06 m/s
 * +d) 2.585E+06 m/s
 * -e) 2.844E+06 m/s

5) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=10 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 1.194E+02 J
 * -b) 1.314E+02 J
 * -c) 1.445E+02 J
 * +d) 1.589E+02 J
 * -e) 1.748E+02 J

6) What is the net capacitance if C1=2.3 &mu;F, C2=2.84 &mu;F, and C3=3.41 &mu;F in the configuration shown?


 * -a) 4.255E+00 &mu;F
 * +b) 4.681E+00 &mu;F
 * -c) 5.149E+00 &mu;F
 * -d) 5.664E+00 &mu;F
 * -e) 6.230E+00 &mu;F

7) A make-believe metal has a density of 1.430E+04 kg/m3 and an atomic mass of 37.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 1.882E+29 e&minus;/m3
 * -b) 2.070E+29 e&minus;/m3
 * +c) 2.277E+29 e&minus;/m3
 * -d) 2.505E+29 e&minus;/m3
 * -e) 2.756E+29 e&minus;/m3

8) Calculate the drift speed of electrons in a copper wire with a diameter of 4.38 mm carrying a 5.79 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 2.615E-05 m/s
 * +b) 2.876E-05 m/s
 * -c) 3.164E-05 m/s
 * -d) 3.480E-05 m/s
 * -e) 3.828E-05 m/s

9) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 k&Omega; and  R2=2.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.34 mA and I4=0.955 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 7.031E+00 V
 * +b) 7.734E+00 V
 * -c) 8.507E+00 V
 * -d) 9.358E+00 V
 * -e) 1.029E+01 V

10) Two sources of emf &epsilon;1=13.6 V, and  &epsilon;2=6.53 V are oriented as shownin the circuit. The resistances are R1=2.89 k&Omega; and  R2=2.12 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.11 mA and I4=0.311 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 7.264E-01 mA
 * +b) 7.990E-01 mA
 * -c) 8.789E-01 mA
 * -d) 9.668E-01 mA
 * -e) 1.063E+00 mA

Key: C1
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.


 * +a) 5.825E+00 V/m2
 * -b) 6.407E+00 V/m2
 * -c) 7.048E+00 V/m2
 * -d) 7.753E+00 V/m2
 * -e) 8.528E+00 V/m2

2) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=8 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 3.444E+01 J
 * -b) 3.789E+01 J
 * +c) 4.168E+01 J
 * -d) 4.585E+01 J
 * -e) 5.043E+01 J

3) Calculate the drift speed of electrons in a copper wire with a diameter of 4.9 mm carrying a 6.43 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 2.109E-05 m/s
 * -b) 2.320E-05 m/s
 * +c) 2.552E-05 m/s
 * -d) 2.807E-05 m/s
 * -e) 3.088E-05 m/s

4) What is the net capacitance if C1=3.56 &mu;F, C2=4.23 &mu;F, and C3=2.61 &mu;F in the configuration shown?


 * -a) 3.755E+00 &mu;F
 * -b) 4.130E+00 &mu;F
 * +c) 4.543E+00 &mu;F
 * -d) 4.997E+00 &mu;F
 * -e) 5.497E+00 &mu;F

5) Two sources of emf &epsilon;1=24.8 V, and  &epsilon;2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 k&Omega; and  R2=1.6 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.49 mA and I4=0.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 1.660E+00 mA
 * -b) 1.826E+00 mA
 * -c) 2.009E+00 mA
 * -d) 2.209E+00 mA
 * -e) 2.430E+00 mA

6) A make-believe metal has a density of 1.810E+04 kg/m3 and an atomic mass of 14.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 5.847E+29 e&minus;/m3
 * -b) 6.432E+29 e&minus;/m3
 * -c) 7.075E+29 e&minus;/m3
 * +d) 7.783E+29 e&minus;/m3
 * -e) 8.561E+29 e&minus;/m3

7) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.945E+00 V
 * +b) 9.840E+00 V
 * -c) 1.082E+01 V
 * -d) 1.191E+01 V
 * -e) 1.310E+01 V

8) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?


 * +a) 3.604E+02 N/C
 * -b) 3.964E+02 N/C
 * -c) 4.360E+02 N/C
 * -d) 4.796E+02 N/C
 * -e) 5.276E+02 N/C

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?


 * +a) 9.592E+00 N/C
 * -b) 1.055E+01 N/C
 * -c) 1.161E+01 N/C
 * -d) 1.277E+01 N/C
 * -e) 1.404E+01 N/C

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * -a) 4.638E+06 m/s
 * +b) 5.102E+06 m/s
 * -c) 5.612E+06 m/s
 * -d) 6.173E+06 m/s
 * -e) 6.791E+06 m/s

Key: C2
1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?


 * -a) 2.988E+00 N/C
 * -b) 3.287E+00 N/C
 * -c) 3.616E+00 N/C
 * -d) 3.977E+00 N/C
 * +e) 4.375E+00 N/C

2) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=10 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 1.194E+02 J
 * -b) 1.314E+02 J
 * -c) 1.445E+02 J
 * +d) 1.589E+02 J
 * -e) 1.748E+02 J

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 53 V.


 * -a) 3.244E+06 m/s
 * -b) 3.568E+06 m/s
 * -c) 3.925E+06 m/s
 * +d) 4.318E+06 m/s
 * -e) 4.750E+06 m/s

4) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=2 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?


 * +a) 2.406E+01 N/C
 * -b) 2.646E+01 N/C
 * -c) 2.911E+01 N/C
 * -d) 3.202E+01 N/C
 * -e) 3.522E+01 N/C

5) A make-believe metal has a density of 3.470E+03 kg/m3 and an atomic mass of 33.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 6.180E+28 e&minus;/m3
 * -b) 6.798E+28 e&minus;/m3
 * -c) 7.478E+28 e&minus;/m3
 * -d) 8.226E+28 e&minus;/m3
 * -e) 9.049E+28 e&minus;/m3

6) Two sources of emf &epsilon;1=39.2 V, and  &epsilon;2=12.6 V are oriented as shownin the circuit. The resistances are R1=3.86 k&Omega; and  R2=1.89 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.05 mA and I4=0.701 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.687E+00 V
 * -b) 9.555E+00 V
 * -c) 1.051E+01 V
 * -d) 1.156E+01 V
 * +e) 1.272E+01 V

7) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.96 m if a=0.63 m, b=1.4 m.  The total charge on the rod is 3 nC.


 * -a) 3.719E+00 V/m2
 * +b) 4.091E+00 V/m2
 * -c) 4.500E+00 V/m2
 * -d) 4.950E+00 V/m2
 * -e) 5.445E+00 V/m2

8) Calculate the drift speed of electrons in a copper wire with a diameter of 5.47 mm carrying a 3.48 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.008E-05 m/s
 * +b) 1.108E-05 m/s
 * -c) 1.219E-05 m/s
 * -d) 1.341E-05 m/s
 * -e) 1.475E-05 m/s

9) What is the net capacitance if C1=4.75 &mu;F, C2=2.77 &mu;F, and C3=2.47 &mu;F in the configuration shown?


 * +a) 4.220E+00 &mu;F
 * -b) 4.642E+00 &mu;F
 * -c) 5.106E+00 &mu;F
 * -d) 5.616E+00 &mu;F
 * -e) 6.178E+00 &mu;F

10) Two sources of emf &epsilon;1=36.3 V, and  &epsilon;2=12.9 V are oriented as shownin the circuit. The resistances are R1=4.28 k&Omega; and  R2=1.58 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.16 mA and I4=1.2 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 2.224E+00 mA
 * -b) 2.446E+00 mA
 * -c) 2.691E+00 mA
 * +d) 2.960E+00 mA
 * -e) 3.256E+00 mA

Key: D0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * -a) 5.569E+01 degrees
 * -b) 6.125E+01 degrees
 * +c) 6.738E+01 degrees
 * -d) 7.412E+01 degrees
 * -e) 8.153E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.2 m, and z=z1=4.1 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 5.8m2. An electric field has the xyz components (0, 8.4, 5.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.328E+01 N&middot;m2/C
 * -b) 3.660E+01 N&middot;m2/C
 * -c) 4.026E+01 N&middot;m2/C
 * -d) 4.429E+01 N&middot;m2/C
 * +e) 4.872E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.777E+01 N&middot;m2/C
 * -b) 5.254E+01 N&middot;m2/C
 * -c) 5.780E+01 N&middot;m2/C
 * +d) 6.358E+01 N&middot;m2/C
 * -e) 6.993E+01 N&middot;m2/C

4) When a 4.89 V battery operates a 1.44 W bulb, how many electrons pass through it each second?


 * +a) 1.838E+18 electrons
 * -b) 2.022E+18 electrons
 * -c) 2.224E+18 electrons
 * -d) 2.446E+18 electrons
 * -e) 2.691E+18 electrons

5) Two large parallel conducting plates are separated by 9.6 mm. Equal and opposite surface charges of 7.610E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 71 V?


 * -a) 4.723E-01 mm
 * -b) 5.432E-01 mm
 * -c) 6.246E-01 mm
 * -d) 7.183E-01 mm
 * +e) 8.261E-01 mm

6) In the figure shown C1=17.9 &mu;F, C2=2.71 &mu;F, and C3=4.14 &mu;F. The voltage source provides &epsilon;=7.12 V. What is the charge on C1?


 * +a) 3.527E+01 &mu;C
 * -b) 3.880E+01 &mu;C
 * -c) 4.268E+01 &mu;C
 * -d) 4.695E+01 &mu;C
 * -e) 5.164E+01 &mu;C

7) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.631E-01 &Omega;
 * -b) 2.894E-01 &Omega;
 * -c) 3.184E-01 &Omega;
 * +d) 3.502E-01 &Omega;
 * -e) 3.852E-01 &Omega;

8) What is consumer cost to operate one 76&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.144 per kilowatt-hour?


 * +a) $3.595E+01
 * -b) $3.955E+01
 * -c) $4.350E+01
 * -d) $4.785E+01
 * -e) $5.264E+01

9) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * -a) 1.677E+00 V
 * -b) 1.844E+00 V
 * +c) 2.029E+00 V
 * -d) 2.231E+00 V
 * -e) 2.455E+00 V

10) Three resistors, R1 = 1.43 &Omega;, and R2 = R2 = 3.25 &Omega;, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 5.184E+01 W
 * +b) 5.702E+01 W
 * -c) 6.272E+01 W
 * -d) 6.900E+01 W
 * -e) 7.590E+01 W

Key: D1
1) Three resistors, R1 = 1.31 &Omega;, and R2 = R2 = 2.91 &Omega;, are connected in parallel to a 6.03 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 2.294E+01 W
 * -b) 2.523E+01 W
 * +c) 2.776E+01 W
 * -d) 3.053E+01 W
 * -e) 3.359E+01 W

2) Calculate the resistance of a 12-gauge copper wire that is 81 m long and carries a current of 32 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 3.737E-01 &Omega;
 * +b) 4.111E-01 &Omega;
 * -c) 4.522E-01 &Omega;
 * -d) 4.975E-01 &Omega;
 * -e) 5.472E-01 &Omega;

3) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * -a) $2.791E+01
 * -b) $3.071E+01
 * -c) $3.378E+01
 * -d) $3.715E+01
 * +e) $4.087E+01

4) When a 3.63 V battery operates a 1.34 W bulb, how many electrons pass through it each second?


 * -a) 2.095E+18 electrons
 * +b) 2.304E+18 electrons
 * -c) 2.534E+18 electrons
 * -d) 2.788E+18 electrons
 * -e) 3.067E+18 electrons

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.2 m, z=z0=1.9 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 8.1m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 7.081E+01 N&middot;m2/C
 * -b) 7.789E+01 N&middot;m2/C
 * +c) 8.568E+01 N&middot;m2/C
 * -d) 9.425E+01 N&middot;m2/C
 * -e) 1.037E+02 N&middot;m2/C

6) In the figure shown C1=17.7 &mu;F, C2=2.5 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=12.8 V. What is the charge on C1?


 * -a) 5.066E+01 &mu;C
 * -b) 5.573E+01 &mu;C
 * -c) 6.130E+01 &mu;C
 * +d) 6.743E+01 &mu;C
 * -e) 7.417E+01 &mu;C

7) A battery with a terminal voltage of 7.82 V is connected to a circuit consisting of 2 19.3 &Omega; resistors and one 12.2 &Omega; resistor. What is the voltage drop across the 12.2 &Omega; resistor?


 * -a) 1.552E+00 V
 * -b) 1.707E+00 V
 * +c) 1.878E+00 V
 * -d) 2.066E+00 V
 * -e) 2.272E+00 V

8) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * -a) 5.569E+01 degrees
 * -b) 6.125E+01 degrees
 * +c) 6.738E+01 degrees
 * -d) 7.412E+01 degrees
 * -e) 8.153E+01 degrees

9) Two large parallel conducting plates are separated by 7.01 mm. Equal and opposite surface charges of 7.330E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 55 V?


 * -a) 3.799E-01 mm
 * -b) 4.368E-01 mm
 * -c) 5.024E-01 mm
 * -d) 5.777E-01 mm
 * +e) 6.644E-01 mm

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.134E+01 N&middot;m2/C
 * -b) 2.347E+01 N&middot;m2/C
 * +c) 2.582E+01 N&middot;m2/C
 * -d) 2.840E+01 N&middot;m2/C
 * -e) 3.124E+01 N&middot;m2/C

Key: D2
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.614E+01 N&middot;m2/C
 * +b) 7.275E+01 N&middot;m2/C
 * -c) 8.003E+01 N&middot;m2/C
 * -d) 8.803E+01 N&middot;m2/C
 * -e) 9.683E+01 N&middot;m2/C

2) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 4.957E-02 &Omega;
 * -b) 5.453E-02 &Omega;
 * -c) 5.998E-02 &Omega;
 * +d) 6.598E-02 &Omega;
 * -e) 7.258E-02 &Omega;

3) A battery with a terminal voltage of 13.2 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * -a) 1.958E+00 V
 * -b) 2.153E+00 V
 * +c) 2.369E+00 V
 * -d) 2.606E+00 V
 * -e) 2.866E+00 V

4) Two large parallel conducting plates are separated by 6.95 mm. Equal and opposite surface charges of 7.360E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 83 V?


 * -a) 6.565E-01 mm
 * -b) 7.550E-01 mm
 * -c) 8.683E-01 mm
 * +d) 9.985E-01 mm
 * -e) 1.148E+00 mm

5) Three resistors, R1 = 1.2 &Omega;, and R2 = R2 = 2.75 &Omega;, are connected in parallel to a 6.42 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 2.581E+01 W
 * -b) 2.839E+01 W
 * -c) 3.122E+01 W
 * +d) 3.435E+01 W
 * -e) 3.778E+01 W

6) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * -a) $2.791E+01
 * -b) $3.071E+01
 * -c) $3.378E+01
 * -d) $3.715E+01
 * +e) $4.087E+01

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 8.921E+01 N&middot;m2/C
 * -b) 9.813E+01 N&middot;m2/C
 * -c) 1.079E+02 N&middot;m2/C
 * -d) 1.187E+02 N&middot;m2/C
 * -e) 1.306E+02 N&middot;m2/C

8) In the figure shown C1=15.4 &mu;F, C2=2.22 &mu;F, and C3=4.77 &mu;F. The voltage source provides &epsilon;=6.8 V. What is the charge on C1?


 * -a) 2.702E+01 &mu;C
 * -b) 2.972E+01 &mu;C
 * +c) 3.269E+01 &mu;C
 * -d) 3.596E+01 &mu;C
 * -e) 3.956E+01 &mu;C

9) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=5e$$?


 * -a) 6.125E+01 degrees
 * +b) 6.738E+01 degrees
 * -c) 7.412E+01 degrees
 * -d) 8.153E+01 degrees
 * -e) 8.968E+01 degrees

10) When a 4.91 V battery operates a 1.43 W bulb, how many electrons pass through it each second?


 * -a) 1.242E+18 electrons
 * -b) 1.366E+18 electrons
 * -c) 1.502E+18 electrons
 * -d) 1.653E+18 electrons
 * +e) 1.818E+18 electrons

Key: E0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.


 * -a) 5.134E-01 V/m2
 * +b) 5.648E-01 V/m2
 * -c) 6.212E-01 V/m2
 * -d) 6.834E-01 V/m2
 * -e) 7.517E-01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.740E+01 N&middot;m2/C
 * -b) 1.914E+01 N&middot;m2/C
 * -c) 2.106E+01 N&middot;m2/C
 * -d) 2.316E+01 N&middot;m2/C
 * +e) 2.548E+01 N&middot;m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.8 m from the center of the shells?


 * -a) 5.865E+00 N/C
 * -b) 6.451E+00 N/C
 * -c) 7.096E+00 N/C
 * +d) 7.806E+00 N/C
 * -e) 8.587E+00 N/C

4) Two large parallel conducting plates are separated by 7.77 mm. Equal and opposite surface charges of 7.310E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?


 * -a) 5.814E-01 mm
 * -b) 6.686E-01 mm
 * -c) 7.689E-01 mm
 * +d) 8.842E-01 mm
 * -e) 1.017E+00 mm

5) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * -a) 4.324E+02 V
 * -b) 4.757E+02 V
 * +c) 5.232E+02 V
 * -d) 5.755E+02 V
 * -e) 6.331E+02 V

6) In the figure shown C1=16.1 &mu;F, C2=2.14 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * +a) 1.199E+01 &mu;J
 * -b) 1.319E+01 &mu;J
 * -c) 1.450E+01 &mu;J
 * -d) 1.595E+01 &mu;J
 * -e) 1.755E+01 &mu;J

7) A make-believe metal has a density of 3.530E+03 kg/m3 and an atomic mass of 10.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 1.673E+29 e&minus;/m3
 * -b) 1.840E+29 e&minus;/m3
 * +c) 2.024E+29 e&minus;/m3
 * -d) 2.226E+29 e&minus;/m3
 * -e) 2.449E+29 e&minus;/m3

8) Calculate the resistance of a 12-gauge copper wire that is 52 m long and carries a current of 99 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 1.983E-01 &Omega;
 * -b) 2.181E-01 &Omega;
 * -c) 2.399E-01 &Omega;
 * +d) 2.639E-01 &Omega;
 * -e) 2.903E-01 &Omega;

9) A given battery has a 14 V emf and an internal resistance of 0.192 &Omega;. If it is connected to a 0.766 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.229E+02 W
 * -b) 1.352E+02 W
 * -c) 1.487E+02 W
 * +d) 1.636E+02 W
 * -e) 1.799E+02 W

10) Two sources of emf &epsilon;1=31.0 V, and  &epsilon;2=10.0 V are oriented as shownin the circuit. The resistances are R1=4.22 k&Omega; and  R2=1.37 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.32 mA and I4=1.03 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 2.290E+00 mA
 * -b) 2.519E+00 mA
 * -c) 2.771E+00 mA
 * -d) 3.048E+00 mA
 * -e) 3.353E+00 mA

Key: E1
1) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 4.957E-02 &Omega;
 * -b) 5.453E-02 &Omega;
 * -c) 5.998E-02 &Omega;
 * +d) 6.598E-02 &Omega;
 * -e) 7.258E-02 &Omega;

2) A given battery has a 14 V emf and an internal resistance of 0.192 &Omega;. If it is connected to a 0.766 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.229E+02 W
 * -b) 1.352E+02 W
 * -c) 1.487E+02 W
 * +d) 1.636E+02 W
 * -e) 1.799E+02 W

3) Two sources of emf &epsilon;1=24.9 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 k&Omega; and  R2=2.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.74 mA and I4=0.444 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 1.725E+00 mA
 * -b) 1.898E+00 mA
 * -c) 2.087E+00 mA
 * +d) 2.296E+00 mA
 * -e) 2.526E+00 mA

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=6.8\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.6\text{ m}$$.


 * -a) 1.258E+00 V/m2
 * -b) 1.384E+00 V/m2
 * -c) 1.522E+00 V/m2
 * +d) 1.674E+00 V/m2
 * -e) 1.842E+00 V/m2

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 8.5m2. Those in the xy plane have area 2.8m2 ,and those in the zx plane have area 3.7m2. An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.079E+01 N&middot;m2/C
 * -b) 2.287E+01 N&middot;m2/C
 * -c) 2.516E+01 N&middot;m2/C
 * +d) 2.768E+01 N&middot;m2/C
 * -e) 3.044E+01 N&middot;m2/C

6) A make-believe metal has a density of 3.230E+03 kg/m3 and an atomic mass of 116.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 1.385E+28 e&minus;/m3
 * -b) 1.524E+28 e&minus;/m3
 * +c) 1.676E+28 e&minus;/m3
 * -d) 1.844E+28 e&minus;/m3
 * -e) 2.028E+28 e&minus;/m3

7) In the figure shown C1=18.7 &mu;F, C2=2.15 &mu;F, and C3=4.88 &mu;F. The voltage source provides &epsilon;=11.9 V. What is the energy stored in C2?


 * -a) 1.270E+01 &mu;J
 * -b) 1.397E+01 &mu;J
 * -c) 1.537E+01 &mu;J
 * -d) 1.690E+01 &mu;J
 * +e) 1.859E+01 &mu;J

8) Two large parallel conducting plates are separated by 8.0 mm. Equal and opposite surface charges of 7.520E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?


 * -a) 5.431E-01 mm
 * -b) 6.245E-01 mm
 * +c) 7.182E-01 mm
 * -d) 8.260E-01 mm
 * -e) 9.499E-01 mm

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?


 * -a) 2.964E+00 N/C
 * -b) 3.260E+00 N/C
 * -c) 3.586E+00 N/C
 * +d) 3.944E+00 N/C
 * -e) 4.339E+00 N/C

10) A diploe has a charge magnitude of q=6 nC and a separation distance of d=3.89 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.24 cm, y=1.95 cm)? Note that following the textbook's example, the y-value of the field point at 1.95 cm matches the disance of the positive charge above the x-axis.


 * -a) 4.104E+02 V
 * -b) 4.514E+02 V
 * -c) 4.965E+02 V
 * -d) 5.462E+02 V
 * +e) 6.008E+02 V

Key: E2
1) Two sources of emf &epsilon;1=24.8 V, and  &epsilon;2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 k&Omega; and  R2=1.6 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.49 mA and I4=0.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 1.660E+00 mA
 * -b) 1.826E+00 mA
 * -c) 2.009E+00 mA
 * -d) 2.209E+00 mA
 * -e) 2.430E+00 mA

2) In the figure shown C1=16.3 &mu;F, C2=2.17 &mu;F, and C3=4.67 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * -a) 8.718E+00 &mu;J
 * -b) 9.589E+00 &mu;J
 * -c) 1.055E+01 &mu;J
 * -d) 1.160E+01 &mu;J
 * +e) 1.276E+01 &mu;J

3) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.


 * -a) 5.261E+02 V
 * -b) 5.787E+02 V
 * +c) 6.365E+02 V
 * -d) 7.002E+02 V
 * -e) 7.702E+02 V

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?


 * -a) 9.144E+00 N/C
 * -b) 1.006E+01 N/C
 * -c) 1.106E+01 N/C
 * -d) 1.217E+01 N/C
 * +e) 1.339E+01 N/C

5) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=2.0\text{ m}$$ and the surface charge density is $$\sigma=9\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.2\text{ m}$$.


 * -a) 8.933E+00 V/m2
 * -b) 9.826E+00 V/m2
 * +c) 1.081E+01 V/m2
 * -d) 1.189E+01 V/m2
 * -e) 1.308E+01 V/m2

6) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.631E-01 &Omega;
 * -b) 2.894E-01 &Omega;
 * -c) 3.184E-01 &Omega;
 * +d) 3.502E-01 &Omega;
 * -e) 3.852E-01 &Omega;

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.891E+01 N&middot;m2/C
 * -b) 2.080E+01 N&middot;m2/C
 * +c) 2.288E+01 N&middot;m2/C
 * -d) 2.517E+01 N&middot;m2/C
 * -e) 2.768E+01 N&middot;m2/C

8) A make-believe metal has a density of 1.180E+04 kg/m3 and an atomic mass of 121.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 4.010E+28 e&minus;/m3
 * -b) 4.411E+28 e&minus;/m3
 * -c) 4.852E+28 e&minus;/m3
 * -d) 5.337E+28 e&minus;/m3
 * +e) 5.871E+28 e&minus;/m3

9) Two large parallel conducting plates are separated by 7.77 mm. Equal and opposite surface charges of 7.310E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?


 * -a) 5.814E-01 mm
 * -b) 6.686E-01 mm
 * -c) 7.689E-01 mm
 * +d) 8.842E-01 mm
 * -e) 1.017E+00 mm

10) A given battery has a 15 V emf and an internal resistance of 0.113 &Omega;. If it is connected to a 0.645 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.898E+02 W
 * -b) 2.087E+02 W
 * -c) 2.296E+02 W
 * +d) 2.526E+02 W
 * -e) 2.778E+02 W

Key: F0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * -a) 8.690E+00 V/m2
 * -b) 9.559E+00 V/m2
 * +c) 1.051E+01 V/m2
 * -d) 1.157E+01 V/m2
 * -e) 1.272E+01 V/m2

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * -a) 1.969E+02 V&middot;m
 * -b) 2.166E+02 V&middot;m
 * -c) 2.383E+02 V&middot;m
 * -d) 2.621E+02 V&middot;m
 * +e) 2.883E+02 V&middot;m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.920E+01 N&middot;m2/C
 * -b) 7.612E+01 N&middot;m2/C
 * -c) 8.373E+01 N&middot;m2/C
 * +d) 9.210E+01 N&middot;m2/C
 * -e) 1.013E+02 N&middot;m2/C

4) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.39 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.56 cm, y=2.19 cm)? Note that following the textbook's example, the y-value of the field point at 2.19 cm matches the disance of the positive charge above the x-axis.


 * -a) 3.852E+02 V
 * -b) 4.238E+02 V
 * +c) 4.661E+02 V
 * -d) 5.127E+02 V
 * -e) 5.640E+02 V

5) When a 6.32 V battery operates a 1.94 W bulb, how many electrons pass through it each second?


 * -a) 1.439E+18 electrons
 * -b) 1.583E+18 electrons
 * -c) 1.742E+18 electrons
 * +d) 1.916E+18 electrons
 * -e) 2.107E+18 electrons

6) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * -a) 5.969E+01 &mu;C
 * -b) 6.566E+01 &mu;C
 * +c) 7.222E+01 &mu;C
 * -d) 7.944E+01 &mu;C
 * -e) 8.739E+01 &mu;C

7) Calculate the electric field in a 12-gauge copper wire that is 13 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.250E-04 V/m
 * -b) 2.475E-04 V/m
 * -c) 2.722E-04 V/m
 * +d) 2.995E-04 V/m
 * -e) 3.294E-04 V/m

8) Calculate the resistance of a 12-gauge copper wire that is 59 m long and carries a current of 26 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 2.995E-01 &Omega;
 * -b) 3.294E-01 &Omega;
 * -c) 3.623E-01 &Omega;
 * -d) 3.986E-01 &Omega;
 * -e) 4.384E-01 &Omega;

9) A battery with a terminal voltage of 7.63 V is connected to a circuit consisting of 3 20.9 &Omega; resistors and one 12.1 &Omega; resistor. What is the voltage drop across the 12.1 &Omega; resistor?


 * +a) 1.234E+00 V
 * -b) 1.358E+00 V
 * -c) 1.493E+00 V
 * -d) 1.643E+00 V
 * -e) 1.807E+00 V

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 569 V.  If the combined external and internal resistance is 137 &Omega and the capacitance is  76 mF, how long will it take for the capacitor's voltage to reach 419.0 V?


 * -a) 1.043E+01 s
 * -b) 1.147E+01 s
 * -c) 1.262E+01 s
 * +d) 1.388E+01 s
 * -e) 1.527E+01 s

Key: F1
1) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 190 V.  If the combined external and internal resistance is 255 &Omega and the capacitance is  54 mF, how long will it take for the capacitor's voltage to reach 101.0 V?


 * +a) 1.044E+01 s
 * -b) 1.149E+01 s
 * -c) 1.264E+01 s
 * -d) 1.390E+01 s
 * -e) 1.529E+01 s

2) Calculate the electric field in a 12-gauge copper wire that is 23 m long and carries a current of 64 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.953E-04 V/m
 * +b) 3.248E-04 V/m
 * -c) 3.573E-04 V/m
 * -d) 3.930E-04 V/m
 * -e) 4.324E-04 V/m

3) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.3 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.86 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * -a) 6.325E+02 V
 * +b) 6.957E+02 V
 * -c) 7.653E+02 V
 * -d) 8.418E+02 V
 * -e) 9.260E+02 V

4) When a 4.89 V battery operates a 1.44 W bulb, how many electrons pass through it each second?


 * +a) 1.838E+18 electrons
 * -b) 2.022E+18 electrons
 * -c) 2.224E+18 electrons
 * -d) 2.446E+18 electrons
 * -e) 2.691E+18 electrons

5) Calculate the resistance of a 12-gauge copper wire that is 19 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 7.970E-02 &Omega;
 * -b) 8.767E-02 &Omega;
 * +c) 9.644E-02 &Omega;
 * -d) 1.061E-01 &Omega;
 * -e) 1.167E-01 &Omega;

6) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.0 m, b=1.8 m.  The total charge on the rod is 6 nC.


 * -a) 3.610E+00 V/m2
 * +b) 3.971E+00 V/m2
 * -c) 4.368E+00 V/m2
 * -d) 4.804E+00 V/m2
 * -e) 5.285E+00 V/m2

7) In the figure shown C1=17.7 &mu;F, C2=2.5 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=12.8 V. What is the charge on C1?


 * -a) 5.066E+01 &mu;C
 * -b) 5.573E+01 &mu;C
 * -c) 6.130E+01 &mu;C
 * +d) 6.743E+01 &mu;C
 * -e) 7.417E+01 &mu;C

8) A battery with a terminal voltage of 10.6 V is connected to a circuit consisting of 2 21.1 &Omega; resistors and one 12.8 &Omega; resistor. What is the voltage drop across the 12.8 &Omega; resistor?


 * +a) 2.467E+00 V
 * -b) 2.714E+00 V
 * -c) 2.985E+00 V
 * -d) 3.283E+00 V
 * -e) 3.612E+00 V

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.920E+01 N&middot;m2/C
 * -b) 7.612E+01 N&middot;m2/C
 * -c) 8.373E+01 N&middot;m2/C
 * +d) 9.210E+01 N&middot;m2/C
 * -e) 1.013E+02 N&middot;m2/C

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * +a) 3.429E+03 V&middot;m
 * -b) 3.771E+03 V&middot;m
 * -c) 4.149E+03 V&middot;m
 * -d) 4.564E+03 V&middot;m
 * -e) 5.020E+03 V&middot;m

Key: F2
1) Calculate the electric field in a 12-gauge copper wire that is 21 m long and carries a current of 42 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 1.602E-04 V/m
 * -b) 1.762E-04 V/m
 * -c) 1.938E-04 V/m
 * +d) 2.132E-04 V/m
 * -e) 2.345E-04 V/m

2) Calculate the resistance of a 12-gauge copper wire that is 48 m long and carries a current of 50 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.215E-01 &Omega;
 * +b) 2.436E-01 &Omega;
 * -c) 2.680E-01 &Omega;
 * -d) 2.948E-01 &Omega;
 * -e) 3.243E-01 &Omega;

3) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 467 V.  If the combined external and internal resistance is 172 &Omega and the capacitance is  74 mF, how long will it take for the capacitor's voltage to reach 258.0 V?


 * -a) 7.688E+00 s
 * -b) 8.457E+00 s
 * -c) 9.303E+00 s
 * +d) 1.023E+01 s
 * -e) 1.126E+01 s

4) In the figure shown C1=17.9 &mu;F, C2=2.71 &mu;F, and C3=4.14 &mu;F. The voltage source provides &epsilon;=7.12 V. What is the charge on C1?


 * +a) 3.527E+01 &mu;C
 * -b) 3.880E+01 &mu;C
 * -c) 4.268E+01 &mu;C
 * -d) 4.695E+01 &mu;C
 * -e) 5.164E+01 &mu;C

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.186E+01 N&middot;m2/C
 * -b) 2.404E+01 N&middot;m2/C
 * +c) 2.645E+01 N&middot;m2/C
 * -d) 2.909E+01 N&middot;m2/C
 * -e) 3.200E+01 N&middot;m2/C

6) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.62 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * -a) 6.311E+00 V/m2
 * -b) 6.943E+00 V/m2
 * +c) 7.637E+00 V/m2
 * -d) 8.401E+00 V/m2
 * -e) 9.241E+00 V/m2

7) A battery with a terminal voltage of 14.6 V is connected to a circuit consisting of 2 21.7 &Omega; resistors and one 14.4 &Omega; resistor. What is the voltage drop across the 14.4 &Omega; resistor?


 * +a) 3.637E+00 V
 * -b) 4.001E+00 V
 * -c) 4.401E+00 V
 * -d) 4.841E+00 V
 * -e) 5.325E+00 V

8) A diploe has a charge magnitude of q=6 nC and a separation distance of d=3.89 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.24 cm, y=1.95 cm)? Note that following the textbook's example, the y-value of the field point at 1.95 cm matches the disance of the positive charge above the x-axis.


 * -a) 4.104E+02 V
 * -b) 4.514E+02 V
 * -c) 4.965E+02 V
 * -d) 5.462E+02 V
 * +e) 6.008E+02 V

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.8}\hat i +1x^{2.3}\hat j +2y^{2.9}\hat k$$


 * -a) 2.210E+04 V&middot;m
 * +b) 2.431E+04 V&middot;m
 * -c) 2.674E+04 V&middot;m
 * -d) 2.941E+04 V&middot;m
 * -e) 3.235E+04 V&middot;m

10) When a 4.21 V battery operates a 2.17 W bulb, how many electrons pass through it each second?


 * -a) 2.659E+18 electrons
 * -b) 2.925E+18 electrons
 * +c) 3.217E+18 electrons
 * -d) 3.539E+18 electrons
 * -e) 3.893E+18 electrons

Key: G0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.8\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.1\text{ m}$$.


 * -a) 7.517E+00 V/m2
 * -b) 8.269E+00 V/m2
 * -c) 9.096E+00 V/m2
 * -d) 1.001E+01 V/m2
 * +e) 1.101E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.988E+01 N&middot;m2/C
 * -b) 5.487E+01 N&middot;m2/C
 * -c) 6.035E+01 N&middot;m2/C
 * -d) 6.639E+01 N&middot;m2/C
 * +e) 7.303E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * -a) 1.969E+02 V&middot;m
 * -b) 2.166E+02 V&middot;m
 * -c) 2.383E+02 V&middot;m
 * -d) 2.621E+02 V&middot;m
 * +e) 2.883E+02 V&middot;m

4) A 7 C charge is separated from a 15 C charge by distance of 14 cm.  What is the work done by increasing this separation to 20 cm?


 * -a) 1.519E-06 J
 * -b) 1.671E-06 J
 * -c) 1.838E-06 J
 * +d) 2.022E-06 J
 * -e) 2.224E-06 J

5) Assume that a 16 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (6 cm, 0&deg;) and  P2 is at (14 cm, 27&deg;).


 * -a) 9.354E+02 V
 * -b) 1.029E+03 V
 * -c) 1.132E+03 V
 * -d) 1.245E+03 V
 * +e) 1.370E+03 V

6) What is the net capacitance if C1=4.55 &mu;F, C2=4.39 &mu;F, and C3=3.32 &mu;F in the configuration shown?


 * -a) 4.173E+00 &mu;F
 * -b) 4.590E+00 &mu;F
 * -c) 5.049E+00 &mu;F
 * +d) 5.554E+00 &mu;F
 * -e) 6.110E+00 &mu;F

7) A DC winch moter draws 25 amps at 128 volts as it lifts a 5.710E+03 N weight at a constant speed of 0.449 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 8.413E-01 &Omega;
 * -b) 9.254E-01 &Omega;
 * +c) 1.018E+00 &Omega;
 * -d) 1.120E+00 &Omega;
 * -e) 1.232E+00 &Omega;

8) Calculate the electric field in a 12-gauge copper wire that is 41 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 3.604E-04 V/m
 * -b) 3.964E-04 V/m
 * -c) 4.360E-04 V/m
 * -d) 4.796E-04 V/m
 * -e) 5.276E-04 V/m

9) In the circuit shown V=11.8 V, R1=2.38 &Omega;, R2=5.11 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * -a) 8.489E+00 W
 * -b) 9.338E+00 W
 * +c) 1.027E+01 W
 * -d) 1.130E+01 W
 * -e) 1.243E+01 W

10) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=14.4 V are oriented as shownin the circuit. The resistances are R1=4.33 k&Omega; and  R2=1.65 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.59 mA and I4=1.07 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 9.142E+00 V
 * -b) 1.006E+01 V
 * +c) 1.106E+01 V
 * -d) 1.217E+01 V
 * -e) 1.338E+01 V

Key: G1
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.4\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=0.56\text{ m}$$.


 * -a) 2.567E+01 V/m2
 * -b) 2.824E+01 V/m2
 * -c) 3.106E+01 V/m2
 * -d) 3.417E+01 V/m2
 * +e) 3.759E+01 V/m2

2) Assume that a 6 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (16 cm, 71&deg;).


 * -a) 1.969E+02 V
 * -b) 2.166E+02 V
 * -c) 2.383E+02 V
 * +d) 2.621E+02 V
 * -e) 2.884E+02 V

3) Calculate the electric field in a 12-gauge copper wire that is 17 m long and carries a current of 56 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 1.941E-04 V/m
 * -b) 2.135E-04 V/m
 * -c) 2.349E-04 V/m
 * -d) 2.584E-04 V/m
 * +e) 2.842E-04 V/m

4) In the circuit shown V=16.1 V, R1=1.18 &Omega;, R2=5.28 &Omega;, and R3=14.8 &Omega;. What is the power dissipated by R2?


 * -a) 2.172E+01 W
 * -b) 2.389E+01 W
 * -c) 2.628E+01 W
 * +d) 2.891E+01 W
 * -e) 3.180E+01 W

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.777E+01 N&middot;m2/C
 * -b) 5.254E+01 N&middot;m2/C
 * -c) 5.780E+01 N&middot;m2/C
 * +d) 6.358E+01 N&middot;m2/C
 * -e) 6.993E+01 N&middot;m2/C

6) A 5 C charge is separated from a 12 C charge by distance of 10 cm.  What is the work done by increasing this separation to 16 cm?


 * -a) 1.381E-06 J
 * -b) 1.519E-06 J
 * -c) 1.671E-06 J
 * -d) 1.838E-06 J
 * +e) 2.022E-06 J

7) What is the net capacitance if C1=2.55 &mu;F, C2=4.13 &mu;F, and C3=2.5 &mu;F in the configuration shown?


 * +a) 4.077E+00 &mu;F
 * -b) 4.484E+00 &mu;F
 * -c) 4.933E+00 &mu;F
 * -d) 5.426E+00 &mu;F
 * -e) 5.969E+00 &mu;F

8) A DC winch moter draws 26 amps at 177 volts as it lifts a 4.820E+03 N weight at a constant speed of 0.696 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 1.677E+00 &Omega;
 * +b) 1.845E+00 &Omega;
 * -c) 2.030E+00 &Omega;
 * -d) 2.233E+00 &Omega;
 * -e) 2.456E+00 &Omega;

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * -a) 4.286E+03 V&middot;m
 * -b) 4.714E+03 V&middot;m
 * +c) 5.186E+03 V&middot;m
 * -d) 5.704E+03 V&middot;m
 * -e) 6.275E+03 V&middot;m

10) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.11 mA and I4=0.746 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 4.275E+00 V
 * -b) 4.703E+00 V
 * +c) 5.173E+00 V
 * -d) 5.691E+00 V
 * -e) 6.260E+00 V

Key: G2
1) What is the net capacitance if C1=3.97 &mu;F, C2=3.51 &mu;F, and C3=2.18 &mu;F in the configuration shown?


 * -a) 3.038E+00 &mu;F
 * -b) 3.341E+00 &mu;F
 * -c) 3.675E+00 &mu;F
 * +d) 4.043E+00 &mu;F
 * -e) 4.447E+00 &mu;F

2) Calculate the electric field in a 12-gauge copper wire that is 26 m long and carries a current of 24 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 9.152E-05 V/m
 * -b) 1.007E-04 V/m
 * -c) 1.107E-04 V/m
 * +d) 1.218E-04 V/m
 * -e) 1.340E-04 V/m

3) Assume that a 5 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 31&deg;).


 * -a) 1.397E+02 V
 * +b) 1.536E+02 V
 * -c) 1.690E+02 V
 * -d) 1.859E+02 V
 * -e) 2.045E+02 V

4) Two sources of emf &epsilon;1=21.0 V, and  &epsilon;2=8.72 V are oriented as shownin the circuit. The resistances are R1=3.12 k&Omega; and  R2=1.15 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.41 mA and I4=0.816 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * +a) 5.267E+00 V
 * -b) 5.794E+00 V
 * -c) 6.373E+00 V
 * -d) 7.011E+00 V
 * -e) 7.712E+00 V

5) In the circuit shown V=16.1 V, R1=1.18 &Omega;, R2=5.28 &Omega;, and R3=14.8 &Omega;. What is the power dissipated by R2?


 * -a) 2.172E+01 W
 * -b) 2.389E+01 W
 * -c) 2.628E+01 W
 * +d) 2.891E+01 W
 * -e) 3.180E+01 W

6) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.0}\hat i +2x^{2.1}\hat j +3y^{2.5}\hat k$$


 * -a) 9.027E+03 V&middot;m
 * +b) 9.930E+03 V&middot;m
 * -c) 1.092E+04 V&middot;m
 * -d) 1.202E+04 V&middot;m
 * -e) 1.322E+04 V&middot;m

7) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=4.3\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.4\text{ m}$$.


 * +a) 5.647E+00 V/m2
 * -b) 6.212E+00 V/m2
 * -c) 6.833E+00 V/m2
 * -d) 7.517E+00 V/m2
 * -e) 8.268E+00 V/m2

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 9.823E+00 N&middot;m2/C
 * +b) 1.080E+01 N&middot;m2/C
 * -c) 1.189E+01 N&middot;m2/C
 * -d) 1.307E+01 N&middot;m2/C
 * -e) 1.438E+01 N&middot;m2/C

9) A 2 C charge is separated from a 6 C charge by distance of 13 cm.  What is the work done by increasing this separation to 16 cm?


 * +a) 1.556E-07 J
 * -b) 1.711E-07 J
 * -c) 1.882E-07 J
 * -d) 2.070E-07 J
 * -e) 2.277E-07 J

10) A DC winch moter draws 17 amps at 187 volts as it lifts a 5.600E+03 N weight at a constant speed of 0.381 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 2.471E+00 &Omega;
 * -b) 2.718E+00 &Omega;
 * -c) 2.990E+00 &Omega;
 * -d) 3.288E+00 &Omega;
 * +e) 3.617E+00 &Omega;

Key: H0
1) A large thin isolated square plate has an area of 6 m2. It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?


 * -a) 3.214E+01 N/C
 * -b) 3.536E+01 N/C
 * -c) 3.889E+01 N/C
 * -d) 4.278E+01 N/C
 * +e) 4.706E+01 N/C

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.662E+01 N&middot;m2/C
 * +b) 4.028E+01 N&middot;m2/C
 * -c) 4.430E+01 N&middot;m2/C
 * -d) 4.873E+01 N&middot;m2/C
 * -e) 5.361E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.125E+01 N&middot;m2/C
 * -b) 4.537E+01 N&middot;m2/C
 * -c) 4.991E+01 N&middot;m2/C
 * +d) 5.490E+01 N&middot;m2/C
 * -e) 6.039E+01 N&middot;m2/C

4) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?


 * -a) 1.439E+18 electrons
 * +b) 1.582E+18 electrons
 * -c) 1.741E+18 electrons
 * -d) 1.915E+18 electrons
 * -e) 2.106E+18 electrons

5) Two large parallel conducting plates are separated by 9.71 mm. Equal and opposite surface charges of 7.550E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 73 V?


 * -a) 7.444E-01 mm
 * +b) 8.561E-01 mm
 * -c) 9.845E-01 mm
 * -d) 1.132E+00 mm
 * -e) 1.302E+00 mm

6) In the figure shown C1=19.9 &mu;F, C2=2.25 &mu;F, and C3=4.75 &mu;F. The voltage source provides &epsilon;=6.93 V. What is the charge on C1?


 * -a) 2.451E+01 &mu;C
 * -b) 2.696E+01 &mu;C
 * -c) 2.966E+01 &mu;C
 * -d) 3.262E+01 &mu;C
 * +e) 3.589E+01 &mu;C

7) Calculate the resistance of a 12-gauge copper wire that is 86 m long and carries a current of 97 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 4.365E-01 &Omega;
 * -b) 4.801E-01 &Omega;
 * -c) 5.282E-01 &Omega;
 * -d) 5.810E-01 &Omega;
 * -e) 6.391E-01 &Omega;

8) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 2.292E+29 e&minus;/m3
 * -b) 2.521E+29 e&minus;/m3
 * -c) 2.773E+29 e&minus;/m3
 * -d) 3.051E+29 e&minus;/m3
 * -e) 3.356E+29 e&minus;/m3

9) Two sources of emf &epsilon;1=54.9 V, and  &epsilon;2=19.8 V are oriented as shownin the circuit. The resistances are R1=3.93 k&Omega; and  R2=1.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.18 mA and I4=1.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.779E+01 V
 * -b) 1.957E+01 V
 * -c) 2.153E+01 V
 * -d) 2.368E+01 V
 * -e) 2.605E+01 V

10) A battery with a terminal voltage of 13.2 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * -a) 1.958E+00 V
 * -b) 2.153E+00 V
 * +c) 2.369E+00 V
 * -d) 2.606E+00 V
 * -e) 2.866E+00 V

Key: H1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.978E+01 N&middot;m2/C
 * -b) 6.576E+01 N&middot;m2/C
 * -c) 7.233E+01 N&middot;m2/C
 * -d) 7.957E+01 N&middot;m2/C
 * -e) 8.752E+01 N&middot;m2/C

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.737E+01 N&middot;m2/C
 * -b) 1.910E+01 N&middot;m2/C
 * -c) 2.101E+01 N&middot;m2/C
 * -d) 2.311E+01 N&middot;m2/C
 * +e) 2.543E+01 N&middot;m2/C

3) Calculate the resistance of a 12-gauge copper wire that is 42 m long and carries a current of 63 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 1.938E-01 &Omega;
 * +b) 2.132E-01 &Omega;
 * -c) 2.345E-01 &Omega;
 * -d) 2.579E-01 &Omega;
 * -e) 2.837E-01 &Omega;

4) Two sources of emf &epsilon;1=27.9 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=2.82 k&Omega; and  R2=2.25 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.1 mA and I4=0.676 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 8.334E+00 V
 * -b) 9.167E+00 V
 * +c) 1.008E+01 V
 * -d) 1.109E+01 V
 * -e) 1.220E+01 V

5) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 2.292E+29 e&minus;/m3
 * -b) 2.521E+29 e&minus;/m3
 * -c) 2.773E+29 e&minus;/m3
 * -d) 3.051E+29 e&minus;/m3
 * -e) 3.356E+29 e&minus;/m3

6) When a 4.91 V battery operates a 1.43 W bulb, how many electrons pass through it each second?


 * -a) 1.242E+18 electrons
 * -b) 1.366E+18 electrons
 * -c) 1.502E+18 electrons
 * -d) 1.653E+18 electrons
 * +e) 1.818E+18 electrons

7) In the figure shown C1=19.0 &mu;F, C2=2.35 &mu;F, and C3=5.22 &mu;F. The voltage source provides &epsilon;=6.01 V. What is the charge on C1?


 * -a) 2.444E+01 &mu;C
 * -b) 2.689E+01 &mu;C
 * -c) 2.958E+01 &mu;C
 * +d) 3.253E+01 &mu;C
 * -e) 3.579E+01 &mu;C

8) Two large parallel conducting plates are separated by 9.87 mm. Equal and opposite surface charges of 7.610E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 66 V?


 * -a) 4.391E-01 mm
 * -b) 5.049E-01 mm
 * -c) 5.806E-01 mm
 * -d) 6.677E-01 mm
 * +e) 7.679E-01 mm

9) A large thin isolated square plate has an area of 5 m2. It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * -a) 6.534E+01 N/C
 * -b) 7.187E+01 N/C
 * +c) 7.906E+01 N/C
 * -d) 8.696E+01 N/C
 * -e) 9.566E+01 N/C

10) A battery with a terminal voltage of 8.01 V is connected to a circuit consisting of 3 22.1 &Omega; resistors and one 14.5 &Omega; resistor. What is the voltage drop across the 14.5 &Omega; resistor?


 * -a) 9.818E-01 V
 * -b) 1.080E+00 V
 * -c) 1.188E+00 V
 * -d) 1.307E+00 V
 * +e) 1.437E+00 V

Key: H2
1) A large thin isolated square plate has an area of 8 m2. It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * -a) 2.652E+01 N/C
 * -b) 2.917E+01 N/C
 * -c) 3.209E+01 N/C
 * +d) 3.529E+01 N/C
 * -e) 3.882E+01 N/C

2) Two sources of emf &epsilon;1=17.3 V, and  &epsilon;2=6.46 V are oriented as shownin the circuit. The resistances are R1=2.54 k&Omega; and  R2=2.79 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.1 mA and I4=0.281 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 6.488E+00 V
 * +b) 7.137E+00 V
 * -c) 7.850E+00 V
 * -d) 8.635E+00 V
 * -e) 9.499E+00 V

3) Two large parallel conducting plates are separated by 9.6 mm. Equal and opposite surface charges of 7.610E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 71 V?


 * -a) 4.723E-01 mm
 * -b) 5.432E-01 mm
 * -c) 6.246E-01 mm
 * -d) 7.183E-01 mm
 * +e) 8.261E-01 mm

4) Calculate the resistance of a 12-gauge copper wire that is 86 m long and carries a current of 97 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 4.365E-01 &Omega;
 * -b) 4.801E-01 &Omega;
 * -c) 5.282E-01 &Omega;
 * -d) 5.810E-01 &Omega;
 * -e) 6.391E-01 &Omega;

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.662E+01 N&middot;m2/C
 * +b) 4.028E+01 N&middot;m2/C
 * -c) 4.430E+01 N&middot;m2/C
 * -d) 4.873E+01 N&middot;m2/C
 * -e) 5.361E+01 N&middot;m2/C

6) A make-believe metal has a density of 3.470E+03 kg/m3 and an atomic mass of 33.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 6.180E+28 e&minus;/m3
 * -b) 6.798E+28 e&minus;/m3
 * -c) 7.478E+28 e&minus;/m3
 * -d) 8.226E+28 e&minus;/m3
 * -e) 9.049E+28 e&minus;/m3

7) When a 4.21 V battery operates a 2.17 W bulb, how many electrons pass through it each second?


 * -a) 2.659E+18 electrons
 * -b) 2.925E+18 electrons
 * +c) 3.217E+18 electrons
 * -d) 3.539E+18 electrons
 * -e) 3.893E+18 electrons

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.978E+01 N&middot;m2/C
 * -b) 6.576E+01 N&middot;m2/C
 * -c) 7.233E+01 N&middot;m2/C
 * -d) 7.957E+01 N&middot;m2/C
 * -e) 8.752E+01 N&middot;m2/C

9) A battery with a terminal voltage of 14.1 V is connected to a circuit consisting of 2 20.3 &Omega; resistors and one 13.1 &Omega; resistor. What is the voltage drop across the 13.1 &Omega; resistor?


 * -a) 2.843E+00 V
 * -b) 3.127E+00 V
 * +c) 3.440E+00 V
 * -d) 3.784E+00 V
 * -e) 4.162E+00 V

10) In the figure shown C1=19.2 &mu;F, C2=2.86 &mu;F, and C3=5.03 &mu;F. The voltage source provides &epsilon;=9.46 V. What is the charge on C1?


 * -a) 4.809E+01 &mu;C
 * +b) 5.290E+01 &mu;C
 * -c) 5.819E+01 &mu;C
 * -d) 6.401E+01 &mu;C
 * -e) 7.041E+01 &mu;C

Key: I0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=3.0\text{ m}$$ and the surface charge density is $$\sigma=8\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.0\text{ m}$$.


 * -a) 9.459E+00 V/m2
 * +b) 1.040E+01 V/m2
 * -c) 1.145E+01 V/m2
 * -d) 1.259E+01 V/m2
 * -e) 1.385E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.521E+01 N&middot;m2/C
 * -b) 4.973E+01 N&middot;m2/C
 * -c) 5.470E+01 N&middot;m2/C
 * -d) 6.017E+01 N&middot;m2/C
 * +e) 6.619E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is, $$\vec E=4y^{1.4}\hat i +2x^{2.3}\hat j +4y^{2.3}\hat k$$


 * -a) 2.694E+03 V&middot;m
 * -b) 2.963E+03 V&middot;m
 * -c) 3.259E+03 V&middot;m
 * +d) 3.585E+03 V&middot;m
 * -e) 3.944E+03 V&middot;m

4) When a 6.03 V battery operates a 1.56 W bulb, how many electrons pass through it each second?


 * +a) 1.615E+18 electrons
 * -b) 1.776E+18 electrons
 * -c) 1.954E+18 electrons
 * -d) 2.149E+18 electrons
 * -e) 2.364E+18 electrons

5) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.48 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.8 cm, y=2.24 cm)? Note that following the textbook's example, the y-value of the field point at 2.24 cm matches the disance of the positive charge above the x-axis.


 * -a) 5.134E+02 V
 * -b) 5.648E+02 V
 * -c) 6.212E+02 V
 * -d) 6.834E+02 V
 * +e) 7.517E+02 V

6) In the figure shown C1=16.0 &mu;F, C2=2.27 &mu;F, and C3=4.4 &mu;F. The voltage source provides &epsilon;=7.11 V. What is the charge on C1?


 * -a) 2.515E+01 &mu;C
 * -b) 2.766E+01 &mu;C
 * -c) 3.043E+01 &mu;C
 * +d) 3.347E+01 &mu;C
 * -e) 3.682E+01 &mu;C

7) Calculate the drift speed of electrons in a copper wire with a diameter of 5.33 mm carrying a 5.1 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * +a) 1.711E-05 m/s
 * -b) 1.882E-05 m/s
 * -c) 2.070E-05 m/s
 * -d) 2.277E-05 m/s
 * -e) 2.505E-05 m/s

8) Calculate the resistance of a 12-gauge copper wire that is 14 m long and carries a current of 38 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 5.873E-02 &Omega;
 * -b) 6.460E-02 &Omega;
 * +c) 7.106E-02 &Omega;
 * -d) 7.816E-02 &Omega;
 * -e) 8.598E-02 &Omega;

9) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.11 mA and I4=0.746 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 4.275E+00 V
 * -b) 4.703E+00 V
 * +c) 5.173E+00 V
 * -d) 5.691E+00 V
 * -e) 6.260E+00 V

10) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.440E+01 V
 * -b) 1.584E+01 V
 * -c) 1.742E+01 V
 * -d) 1.916E+01 V
 * -e) 2.108E+01 V

Key: I1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 5.3m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 7.793E+01 N&middot;m2/C
 * -b) 8.572E+01 N&middot;m2/C
 * -c) 9.429E+01 N&middot;m2/C
 * -d) 1.037E+02 N&middot;m2/C
 * -e) 1.141E+02 N&middot;m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * -a) 4.286E+03 V&middot;m
 * -b) 4.714E+03 V&middot;m
 * +c) 5.186E+03 V&middot;m
 * -d) 5.704E+03 V&middot;m
 * -e) 6.275E+03 V&middot;m

3) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 k&Omega; and  R2=2.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.34 mA and I4=0.955 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 7.031E+00 V
 * +b) 7.734E+00 V
 * -c) 8.507E+00 V
 * -d) 9.358E+00 V
 * -e) 1.029E+01 V

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.


 * -a) 5.134E-01 V/m2
 * +b) 5.648E-01 V/m2
 * -c) 6.212E-01 V/m2
 * -d) 6.834E-01 V/m2
 * -e) 7.517E-01 V/m2

5) Two sources of emf &epsilon;1=54.9 V, and  &epsilon;2=19.8 V are oriented as shownin the circuit. The resistances are R1=3.93 k&Omega; and  R2=1.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.18 mA and I4=1.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.779E+01 V
 * -b) 1.957E+01 V
 * -c) 2.153E+01 V
 * -d) 2.368E+01 V
 * -e) 2.605E+01 V

6) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.09 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.45 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * -a) 3.814E+02 V
 * -b) 4.195E+02 V
 * +c) 4.615E+02 V
 * -d) 5.077E+02 V
 * -e) 5.584E+02 V

7) Calculate the drift speed of electrons in a copper wire with a diameter of 5.47 mm carrying a 3.48 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.008E-05 m/s
 * +b) 1.108E-05 m/s
 * -c) 1.219E-05 m/s
 * -d) 1.341E-05 m/s
 * -e) 1.475E-05 m/s

8) When a 8.6 V battery operates a 2.76 W bulb, how many electrons pass through it each second?


 * -a) 1.655E+18 electrons
 * -b) 1.821E+18 electrons
 * +c) 2.003E+18 electrons
 * -d) 2.203E+18 electrons
 * -e) 2.424E+18 electrons

9) In the figure shown C1=17.5 &mu;F, C2=2.63 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=15.9 V. What is the charge on C1?


 * -a) 8.197E+01 &mu;C
 * +b) 9.017E+01 &mu;C
 * -c) 9.919E+01 &mu;C
 * -d) 1.091E+02 &mu;C
 * -e) 1.200E+02 &mu;C

10) Calculate the resistance of a 12-gauge copper wire that is 30 m long and carries a current of 31 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 1.384E-01 &Omega;
 * +b) 1.523E-01 &Omega;
 * -c) 1.675E-01 &Omega;
 * -d) 1.842E-01 &Omega;
 * -e) 2.027E-01 &Omega;

Key: I2
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.698E+01 N&middot;m2/C
 * -b) 1.868E+01 N&middot;m2/C
 * -c) 2.055E+01 N&middot;m2/C
 * -d) 2.260E+01 N&middot;m2/C
 * +e) 2.486E+01 N&middot;m2/C

2) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.17 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.08 cm)? Note that following the textbook's example, the y-value of the field point at 2.08 cm matches the disance of the positive charge above the x-axis.


 * -a) 5.261E+02 V
 * -b) 5.787E+02 V
 * +c) 6.365E+02 V
 * -d) 7.002E+02 V
 * -e) 7.702E+02 V

3) Calculate the drift speed of electrons in a copper wire with a diameter of 3.53 mm carrying a 2.8 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.947E-05 m/s
 * +b) 2.141E-05 m/s
 * -c) 2.355E-05 m/s
 * -d) 2.591E-05 m/s
 * -e) 2.850E-05 m/s

4) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * -a) 5.969E+01 &mu;C
 * -b) 6.566E+01 &mu;C
 * +c) 7.222E+01 &mu;C
 * -d) 7.944E+01 &mu;C
 * -e) 8.739E+01 &mu;C

5) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.3\text{ m}$$ and the surface charge density is $$\sigma=5\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.3\text{ m}$$.


 * +a) 1.022E+00 V/m2
 * -b) 1.125E+00 V/m2
 * -c) 1.237E+00 V/m2
 * -d) 1.361E+00 V/m2
 * -e) 1.497E+00 V/m2

6) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.631E-01 &Omega;
 * -b) 2.894E-01 &Omega;
 * -c) 3.184E-01 &Omega;
 * +d) 3.502E-01 &Omega;
 * -e) 3.852E-01 &Omega;

7) Two sources of emf &epsilon;1=28.6 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=3.73 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.27 mA and I4=0.774 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 6.641E+00 V
 * +b) 7.305E+00 V
 * -c) 8.035E+00 V
 * -d) 8.839E+00 V
 * -e) 9.723E+00 V

8) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.440E+01 V
 * -b) 1.584E+01 V
 * -c) 1.742E+01 V
 * -d) 1.916E+01 V
 * -e) 2.108E+01 V

9) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is, $$\vec E=2y^{1.8}\hat i +3x^{1.9}\hat j +5y^{3.2}\hat k$$


 * -a) 9.952E+03 V&middot;m
 * -b) 1.095E+04 V&middot;m
 * -c) 1.204E+04 V&middot;m
 * +d) 1.325E+04 V&middot;m
 * -e) 1.457E+04 V&middot;m

10) When a 7.78 V battery operates a 1.35 W bulb, how many electrons pass through it each second?


 * -a) 7.397E+17 electrons
 * -b) 8.137E+17 electrons
 * -c) 8.951E+17 electrons
 * -d) 9.846E+17 electrons
 * +e) 1.083E+18 electrons

Key: J0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=4e$$?


 * -a) 3.719E+01 degrees
 * -b) 4.091E+01 degrees
 * +c) 4.500E+01 degrees
 * -d) 4.950E+01 degrees
 * -e) 5.445E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.712E+01 N&middot;m2/C
 * -b) 4.083E+01 N&middot;m2/C
 * +c) 4.491E+01 N&middot;m2/C
 * -d) 4.940E+01 N&middot;m2/C
 * -e) 5.434E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.2}\hat i +1x^{3.3}\hat j +5y^{2.4}\hat k$$


 * -a) 7.054E+03 V&middot;m
 * -b) 7.759E+03 V&middot;m
 * -c) 8.535E+03 V&middot;m
 * -d) 9.388E+03 V&middot;m
 * +e) 1.033E+04 V&middot;m

4) Two large parallel conducting plates are separated by 7.81 mm. Equal and opposite surface charges of 7.440E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 80 V?


 * +a) 9.521E-01 mm
 * -b) 1.095E+00 mm
 * -c) 1.259E+00 mm
 * -d) 1.448E+00 mm
 * -e) 1.665E+00 mm

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 16 V.


 * -a) 2.157E+06 m/s
 * +b) 2.372E+06 m/s
 * -c) 2.610E+06 m/s
 * -d) 2.871E+06 m/s
 * -e) 3.158E+06 m/s

6) In the figure shown C1=17.7 &mu;F, C2=2.5 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=12.8 V. What is the charge on C1?


 * -a) 5.066E+01 &mu;C
 * -b) 5.573E+01 &mu;C
 * -c) 6.130E+01 &mu;C
 * +d) 6.743E+01 &mu;C
 * -e) 7.417E+01 &mu;C

7) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?


 * -a) 2.240E+02 A
 * -b) 2.464E+02 A
 * +c) 2.711E+02 A
 * -d) 2.982E+02 A
 * -e) 3.280E+02 A

8) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * -a) $2.791E+01
 * -b) $3.071E+01
 * -c) $3.378E+01
 * -d) $3.715E+01
 * +e) $4.087E+01

9) A battery with a terminal voltage of 6.49 V is connected to a circuit consisting of 3 18.0 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * -a) 7.101E-01 V
 * -b) 7.811E-01 V
 * -c) 8.592E-01 V
 * -d) 9.451E-01 V
 * +e) 1.040E+00 V

10) A given battery has a 13 V emf and an internal resistance of 0.106 &Omega;. If it is connected to a 0.752 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.569E+02 W
 * +b) 1.726E+02 W
 * -c) 1.899E+02 W
 * -d) 2.089E+02 W
 * -e) 2.298E+02 W

Key: J1
1) What is consumer cost to operate one 74&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.119 per kilowatt-hour?


 * -a) $1.976E+01
 * -b) $2.173E+01
 * -c) $2.391E+01
 * -d) $2.630E+01
 * +e) $2.893E+01

2) In the figure shown C1=15.4 &mu;F, C2=2.22 &mu;F, and C3=4.77 &mu;F. The voltage source provides &epsilon;=6.8 V. What is the charge on C1?


 * -a) 2.702E+01 &mu;C
 * -b) 2.972E+01 &mu;C
 * +c) 3.269E+01 &mu;C
 * -d) 3.596E+01 &mu;C
 * -e) 3.956E+01 &mu;C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k$$


 * -a) 8.731E+02 V&middot;m
 * -b) 9.604E+02 V&middot;m
 * -c) 1.056E+03 V&middot;m
 * +d) 1.162E+03 V&middot;m
 * -e) 1.278E+03 V&middot;m

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.898E+01 N&middot;m2/C
 * +b) 7.588E+01 N&middot;m2/C
 * -c) 8.347E+01 N&middot;m2/C
 * -d) 9.181E+01 N&middot;m2/C
 * -e) 1.010E+02 N&middot;m2/C

5) What is the average current involved when a truck battery sets in motion 779 C of charge in 3.96 s while starting an engine?


 * -a) 1.626E+02 A
 * -b) 1.788E+02 A
 * +c) 1.967E+02 A
 * -d) 2.164E+02 A
 * -e) 2.380E+02 A

6) A battery with a terminal voltage of 8.41 V is connected to a circuit consisting of 3 16.1 &Omega; resistors and one 10.9 &Omega; resistor. What is the voltage drop across the 10.9 &Omega; resistor?


 * -a) 1.058E+00 V
 * -b) 1.163E+00 V
 * -c) 1.280E+00 V
 * -d) 1.408E+00 V
 * +e) 1.548E+00 V

7) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * -a) 4.766E+01 degrees
 * -b) 5.243E+01 degrees
 * -c) 5.767E+01 degrees
 * +d) 6.343E+01 degrees
 * -e) 6.978E+01 degrees

8) Two large parallel conducting plates are separated by 7.83 mm. Equal and opposite surface charges of 7.530E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 86 V?


 * -a) 8.793E-01 mm
 * +b) 1.011E+00 mm
 * -c) 1.163E+00 mm
 * -d) 1.337E+00 mm
 * -e) 1.538E+00 mm

9) A given battery has a 11 V emf and an internal resistance of 0.0998 &Omega;. If it is connected to a 0.417 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.419E+02 W
 * -b) 1.561E+02 W
 * -c) 1.717E+02 W
 * +d) 1.889E+02 W
 * -e) 2.078E+02 W

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 6 V.


 * -a) 1.091E+06 m/s
 * -b) 1.201E+06 m/s
 * -c) 1.321E+06 m/s
 * +d) 1.453E+06 m/s
 * -e) 1.598E+06 m/s

Key: J2
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.2}\hat i +1x^{3.0}\hat j +2y^{1.7}\hat k$$


 * -a) 8.545E+01 V&middot;m
 * -b) 9.400E+01 V&middot;m
 * -c) 1.034E+02 V&middot;m
 * -d) 1.137E+02 V&middot;m
 * +e) 1.251E+02 V&middot;m

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.712E+01 N&middot;m2/C
 * -b) 4.083E+01 N&middot;m2/C
 * +c) 4.491E+01 N&middot;m2/C
 * -d) 4.940E+01 N&middot;m2/C
 * -e) 5.434E+01 N&middot;m2/C

3) What is consumer cost to operate one 73&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.113 per kilowatt-hour?


 * +a) $3.312E+01
 * -b) $3.643E+01
 * -c) $4.007E+01
 * -d) $4.408E+01
 * -e) $4.849E+01

4) A given battery has a 15 V emf and an internal resistance of 0.0536 &Omega;. If it is connected to a 0.64 &Omega; resistor what is the power dissipated by that load?


 * -a) 2.721E+02 W
 * +b) 2.993E+02 W
 * -c) 3.293E+02 W
 * -d) 3.622E+02 W
 * -e) 3.984E+02 W

5) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 &Omega; resistors and one 12.1 &Omega; resistor. What is the voltage drop across the 12.1 &Omega; resistor?


 * -a) 1.333E+00 V
 * -b) 1.466E+00 V
 * -c) 1.612E+00 V
 * -d) 1.774E+00 V
 * +e) 1.951E+00 V

6) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * -a) 5.969E+01 &mu;C
 * -b) 6.566E+01 &mu;C
 * +c) 7.222E+01 &mu;C
 * -d) 7.944E+01 &mu;C
 * -e) 8.739E+01 &mu;C

7) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?


 * -a) 6.525E-01 mm
 * +b) 7.504E-01 mm
 * -c) 8.629E-01 mm
 * -d) 9.923E-01 mm
 * -e) 1.141E+00 mm

8) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=5e$$?


 * -a) 5.272E+01 degrees
 * +b) 5.799E+01 degrees
 * -c) 6.379E+01 degrees
 * -d) 7.017E+01 degrees
 * -e) 7.719E+01 degrees

9) Calculate the final speed of a free electron accelerated from rest through a potential difference of 56 V.


 * -a) 3.031E+06 m/s
 * -b) 3.335E+06 m/s
 * -c) 3.668E+06 m/s
 * -d) 4.035E+06 m/s
 * +e) 4.438E+06 m/s

10) What is the average current involved when a truck battery sets in motion 779 C of charge in 3.96 s while starting an engine?


 * -a) 1.626E+02 A
 * -b) 1.788E+02 A
 * +c) 1.967E+02 A
 * -d) 2.164E+02 A
 * -e) 2.380E+02 A

Key: K0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * -a) 8.690E+00 V/m2
 * -b) 9.559E+00 V/m2
 * +c) 1.051E+01 V/m2
 * -d) 1.157E+01 V/m2
 * -e) 1.272E+01 V/m2

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * -a) 4.286E+03 V&middot;m
 * -b) 4.714E+03 V&middot;m
 * +c) 5.186E+03 V&middot;m
 * -d) 5.704E+03 V&middot;m
 * -e) 6.275E+03 V&middot;m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.740E+01 N&middot;m2/C
 * -b) 1.914E+01 N&middot;m2/C
 * -c) 2.106E+01 N&middot;m2/C
 * -d) 2.316E+01 N&middot;m2/C
 * +e) 2.548E+01 N&middot;m2/C

4) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * +a) 8.672E+02 V
 * -b) 9.539E+02 V
 * -c) 1.049E+03 V
 * -d) 1.154E+03 V
 * -e) 1.270E+03 V

5) A Van de Graff generator has a 141 cm diameter metal sphere that produces 280 kV near its surface. What  is the excess charge on the sphere?


 * -a) 1.500E+01 &mu;C
 * -b) 1.650E+01 &mu;C
 * -c) 1.815E+01 &mu;C
 * -d) 1.997E+01 &mu;C
 * +e) 2.196E+01 &mu;C

6) In the figure shown C1=17.5 &mu;F, C2=2.63 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=15.9 V. What is the charge on C1?


 * -a) 8.197E+01 &mu;C
 * +b) 9.017E+01 &mu;C
 * -c) 9.919E+01 &mu;C
 * -d) 1.091E+02 &mu;C
 * -e) 1.200E+02 &mu;C

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.58 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 5.520E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 349 &deg;C?


 * -a) 9.526E+00 &Omega;
 * +b) 1.000E+01 &Omega;
 * -c) 1.050E+01 &Omega;
 * -d) 1.103E+01 &Omega;
 * -e) 1.158E+01 &Omega;

8) Calculate the drift speed of electrons in a copper wire with a diameter of 4.38 mm carrying a 5.79 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 2.615E-05 m/s
 * +b) 2.876E-05 m/s
 * -c) 3.164E-05 m/s
 * -d) 3.480E-05 m/s
 * -e) 3.828E-05 m/s

9) The resistances in the figure shown are R1= 1.18 &Omega;, R2= 0.878 &Omega;, and R2= 2.11 &Omega;. V1 and V3 are text 0.637 V and 3.51 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.547 V. What is the absolute value of the current through R1?


 * -a) 1.701E-01 A
 * +b) 1.871E-01 A
 * -c) 2.058E-01 A
 * -d) 2.264E-01 A
 * -e) 2.490E-01 A

10) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 k&Omega; and  R2=2.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.34 mA and I4=0.955 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 7.031E+00 V
 * +b) 7.734E+00 V
 * -c) 8.507E+00 V
 * -d) 9.358E+00 V
 * -e) 1.029E+01 V

Key: K1
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.5 m if a=0.67 m, b=2.4 m.  The total charge on the rod is 9 nC.


 * -a) 5.465E+00 V/m2
 * -b) 6.012E+00 V/m2
 * -c) 6.613E+00 V/m2
 * +d) 7.274E+00 V/m2
 * -e) 8.002E+00 V/m2

2) In the figure shown C1=18.0 &mu;F, C2=2.88 &mu;F, and C3=5.34 &mu;F. The voltage source provides &epsilon;=11.9 V. What is the charge on C1?


 * -a) 5.045E+01 &mu;C
 * -b) 5.550E+01 &mu;C
 * -c) 6.105E+01 &mu;C
 * +d) 6.715E+01 &mu;C
 * -e) 7.387E+01 &mu;C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k$$


 * -a) 1.997E+03 V&middot;m
 * +b) 2.197E+03 V&middot;m
 * -c) 2.417E+03 V&middot;m
 * -d) 2.659E+03 V&middot;m
 * -e) 2.924E+03 V&middot;m

4) Calculate the drift speed of electrons in a copper wire with a diameter of 5.46 mm carrying a 8.19 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 2.380E-05 m/s
 * +b) 2.618E-05 m/s
 * -c) 2.880E-05 m/s
 * -d) 3.168E-05 m/s
 * -e) 3.485E-05 m/s

5) Two sources of emf &epsilon;1=26.8 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.2 k&Omega; and  R2=2.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.29 mA and I4=0.464 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 3.436E+00 V
 * -b) 3.779E+00 V
 * -c) 4.157E+00 V
 * -d) 4.573E+00 V
 * +e) 5.030E+00 V

6) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.75 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 4.300E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 423 &deg;C?


 * +a) 1.018E+01 &Omega;
 * -b) 1.069E+01 &Omega;
 * -c) 1.123E+01 &Omega;
 * -d) 1.179E+01 &Omega;
 * -e) 1.238E+01 &Omega;

7) The resistances in the figure shown are R1= 2.42 &Omega;, R2= 1.09 &Omega;, and R2= 3.89 &Omega;. V1 and V3 are text 0.677 V and 1.86 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.745 V. What is the absolute value of the current through R1?


 * -a) 2.089E-01 A
 * -b) 2.298E-01 A
 * +c) 2.528E-01 A
 * -d) 2.781E-01 A
 * -e) 3.059E-01 A

8) A Van de Graff generator has a 149 cm diameter metal sphere that produces 172 kV near its surface. What  is the excess charge on the sphere?


 * -a) 1.071E+01 &mu;C
 * -b) 1.178E+01 &mu;C
 * -c) 1.296E+01 &mu;C
 * +d) 1.426E+01 &mu;C
 * -e) 1.568E+01 &mu;C

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.740E+01 N&middot;m2/C
 * -b) 1.914E+01 N&middot;m2/C
 * -c) 2.106E+01 N&middot;m2/C
 * -d) 2.316E+01 N&middot;m2/C
 * +e) 2.548E+01 N&middot;m2/C

10) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.3 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.86 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * -a) 6.325E+02 V
 * +b) 6.957E+02 V
 * -c) 7.653E+02 V
 * -d) 8.418E+02 V
 * -e) 9.260E+02 V

Key: K2
1) A Van de Graff generator has a 76 cm diameter metal sphere that produces 193 kV near its surface. What  is the excess charge on the sphere?


 * -a) 7.418E+00 &mu;C
 * +b) 8.160E+00 &mu;C
 * -c) 8.976E+00 &mu;C
 * -d) 9.874E+00 &mu;C
 * -e) 1.086E+01 &mu;C

2) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.48 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.69 cm, y=2.24 cm)? Note that following the textbook's example, the y-value of the field point at 2.24 cm matches the disance of the positive charge above the x-axis.


 * -a) 5.645E+02 V
 * +b) 6.210E+02 V
 * -c) 6.831E+02 V
 * -d) 7.514E+02 V
 * -e) 8.266E+02 V

3) Two sources of emf &epsilon;1=38.9 V, and  &epsilon;2=14.4 V are oriented as shownin the circuit. The resistances are R1=4.33 k&Omega; and  R2=1.65 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.59 mA and I4=1.07 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 9.142E+00 V
 * -b) 1.006E+01 V
 * +c) 1.106E+01 V
 * -d) 1.217E+01 V
 * -e) 1.338E+01 V

4) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * -a) 5.969E+01 &mu;C
 * -b) 6.566E+01 &mu;C
 * +c) 7.222E+01 &mu;C
 * -d) 7.944E+01 &mu;C
 * -e) 8.739E+01 &mu;C

5) Calculate the drift speed of electrons in a copper wire with a diameter of 5.19 mm carrying a 18.2 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 5.321E-05 m/s
 * -b) 5.853E-05 m/s
 * +c) 6.439E-05 m/s
 * -d) 7.083E-05 m/s
 * -e) 7.791E-05 m/s

6) The resistances in the figure shown are R1= 2.04 &Omega;, R2= 1.19 &Omega;, and R2= 2.5 &Omega;. V1 and V3 are text 0.507 V and 3.07 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.602 V. What is the absolute value of the current through R1?


 * +a) 1.401E-01 A
 * -b) 1.542E-01 A
 * -c) 1.696E-01 A
 * -d) 1.865E-01 A
 * -e) 2.052E-01 A

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.0}\hat i +3x^{2.0}\hat j +3y^{3.0}\hat k$$


 * -a) 4.820E+03 V&middot;m
 * -b) 5.302E+03 V&middot;m
 * +c) 5.832E+03 V&middot;m
 * -d) 6.415E+03 V&middot;m
 * -e) 7.057E+03 V&middot;m

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.95 &Omega; at a temperature of 96&deg;C and that the temperature coefficient of expansion is 4.400E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 469 &deg;C?


 * -a) 4.449E+00 &Omega;
 * -b) 4.672E+00 &Omega;
 * -c) 4.905E+00 &Omega;
 * +d) 5.150E+00 &Omega;
 * -e) 5.408E+00 &Omega;

9) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=1.0 m, b=2.0 m.  The total charge on the rod is 3 nC.


 * -a) 1.665E+00 V/m2
 * -b) 1.831E+00 V/m2
 * -c) 2.014E+00 V/m2
 * +d) 2.216E+00 V/m2
 * -e) 2.437E+00 V/m2

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 6.192E+01 N&middot;m2/C
 * -b) 6.811E+01 N&middot;m2/C
 * -c) 7.492E+01 N&middot;m2/C
 * -d) 8.242E+01 N&middot;m2/C
 * -e) 9.066E+01 N&middot;m2/C

Key: L0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.


 * -a) 8.690E+00 V/m2
 * -b) 9.559E+00 V/m2
 * +c) 1.051E+01 V/m2
 * -d) 1.157E+01 V/m2
 * -e) 1.272E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.388E+01 N&middot;m2/C
 * +b) 1.526E+01 N&middot;m2/C
 * -c) 1.679E+01 N&middot;m2/C
 * -d) 1.847E+01 N&middot;m2/C
 * -e) 2.032E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * +a) 3.429E+03 V&middot;m
 * -b) 3.771E+03 V&middot;m
 * -c) 4.149E+03 V&middot;m
 * -d) 4.564E+03 V&middot;m
 * -e) 5.020E+03 V&middot;m

4) If a 23 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=66 V is x2 + y2 + z2 = R2, where R=


 * -a) 2.139E+00 m
 * -b) 2.353E+00 m
 * -c) 2.588E+00 m
 * -d) 2.847E+00 m
 * +e) 3.132E+00 m

5) A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.


 * -a) 2.727E+02 V
 * -b) 2.999E+02 V
 * -c) 3.299E+02 V
 * +d) 3.629E+02 V
 * -e) 3.992E+02 V

6) In the figure shown C1=16.9 &mu;F, C2=2.3 &mu;F, and C3=4.67 &mu;F. The voltage source provides &epsilon;=13.4 V. What is the charge on C1?


 * -a) 6.011E+01 &mu;C
 * +b) 6.613E+01 &mu;C
 * -c) 7.274E+01 &mu;C
 * -d) 8.001E+01 &mu;C
 * -e) 8.801E+01 &mu;C

7) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?


 * -a) 2.240E+02 A
 * -b) 2.464E+02 A
 * +c) 2.711E+02 A
 * -d) 2.982E+02 A
 * -e) 3.280E+02 A

8) Calculate the drift speed of electrons in a copper wire with a diameter of 5.82 mm carrying a 9.11 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.926E-05 m/s
 * -b) 2.118E-05 m/s
 * -c) 2.330E-05 m/s
 * +d) 2.563E-05 m/s
 * -e) 2.819E-05 m/s

9) In the circuit shown V=17.8 V, R1=2.27 &Omega;, R2=6.79 &Omega;, and R3=15.1 &Omega;. What is the power dissipated by R2?


 * -a) 1.446E+01 W
 * -b) 1.591E+01 W
 * -c) 1.750E+01 W
 * -d) 1.925E+01 W
 * +e) 2.117E+01 W

10) Two sources of emf &epsilon;1=30.5 V, and  &epsilon;2=12.0 V are oriented as shownin the circuit. The resistances are R1=3.79 k&Omega; and  R2=1.86 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.07 mA and I4=0.73 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 2.281E+00 mA
 * -b) 2.509E+00 mA
 * -c) 2.760E+00 mA
 * -d) 3.036E+00 mA
 * +e) 3.340E+00 mA

Key: L1
1) In the circuit shown V=15.4 V, R1=2.77 &Omega;, R2=6.07 &Omega;, and R3=14.5 &Omega;. What is the power dissipated by R2?


 * -a) 1.190E+01 W
 * -b) 1.309E+01 W
 * +c) 1.440E+01 W
 * -d) 1.584E+01 W
 * -e) 1.742E+01 W

2) Calculate the drift speed of electrons in a copper wire with a diameter of 4.79 mm carrying a 10.9 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 3.401E-05 m/s
 * -b) 3.741E-05 m/s
 * -c) 4.116E-05 m/s
 * +d) 4.527E-05 m/s
 * -e) 4.980E-05 m/s

3) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * +a) 8.672E+02 V
 * -b) 9.539E+02 V
 * -c) 1.049E+03 V
 * -d) 1.154E+03 V
 * -e) 1.270E+03 V

4) If a 23 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=66 V is x2 + y2 + z2 = R2, where R=


 * -a) 2.139E+00 m
 * -b) 2.353E+00 m
 * -c) 2.588E+00 m
 * -d) 2.847E+00 m
 * +e) 3.132E+00 m

5) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * -a) 1.969E+02 V&middot;m
 * -b) 2.166E+02 V&middot;m
 * -c) 2.383E+02 V&middot;m
 * -d) 2.621E+02 V&middot;m
 * +e) 2.883E+02 V&middot;m

6) What is the average current involved when a truck battery sets in motion 682 C of charge in 5.29 s while starting an engine?


 * -a) 1.065E+02 A
 * -b) 1.172E+02 A
 * +c) 1.289E+02 A
 * -d) 1.418E+02 A
 * -e) 1.560E+02 A

7) Two sources of emf &epsilon;1=44.4 V, and  &epsilon;2=16.8 V are oriented as shownin the circuit. The resistances are R1=4.58 k&Omega; and  R2=1.2 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=8.43 mA and I4=1.46 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 6.970E+00 mA
 * -b) 7.667E+00 mA
 * -c) 8.434E+00 mA
 * -d) 9.277E+00 mA
 * -e) 1.020E+01 mA

8) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=0.76 m, b=1.7 m.  The total charge on the rod is 8 nC.


 * -a) 1.399E+01 V/m2
 * +b) 1.539E+01 V/m2
 * -c) 1.693E+01 V/m2
 * -d) 1.862E+01 V/m2
 * -e) 2.049E+01 V/m2

9) In the figure shown C1=17.1 &mu;F, C2=2.87 &mu;F, and C3=4.74 &mu;F. The voltage source provides &epsilon;=6.63 V. What is the charge on C1?


 * -a) 2.385E+01 &mu;C
 * -b) 2.623E+01 &mu;C
 * -c) 2.886E+01 &mu;C
 * -d) 3.174E+01 &mu;C
 * +e) 3.492E+01 &mu;C

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.125E+01 N&middot;m2/C
 * -b) 4.537E+01 N&middot;m2/C
 * -c) 4.991E+01 N&middot;m2/C
 * +d) 5.490E+01 N&middot;m2/C
 * -e) 6.039E+01 N&middot;m2/C

Key: L2
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.901E+01 N&middot;m2/C
 * -b) 3.192E+01 N&middot;m2/C
 * -c) 3.511E+01 N&middot;m2/C
 * -d) 3.862E+01 N&middot;m2/C
 * +e) 4.248E+01 N&middot;m2/C

2) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.96 m if a=0.95 m, b=1.8 m.  The total charge on the rod is 7 nC.


 * -a) 3.385E+00 V/m2
 * -b) 3.724E+00 V/m2
 * -c) 4.096E+00 V/m2
 * +d) 4.506E+00 V/m2
 * -e) 4.957E+00 V/m2

3) Calculate the drift speed of electrons in a copper wire with a diameter of 2.72 mm carrying a 16.2 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * +a) 2.087E-04 m/s
 * -b) 2.295E-04 m/s
 * -c) 2.525E-04 m/s
 * -d) 2.777E-04 m/s
 * -e) 3.055E-04 m/s

4) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * +a) 8.672E+02 V
 * -b) 9.539E+02 V
 * -c) 1.049E+03 V
 * -d) 1.154E+03 V
 * -e) 1.270E+03 V

5) Two sources of emf &epsilon;1=18.2 V, and  &epsilon;2=6.59 V are oriented as shownin the circuit. The resistances are R1=5.47 k&Omega; and  R2=2.81 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.64 mA and I4=0.341 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 1.299E+00 mA
 * -b) 1.429E+00 mA
 * -c) 1.572E+00 mA
 * -d) 1.729E+00 mA
 * -e) 1.902E+00 mA

6) What is the average current involved when a truck battery sets in motion 760 C of charge in 5.35 s while starting an engine?


 * -a) 1.291E+02 A
 * +b) 1.421E+02 A
 * -c) 1.563E+02 A
 * -d) 1.719E+02 A
 * -e) 1.891E+02 A

7) In the circuit shown V=19.6 V, R1=1.45 &Omega;, R2=7.85 &Omega;, and R3=15.8 &Omega;. What is the power dissipated by R2?


 * -a) 2.730E+01 W
 * +b) 3.003E+01 W
 * -c) 3.304E+01 W
 * -d) 3.634E+01 W
 * -e) 3.998E+01 W

8) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.7}\hat i +1x^{2.5}\hat j +3y^{3.3}\hat k$$


 * -a) 1.128E+04 V&middot;m
 * -b) 1.241E+04 V&middot;m
 * -c) 1.365E+04 V&middot;m
 * +d) 1.502E+04 V&middot;m
 * -e) 1.652E+04 V&middot;m

9) In the figure shown C1=18.0 &mu;F, C2=2.88 &mu;F, and C3=5.34 &mu;F. The voltage source provides &epsilon;=11.9 V. What is the charge on C1?


 * -a) 5.045E+01 &mu;C
 * -b) 5.550E+01 &mu;C
 * -c) 6.105E+01 &mu;C
 * +d) 6.715E+01 &mu;C
 * -e) 7.387E+01 &mu;C

10) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=76 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.422E+00 m
 * -b) 1.564E+00 m
 * -c) 1.720E+00 m
 * +d) 1.892E+00 m
 * -e) 2.081E+00 m

Key: M0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=4e$$?


 * -a) 5.914E+01 degrees
 * -b) 6.506E+01 degrees
 * +c) 7.157E+01 degrees
 * -d) 7.872E+01 degrees
 * -e) 8.659E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.978E+01 N&middot;m2/C
 * -b) 6.576E+01 N&middot;m2/C
 * -c) 7.233E+01 N&middot;m2/C
 * -d) 7.957E+01 N&middot;m2/C
 * -e) 8.752E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.777E+01 N&middot;m2/C
 * -b) 5.254E+01 N&middot;m2/C
 * -c) 5.780E+01 N&middot;m2/C
 * +d) 6.358E+01 N&middot;m2/C
 * -e) 6.993E+01 N&middot;m2/C

4) Assume that a 26 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 42&deg;).


 * -a) 7.263E+02 V
 * +b) 7.989E+02 V
 * -c) 8.788E+02 V
 * -d) 9.667E+02 V
 * -e) 1.063E+03 V

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 30 V.


 * -a) 2.441E+06 m/s
 * -b) 2.685E+06 m/s
 * -c) 2.953E+06 m/s
 * +d) 3.249E+06 m/s
 * -e) 3.573E+06 m/s

6) An empty parallel-plate capacitor with metal plates has an area of 2.42 m2, separated by 1.33 mm. How much charge does it store if the voltage is 1.130E+03 V?


 * -a) 1.368E+01 &mu;C
 * -b) 1.505E+01 &mu;C
 * -c) 1.655E+01 &mu;C
 * +d) 1.820E+01 &mu;C
 * -e) 2.003E+01 &mu;C

7) What is consumer cost to operate one 56&minus;W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.13 per kilowatt-hour?


 * -a) $1.198E+01
 * -b) $1.318E+01
 * -c) $1.449E+01
 * +d) $1.594E+01
 * -e) $1.754E+01

8) What is the average current involved when a truck battery sets in motion 669 C of charge in 4.3 s while starting an engine?


 * -a) 1.063E+02 A
 * -b) 1.169E+02 A
 * -c) 1.286E+02 A
 * -d) 1.414E+02 A
 * +e) 1.556E+02 A

9) The resistances in the figure shown are R1= 2.34 &Omega;, R2= 1.34 &Omega;, and R2= 2.94 &Omega;. V1 and V3 are text 0.609 V and 1.68 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.541 V. What is the absolute value of the current through R1?


 * -a) 1.464E-01 A
 * +b) 1.610E-01 A
 * -c) 1.772E-01 A
 * -d) 1.949E-01 A
 * -e) 2.144E-01 A

10) Two sources of emf &epsilon;1=24.4 V, and  &epsilon;2=6.73 V are oriented as shownin the circuit. The resistances are R1=5.7 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.36 mA and I4=0.418 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 5.418E+00 V
 * -b) 5.960E+00 V
 * -c) 6.556E+00 V
 * -d) 7.212E+00 V
 * +e) 7.933E+00 V

Key: M1
1) Assume that a 3 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (6 cm, 0&deg;) and  P2 is at (12 cm, 32&deg;).


 * -a) 1.857E+02 V
 * -b) 2.043E+02 V
 * +c) 2.247E+02 V
 * -d) 2.472E+02 V
 * -e) 2.719E+02 V

2) Two sources of emf &epsilon;1=14.3 V, and  &epsilon;2=5.6 V are oriented as shownin the circuit. The resistances are R1=5.31 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.12 mA and I4=0.284 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 3.416E+00 V
 * -b) 3.757E+00 V
 * -c) 4.133E+00 V
 * +d) 4.546E+00 V
 * -e) 5.001E+00 V

3) The resistances in the figure shown are R1= 2.41 &Omega;, R2= 1.74 &Omega;, and R2= 3.35 &Omega;. V1 and V3 are text 0.508 V and 1.36 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.595 V. What is the absolute value of the current through R1?


 * -a) 1.203E-01 A
 * -b) 1.324E-01 A
 * +c) 1.456E-01 A
 * -d) 1.602E-01 A
 * -e) 1.762E-01 A

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * -a) 5.569E+01 degrees
 * -b) 6.125E+01 degrees
 * +c) 6.738E+01 degrees
 * -d) 7.412E+01 degrees
 * -e) 8.153E+01 degrees

5) What is the average current involved when a truck battery sets in motion 728 C of charge in 3.94 s while starting an engine?


 * +a) 1.848E+02 A
 * -b) 2.032E+02 A
 * -c) 2.236E+02 A
 * -d) 2.459E+02 A
 * -e) 2.705E+02 A

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 3.222E+01 N&middot;m2/C
 * -b) 3.544E+01 N&middot;m2/C
 * -c) 3.899E+01 N&middot;m2/C
 * -d) 4.289E+01 N&middot;m2/C
 * -e) 4.718E+01 N&middot;m2/C

7) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * -a) $2.791E+01
 * -b) $3.071E+01
 * -c) $3.378E+01
 * -d) $3.715E+01
 * +e) $4.087E+01

8) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * +a) 5.102E+06 m/s
 * -b) 5.612E+06 m/s
 * -c) 6.173E+06 m/s
 * -d) 6.791E+06 m/s
 * -e) 7.470E+06 m/s

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.730E+01 N&middot;m2/C
 * +b) 5.203E+01 N&middot;m2/C
 * -c) 5.723E+01 N&middot;m2/C
 * -d) 6.295E+01 N&middot;m2/C
 * -e) 6.925E+01 N&middot;m2/C

10) An empty parallel-plate capacitor with metal plates has an area of 1.81 m2, separated by 1.26 mm. How much charge does it store if the voltage is 4.610E+03 V?


 * -a) 4.005E+01 &mu;C
 * -b) 4.405E+01 &mu;C
 * -c) 4.846E+01 &mu;C
 * -d) 5.330E+01 &mu;C
 * +e) 5.864E+01 &mu;C

Key: M2
1) What is the average current involved when a truck battery sets in motion 618 C of charge in 2.28 s while starting an engine?


 * -a) 2.240E+02 A
 * -b) 2.464E+02 A
 * +c) 2.711E+02 A
 * -d) 2.982E+02 A
 * -e) 3.280E+02 A

2) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * -a) 4.638E+06 m/s
 * +b) 5.102E+06 m/s
 * -c) 5.612E+06 m/s
 * -d) 6.173E+06 m/s
 * -e) 6.791E+06 m/s

3) What is consumer cost to operate one 87&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.117 per kilowatt-hour?


 * -a) $2.791E+01
 * -b) $3.071E+01
 * -c) $3.378E+01
 * -d) $3.715E+01
 * +e) $4.087E+01

4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 5.989E+01 N&middot;m2/C
 * -b) 6.588E+01 N&middot;m2/C
 * -c) 7.247E+01 N&middot;m2/C
 * +d) 7.971E+01 N&middot;m2/C
 * -e) 8.769E+01 N&middot;m2/C

5) Assume that a 26 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (9 cm, 0&deg;) and  P2 is at (13 cm, 42&deg;).


 * -a) 7.263E+02 V
 * +b) 7.989E+02 V
 * -c) 8.788E+02 V
 * -d) 9.667E+02 V
 * -e) 1.063E+03 V

6) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * -a) 5.569E+01 degrees
 * -b) 6.125E+01 degrees
 * +c) 6.738E+01 degrees
 * -d) 7.412E+01 degrees
 * -e) 8.153E+01 degrees

7) Two sources of emf &epsilon;1=34.7 V, and  &epsilon;2=13.9 V are oriented as shownin the circuit. The resistances are R1=3.68 k&Omega; and  R2=1.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.68 mA and I4=0.933 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 9.286E+00 V
 * -b) 1.021E+01 V
 * -c) 1.124E+01 V
 * +d) 1.236E+01 V
 * -e) 1.360E+01 V

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.614E+01 N&middot;m2/C
 * +b) 7.275E+01 N&middot;m2/C
 * -c) 8.003E+01 N&middot;m2/C
 * -d) 8.803E+01 N&middot;m2/C
 * -e) 9.683E+01 N&middot;m2/C

9) The resistances in the figure shown are R1= 2.04 &Omega;, R2= 1.19 &Omega;, and R2= 2.5 &Omega;. V1 and V3 are text 0.507 V and 3.07 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.602 V. What is the absolute value of the current through R1?


 * +a) 1.401E-01 A
 * -b) 1.542E-01 A
 * -c) 1.696E-01 A
 * -d) 1.865E-01 A
 * -e) 2.052E-01 A

10) An empty parallel-plate capacitor with metal plates has an area of 1.94 m2, separated by 1.27 mm. How much charge does it store if the voltage is 8.780E+03 V?


 * -a) 1.080E+02 &mu;C
 * +b) 1.188E+02 &mu;C
 * -c) 1.306E+02 &mu;C
 * -d) 1.437E+02 &mu;C
 * -e) 1.581E+02 &mu;C

Key: N0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=5e$$?


 * -a) 2.248E-14 N
 * -b) 2.473E-14 N
 * +c) 2.721E-14 N
 * -d) 2.993E-14 N
 * -e) 3.292E-14 N

2) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?


 * -a) 2.274E+02 N/C
 * -b) 2.501E+02 N/C
 * +c) 2.751E+02 N/C
 * -d) 3.026E+02 N/C
 * -e) 3.329E+02 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.186E+01 N&middot;m2/C
 * -b) 2.404E+01 N&middot;m2/C
 * +c) 2.645E+01 N&middot;m2/C
 * -d) 2.909E+01 N&middot;m2/C
 * -e) 3.200E+01 N&middot;m2/C

4) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=7 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 3.116E+01 J
 * -b) 3.427E+01 J
 * -c) 3.770E+01 J
 * -d) 4.147E+01 J
 * +e) 4.562E+01 J

5) An electron gun has parallel plates separated by 2.68 cm and gives electrons 29 keV of energy. What force would the field between the plates exert on a 0.496 &mu;C charge that gets between the plates?


 * +a) 5.367E-01 N
 * -b) 5.904E-01 N
 * -c) 6.494E-01 N
 * -d) 7.144E-01 N
 * -e) 7.858E-01 N

6) An empty parallel-plate capacitor with metal plates has an area of 2.1 m2, separated by 1.13 mm. How much charge does it store if the voltage is 1.680E+03 V?


 * +a) 2.764E+01 &mu;C
 * -b) 3.041E+01 &mu;C
 * -c) 3.345E+01 &mu;C
 * -d) 3.679E+01 &mu;C
 * -e) 4.047E+01 &mu;C

7) What is consumer cost to operate one 79&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.142 per kilowatt-hour?


 * -a) $2.517E+01
 * -b) $2.769E+01
 * -c) $3.046E+01
 * -d) $3.350E+01
 * +e) $3.685E+01

8) Calculate the resistance of a 12-gauge copper wire that is 42 m long and carries a current of 63 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 1.938E-01 &Omega;
 * +b) 2.132E-01 &Omega;
 * -c) 2.345E-01 &Omega;
 * -d) 2.579E-01 &Omega;
 * -e) 2.837E-01 &Omega;

9) A battery with a terminal voltage of 13.2 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.3 &Omega; resistor. What is the voltage drop across the 10.3 &Omega; resistor?


 * -a) 1.958E+00 V
 * -b) 2.153E+00 V
 * +c) 2.369E+00 V
 * -d) 2.606E+00 V
 * -e) 2.866E+00 V

10) Three resistors, R1 = 1.82 &Omega;, and R2 = R2 = 4.14 &Omega;, are connected in parallel to a 5.65 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * +a) 1.754E+01 W
 * -b) 1.929E+01 W
 * -c) 2.122E+01 W
 * -d) 2.335E+01 W
 * -e) 2.568E+01 W

Key: N1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.924E+01 N&middot;m2/C
 * -b) 4.316E+01 N&middot;m2/C
 * -c) 4.748E+01 N&middot;m2/C
 * +d) 5.222E+01 N&middot;m2/C
 * -e) 5.745E+01 N&middot;m2/C

2) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=3 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?


 * +a) 1.457E+02 N/C
 * -b) 1.603E+02 N/C
 * -c) 1.763E+02 N/C
 * -d) 1.939E+02 N/C
 * -e) 2.133E+02 N/C

3) An electron gun has parallel plates separated by 5.31 cm and gives electrons 41 keV of energy. What force would the field between the plates exert on a 0.368 &mu;C charge that gets between the plates?


 * -a) 2.348E-01 N
 * -b) 2.583E-01 N
 * +c) 2.841E-01 N
 * -d) 3.126E-01 N
 * -e) 3.438E-01 N

4) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * -a) 1.677E+00 V
 * -b) 1.844E+00 V
 * +c) 2.029E+00 V
 * -d) 2.231E+00 V
 * -e) 2.455E+00 V

5) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?


 * -a) 5.243E-14 N
 * +b) 5.768E-14 N
 * -c) 6.344E-14 N
 * -d) 6.979E-14 N
 * -e) 7.677E-14 N

6) An empty parallel-plate capacitor with metal plates has an area of 2.02 m2, separated by 1.44 mm. How much charge does it store if the voltage is 2.170E+03 V?


 * -a) 2.450E+01 &mu;C
 * +b) 2.695E+01 &mu;C
 * -c) 2.965E+01 &mu;C
 * -d) 3.261E+01 &mu;C
 * -e) 3.587E+01 &mu;C

7) Three resistors, R1 = 1.43 &Omega;, and R2 = R2 = 3.25 &Omega;, are connected in parallel to a 9.03 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 5.184E+01 W
 * +b) 5.702E+01 W
 * -c) 6.272E+01 W
 * -d) 6.900E+01 W
 * -e) 7.590E+01 W

8) What is consumer cost to operate one 76&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.144 per kilowatt-hour?


 * +a) $3.595E+01
 * -b) $3.955E+01
 * -c) $4.350E+01
 * -d) $4.785E+01
 * -e) $5.264E+01

9) Calculate the resistance of a 12-gauge copper wire that is 19 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 7.970E-02 &Omega;
 * -b) 8.767E-02 &Omega;
 * +c) 9.644E-02 &Omega;
 * -d) 1.061E-01 &Omega;
 * -e) 1.167E-01 &Omega;

10) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=6 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 2.343E+01 J
 * +b) 2.577E+01 J
 * -c) 2.835E+01 J
 * -d) 3.118E+01 J
 * -e) 3.430E+01 J

Key: N2
1) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?


 * +a) 2.285E+01 N/C
 * -b) 2.514E+01 N/C
 * -c) 2.765E+01 N/C
 * -d) 3.042E+01 N/C
 * -e) 3.346E+01 N/C

2) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?


 * -a) 3.876E-14 N
 * -b) 4.263E-14 N
 * -c) 4.690E-14 N
 * +d) 5.159E-14 N
 * -e) 5.675E-14 N

3) An empty parallel-plate capacitor with metal plates has an area of 2.51 m2, separated by 1.44 mm. How much charge does it store if the voltage is 2.230E+03 V?


 * -a) 2.351E+01 &mu;C
 * -b) 2.586E+01 &mu;C
 * -c) 2.844E+01 &mu;C
 * -d) 3.129E+01 &mu;C
 * +e) 3.442E+01 &mu;C

4) An electron gun has parallel plates separated by 4.36 cm and gives electrons 13 keV of energy. What force would the field between the plates exert on a 0.816 &mu;C charge that gets between the plates?


 * -a) 2.212E-01 N
 * +b) 2.433E-01 N
 * -c) 2.676E-01 N
 * -d) 2.944E-01 N
 * -e) 3.238E-01 N

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=8 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 3.444E+01 J
 * -b) 3.789E+01 J
 * +c) 4.168E+01 J
 * -d) 4.585E+01 J
 * -e) 5.043E+01 J

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.385E+01 N&middot;m2/C
 * -b) 5.923E+01 N&middot;m2/C
 * -c) 6.516E+01 N&middot;m2/C
 * -d) 7.167E+01 N&middot;m2/C
 * -e) 7.884E+01 N&middot;m2/C

7) Calculate the resistance of a 12-gauge copper wire that is 15 m long and carries a current of 27 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 5.200E-02 &Omega;
 * -b) 5.720E-02 &Omega;
 * -c) 6.292E-02 &Omega;
 * -d) 6.921E-02 &Omega;
 * +e) 7.613E-02 &Omega;

8) Three resistors, R1 = 0.906 &Omega;, and R2 = R2 = 2.02 &Omega;, are connected in parallel to a 5.98 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 3.262E+01 W
 * -b) 3.588E+01 W
 * +c) 3.947E+01 W
 * -d) 4.342E+01 W
 * -e) 4.776E+01 W

9) What is consumer cost to operate one 104&minus;W incandescent bulb for 6 hours per day for 1 year (365 days) if the cost of electricity is $0.136 per kilowatt-hour?


 * -a) $2.116E+01
 * -b) $2.327E+01
 * -c) $2.560E+01
 * -d) $2.816E+01
 * +e) $3.098E+01

10) A battery with a terminal voltage of 8.72 V is connected to a circuit consisting of 2 15.8 &Omega; resistors and one 9.58 &Omega; resistor. What is the voltage drop across the 9.58 &Omega; resistor?


 * -a) 1.677E+00 V
 * -b) 1.844E+00 V
 * +c) 2.029E+00 V
 * -d) 2.231E+00 V
 * -e) 2.455E+00 V

Key: O0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.


 * -a) 5.134E-01 V/m2
 * +b) 5.648E-01 V/m2
 * -c) 6.212E-01 V/m2
 * -d) 6.834E-01 V/m2
 * -e) 7.517E-01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.9 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 8.1m2. An electric field has the xyz components (0, 8.1, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 6.529E+01 N&middot;m2/C
 * -b) 7.181E+01 N&middot;m2/C
 * -c) 7.900E+01 N&middot;m2/C
 * -d) 8.690E+01 N&middot;m2/C
 * -e) 9.559E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.992E+01 N&middot;m2/C
 * -b) 2.192E+01 N&middot;m2/C
 * +c) 2.411E+01 N&middot;m2/C
 * -d) 2.652E+01 N&middot;m2/C
 * -e) 2.917E+01 N&middot;m2/C

4) A 3 C charge is separated from a 9 C charge by distance of 13 cm.  What is the work done by increasing this separation to 21 cm?


 * -a) 6.465E-07 J
 * +b) 7.111E-07 J
 * -c) 7.822E-07 J
 * -d) 8.604E-07 J
 * -e) 9.465E-07 J

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 4.235E+01 J
 * +b) 4.659E+01 J
 * -c) 5.125E+01 J
 * -d) 5.637E+01 J
 * -e) 6.201E+01 J

6) What is the net capacitance if C1=4.75 &mu;F, C2=2.77 &mu;F, and C3=2.47 &mu;F in the configuration shown?


 * +a) 4.220E+00 &mu;F
 * -b) 4.642E+00 &mu;F
 * -c) 5.106E+00 &mu;F
 * -d) 5.616E+00 &mu;F
 * -e) 6.178E+00 &mu;F

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.75 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 4.300E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 423 &deg;C?


 * +a) 1.018E+01 &Omega;
 * -b) 1.069E+01 &Omega;
 * -c) 1.123E+01 &Omega;
 * -d) 1.179E+01 &Omega;
 * -e) 1.238E+01 &Omega;

8) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=27 C  and $$\tau=$$0.0154 s. What is the current at $$t=$$0.0177 s?


 * -a) 4.591E+02 A
 * -b) 5.050E+02 A
 * +c) 5.555E+02 A
 * -d) 6.111E+02 A
 * -e) 6.722E+02 A

9) Two sources of emf &epsilon;1=40.3 V, and  &epsilon;2=16.8 V are oriented as shownin the circuit. The resistances are R1=2.57 k&Omega; and  R2=2.25 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.96 mA and I4=0.752 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 1.825E+00 mA
 * -b) 2.007E+00 mA
 * +c) 2.208E+00 mA
 * -d) 2.429E+00 mA
 * -e) 2.672E+00 mA

10) Three resistors, R1 = 0.61 &Omega;, and R2 = R2 = 1.35 &Omega;, are connected in parallel to a 7.04 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 7.386E+01 W
 * +b) 8.125E+01 W
 * -c) 8.937E+01 W
 * -d) 9.831E+01 W
 * -e) 1.081E+02 W

Key: O1
1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.73 &Omega; at a temperature of 99&deg;C and that the temperature coefficient of expansion is 5.260E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 420 &deg;C?


 * -a) 1.267E+01 &Omega;
 * -b) 1.331E+01 &Omega;
 * -c) 1.397E+01 &Omega;
 * -d) 1.467E+01 &Omega;
 * +e) 1.540E+01 &Omega;

2) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=63 C  and $$\tau=$$0.0149 s. What is the current at $$t=$$0.0172 s?


 * -a) 1.212E+03 A
 * +b) 1.333E+03 A
 * -c) 1.466E+03 A
 * -d) 1.613E+03 A
 * -e) 1.774E+03 A

3) A 2 C charge is separated from a 10 C charge by distance of 8 cm.  What is the work done by increasing this separation to 14 cm?


 * -a) 8.754E-07 J
 * +b) 9.630E-07 J
 * -c) 1.059E-06 J
 * -d) 1.165E-06 J
 * -e) 1.282E-06 J

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.9\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.1\text{ m}$$.


 * -a) 8.253E-01 V/m2
 * -b) 9.079E-01 V/m2
 * +c) 9.987E-01 V/m2
 * -d) 1.099E+00 V/m2
 * -e) 1.208E+00 V/m2

5) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=6 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 2.617E+01 J
 * -b) 2.879E+01 J
 * -c) 3.167E+01 J
 * -d) 3.484E+01 J
 * +e) 3.832E+01 J

6) Three resistors, R1 = 0.548 &Omega;, and R2 = R2 = 1.24 &Omega;, are connected in parallel to a 7.16 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 7.029E+01 W
 * -b) 7.731E+01 W
 * -c) 8.505E+01 W
 * +d) 9.355E+01 W
 * -e) 1.029E+02 W

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.385E+01 N&middot;m2/C
 * -b) 5.923E+01 N&middot;m2/C
 * -c) 6.516E+01 N&middot;m2/C
 * -d) 7.167E+01 N&middot;m2/C
 * -e) 7.884E+01 N&middot;m2/C

8) Two sources of emf &epsilon;1=39.0 V, and  &epsilon;2=15.9 V are oriented as shownin the circuit. The resistances are R1=3.4 k&Omega; and  R2=2.12 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.58 mA and I4=0.978 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 2.150E+00 mA
 * -b) 2.365E+00 mA
 * +c) 2.602E+00 mA
 * -d) 2.862E+00 mA
 * -e) 3.148E+00 mA

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 6.192E+01 N&middot;m2/C
 * -b) 6.811E+01 N&middot;m2/C
 * -c) 7.492E+01 N&middot;m2/C
 * -d) 8.242E+01 N&middot;m2/C
 * -e) 9.066E+01 N&middot;m2/C

10) What is the net capacitance if C1=4.13 &mu;F, C2=3.56 &mu;F, and C3=3.57 &mu;F in the configuration shown?


 * +a) 5.482E+00 &mu;F
 * -b) 6.030E+00 &mu;F
 * -c) 6.633E+00 &mu;F
 * -d) 7.296E+00 &mu;F
 * -e) 8.026E+00 &mu;F

Key: O2
1) Three resistors, R1 = 1.2 &Omega;, and R2 = R2 = 2.75 &Omega;, are connected in parallel to a 6.42 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)


 * -a) 2.581E+01 W
 * -b) 2.839E+01 W
 * -c) 3.122E+01 W
 * +d) 3.435E+01 W
 * -e) 3.778E+01 W

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.698E+01 N&middot;m2/C
 * -b) 1.868E+01 N&middot;m2/C
 * -c) 2.055E+01 N&middot;m2/C
 * -d) 2.260E+01 N&middot;m2/C
 * +e) 2.486E+01 N&middot;m2/C

3) Two sources of emf &epsilon;1=49.6 V, and  &epsilon;2=19.3 V are oriented as shownin the circuit. The resistances are R1=4.87 k&Omega; and  R2=2.81 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.37 mA and I4=1.01 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 3.055E+00 mA
 * +b) 3.360E+00 mA
 * -c) 3.696E+00 mA
 * -d) 4.066E+00 mA
 * -e) 4.472E+00 mA

4) Imagine a substance could be made into a very hot filament. Suppose the resitance is 4.08 &Omega; at a temperature of 26&deg;C and that the temperature coefficient of expansion is 4.800E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 388 &deg;C?


 * -a) 1.064E+01 &Omega;
 * +b) 1.117E+01 &Omega;
 * -c) 1.173E+01 &Omega;
 * -d) 1.231E+01 &Omega;
 * -e) 1.293E+01 &Omega;

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 3.074E+01 N&middot;m2/C
 * -b) 3.382E+01 N&middot;m2/C
 * -c) 3.720E+01 N&middot;m2/C
 * -d) 4.092E+01 N&middot;m2/C
 * -e) 4.501E+01 N&middot;m2/C

6) What is the net capacitance if C1=3.06 &mu;F, C2=3.09 &mu;F, and C3=2.48 &mu;F in the configuration shown?


 * -a) 3.018E+00 &mu;F
 * -b) 3.320E+00 &mu;F
 * -c) 3.652E+00 &mu;F
 * +d) 4.017E+00 &mu;F
 * -e) 4.419E+00 &mu;F

7) A 9 C charge is separated from a 16 C charge by distance of 10 cm.  What is the work done by increasing this separation to 16 cm?


 * +a) 4.853E-06 J
 * -b) 5.339E-06 J
 * -c) 5.872E-06 J
 * -d) 6.460E-06 J
 * -e) 7.106E-06 J

8) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.8\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.1\text{ m}$$.


 * -a) 7.517E+00 V/m2
 * -b) 8.269E+00 V/m2
 * -c) 9.096E+00 V/m2
 * -d) 1.001E+01 V/m2
 * +e) 1.101E+01 V/m2

9) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=38 C  and $$\tau=$$0.0167 s. What is the current at $$t=$$0.0183 s?


 * -a) 5.715E+02 A
 * -b) 6.286E+02 A
 * -c) 6.915E+02 A
 * +d) 7.606E+02 A
 * -e) 8.367E+02 A

10) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 4.235E+01 J
 * +b) 4.659E+01 J
 * -c) 5.125E+01 J
 * -d) 5.637E+01 J
 * -e) 6.201E+01 J

Key: P0
1) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.4\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=0.56\text{ m}$$.


 * -a) 2.567E+01 V/m2
 * -b) 2.824E+01 V/m2
 * -c) 3.106E+01 V/m2
 * -d) 3.417E+01 V/m2
 * +e) 3.759E+01 V/m2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.898E+01 N&middot;m2/C
 * +b) 7.588E+01 N&middot;m2/C
 * -c) 8.347E+01 N&middot;m2/C
 * -d) 9.181E+01 N&middot;m2/C
 * -e) 1.010E+02 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 8.314E+01 N&middot;m2/C
 * -b) 9.146E+01 N&middot;m2/C
 * -c) 1.006E+02 N&middot;m2/C
 * -d) 1.107E+02 N&middot;m2/C
 * -e) 1.217E+02 N&middot;m2/C

4) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * -a) 7.017E+02 V
 * +b) 7.718E+02 V
 * -c) 8.490E+02 V
 * -d) 9.339E+02 V
 * -e) 1.027E+03 V

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=6 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 2.343E+01 J
 * +b) 2.577E+01 J
 * -c) 2.835E+01 J
 * -d) 3.118E+01 J
 * -e) 3.430E+01 J

6) In the figure shown C1=18.2 &mu;F, C2=2.44 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=7.78 V. What is the energy stored in C2?


 * -a) 1.225E+01 &mu;J
 * +b) 1.347E+01 &mu;J
 * -c) 1.482E+01 &mu;J
 * -d) 1.630E+01 &mu;J
 * -e) 1.793E+01 &mu;J

7) Calculate the electric field in a 12-gauge copper wire that is 41 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 3.604E-04 V/m
 * -b) 3.964E-04 V/m
 * -c) 4.360E-04 V/m
 * -d) 4.796E-04 V/m
 * -e) 5.276E-04 V/m

8) What is consumer cost to operate one 59&minus;W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.132 per kilowatt-hour?


 * -a) $2.584E+01
 * +b) $2.843E+01
 * -c) $3.127E+01
 * -d) $3.440E+01
 * -e) $3.784E+01

9) Two sources of emf &epsilon;1=34.7 V, and  &epsilon;2=13.9 V are oriented as shownin the circuit. The resistances are R1=3.68 k&Omega; and  R2=1.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.68 mA and I4=0.933 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 9.286E+00 V
 * -b) 1.021E+01 V
 * -c) 1.124E+01 V
 * +d) 1.236E+01 V
 * -e) 1.360E+01 V

10) In the circuit shown V=19.6 V, R1=1.45 &Omega;, R2=7.85 &Omega;, and R3=15.8 &Omega;. What is the power dissipated by R2?


 * -a) 2.730E+01 W
 * +b) 3.003E+01 W
 * -c) 3.304E+01 W
 * -d) 3.634E+01 W
 * -e) 3.998E+01 W

Key: P1
1) In the figure shown C1=15.4 &mu;F, C2=2.6 &mu;F, and C3=5.17 &mu;F. The voltage source provides &epsilon;=9.6 V. What is the energy stored in C2?


 * -a) 1.508E+01 &mu;J
 * +b) 1.659E+01 &mu;J
 * -c) 1.825E+01 &mu;J
 * -d) 2.007E+01 &mu;J
 * -e) 2.208E+01 &mu;J

2) What is consumer cost to operate one 79&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.142 per kilowatt-hour?


 * -a) $2.517E+01
 * -b) $2.769E+01
 * -c) $3.046E+01
 * -d) $3.350E+01
 * +e) $3.685E+01

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.186E+01 N&middot;m2/C
 * -b) 2.404E+01 N&middot;m2/C
 * +c) 2.645E+01 N&middot;m2/C
 * -d) 2.909E+01 N&middot;m2/C
 * -e) 3.200E+01 N&middot;m2/C

4) Calculate the electric field in a 12-gauge copper wire that is 23 m long and carries a current of 64 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.953E-04 V/m
 * +b) 3.248E-04 V/m
 * -c) 3.573E-04 V/m
 * -d) 3.930E-04 V/m
 * -e) 4.324E-04 V/m

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.012E+01 N&middot;m2/C
 * -b) 2.213E+01 N&middot;m2/C
 * -c) 2.435E+01 N&middot;m2/C
 * -d) 2.678E+01 N&middot;m2/C
 * +e) 2.946E+01 N&middot;m2/C

6) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=8 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 3.444E+01 J
 * -b) 3.789E+01 J
 * +c) 4.168E+01 J
 * -d) 4.585E+01 J
 * -e) 5.043E+01 J

7) In the circuit shown V=16.2 V, R1=2.84 &Omega;, R2=7.06 &Omega;, and R3=13.1 &Omega;. What is the power dissipated by R2?


 * +a) 1.418E+01 W
 * -b) 1.560E+01 W
 * -c) 1.716E+01 W
 * -d) 1.887E+01 W
 * -e) 2.076E+01 W

8) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=4.3\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.4\text{ m}$$.


 * +a) 5.647E+00 V/m2
 * -b) 6.212E+00 V/m2
 * -c) 6.833E+00 V/m2
 * -d) 7.517E+00 V/m2
 * -e) 8.268E+00 V/m2

9) Two sources of emf &epsilon;1=67.2 V, and  &epsilon;2=18.7 V are oriented as shownin the circuit. The resistances are R1=3.45 k&Omega; and  R2=1.2 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.49 mA and I4=1.81 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 1.906E+01 V
 * +b) 2.097E+01 V
 * -c) 2.306E+01 V
 * -d) 2.537E+01 V
 * -e) 2.790E+01 V

10) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * -a) 7.017E+02 V
 * +b) 7.718E+02 V
 * -c) 8.490E+02 V
 * -d) 9.339E+02 V
 * -e) 1.027E+03 V

Key: P2
1) A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.


 * -a) 2.727E+02 V
 * -b) 2.999E+02 V
 * -c) 3.299E+02 V
 * +d) 3.629E+02 V
 * -e) 3.992E+02 V

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.695E+01 N&middot;m2/C
 * -b) 4.065E+01 N&middot;m2/C
 * -c) 4.472E+01 N&middot;m2/C
 * -d) 4.919E+01 N&middot;m2/C
 * +e) 5.411E+01 N&middot;m2/C

3) In the circuit shown V=15.8 V, R1=1.86 &Omega;, R2=7.66 &Omega;, and R3=12.9 &Omega;. What is the power dissipated by R2?


 * -a) 1.157E+01 W
 * -b) 1.273E+01 W
 * -c) 1.400E+01 W
 * -d) 1.540E+01 W
 * +e) 1.694E+01 W

4) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.2\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.6\text{ m}$$.


 * +a) 1.606E+00 V/m2
 * -b) 1.767E+00 V/m2
 * -c) 1.943E+00 V/m2
 * -d) 2.138E+00 V/m2
 * -e) 2.351E+00 V/m2

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.662E+01 N&middot;m2/C
 * +b) 4.028E+01 N&middot;m2/C
 * -c) 4.430E+01 N&middot;m2/C
 * -d) 4.873E+01 N&middot;m2/C
 * -e) 5.361E+01 N&middot;m2/C

6) Two sources of emf &epsilon;1=17.3 V, and  &epsilon;2=6.46 V are oriented as shownin the circuit. The resistances are R1=2.54 k&Omega; and  R2=2.79 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.1 mA and I4=0.281 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 6.488E+00 V
 * +b) 7.137E+00 V
 * -c) 7.850E+00 V
 * -d) 8.635E+00 V
 * -e) 9.499E+00 V

7) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 7.789E+01 J
 * +b) 8.568E+01 J
 * -c) 9.425E+01 J
 * -d) 1.037E+02 J
 * -e) 1.140E+02 J

8) Calculate the electric field in a 12-gauge copper wire that is 13 m long and carries a current of 59 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.250E-04 V/m
 * -b) 2.475E-04 V/m
 * -c) 2.722E-04 V/m
 * +d) 2.995E-04 V/m
 * -e) 3.294E-04 V/m

9) In the figure shown C1=16.3 &mu;F, C2=2.17 &mu;F, and C3=4.67 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * -a) 8.718E+00 &mu;J
 * -b) 9.589E+00 &mu;J
 * -c) 1.055E+01 &mu;J
 * -d) 1.160E+01 &mu;J
 * +e) 1.276E+01 &mu;J

10) What is consumer cost to operate one 102&minus;W incandescent bulb for 5 hours per day for 1 year (365 days) if the cost of electricity is $0.149 per kilowatt-hour?


 * -a) $2.292E+01
 * -b) $2.521E+01
 * +c) $2.774E+01
 * -d) $3.051E+01
 * -e) $3.356E+01

Key: Q0
1) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?


 * -a) 6.925E+09 N/C2
 * -b) 7.617E+09 N/C2
 * +c) 8.379E+09 N/C2
 * -d) 9.217E+09 N/C2
 * -e) 1.014E+10 N/C2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 8.457E+01 N&middot;m2/C
 * +b) 9.303E+01 N&middot;m2/C
 * -c) 1.023E+02 N&middot;m2/C
 * -d) 1.126E+02 N&middot;m2/C
 * -e) 1.238E+02 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k$$


 * -a) 8.731E+02 V&middot;m
 * -b) 9.604E+02 V&middot;m
 * -c) 1.056E+03 V&middot;m
 * +d) 1.162E+03 V&middot;m
 * -e) 1.278E+03 V&middot;m

4) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=52 V is x2 + y2 + z2 = R2, where R=


 * +a) 2.420E+00 m
 * -b) 2.662E+00 m
 * -c) 2.928E+00 m
 * -d) 3.221E+00 m
 * -e) 3.543E+00 m

5) Two large parallel conducting plates are separated by 9.58 mm. Equal and opposite surface charges of 7.360E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 84 V?


 * -a) 6.644E-01 mm
 * -b) 7.641E-01 mm
 * -c) 8.787E-01 mm
 * +d) 1.011E+00 mm
 * -e) 1.162E+00 mm

6) An empty parallel-plate capacitor with metal plates has an area of 2.21 m2, separated by 1.25 mm. How much charge does it store if the voltage is 1.580E+03 V?


 * -a) 2.249E+01 &mu;C
 * +b) 2.473E+01 &mu;C
 * -c) 2.721E+01 &mu;C
 * -d) 2.993E+01 &mu;C
 * -e) 3.292E+01 &mu;C

7) A DC winch moter draws 27 amps at 190 volts as it lifts a 4.910E+03 N weight at a constant speed of 0.769 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 1.396E+00 &Omega;
 * -b) 1.535E+00 &Omega;
 * -c) 1.689E+00 &Omega;
 * +d) 1.858E+00 &Omega;
 * -e) 2.043E+00 &Omega;

8) What is the average current involved when a truck battery sets in motion 821 C of charge in 5.51 s while starting an engine?


 * -a) 1.231E+02 A
 * -b) 1.355E+02 A
 * +c) 1.490E+02 A
 * -d) 1.639E+02 A
 * -e) 1.803E+02 A

9) In the circuit shown V=11.8 V, R1=2.38 &Omega;, R2=5.11 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * -a) 8.489E+00 W
 * -b) 9.338E+00 W
 * +c) 1.027E+01 W
 * -d) 1.130E+01 W
 * -e) 1.243E+01 W

10) Two sources of emf &epsilon;1=40.6 V, and  &epsilon;2=13.5 V are oriented as shownin the circuit. The resistances are R1=4.35 k&Omega; and  R2=2.44 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.73 mA and I4=0.78 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 1.332E+00 mA
 * -b) 1.465E+00 mA
 * -c) 1.612E+00 mA
 * -d) 1.773E+00 mA
 * +e) 1.950E+00 mA

Key: Q1
1) Two sources of emf &epsilon;1=43.0 V, and  &epsilon;2=13.8 V are oriented as shownin the circuit. The resistances are R1=3.97 k&Omega; and  R2=1.12 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=6.25 mA and I4=1.82 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 3.661E+00 mA
 * -b) 4.027E+00 mA
 * +c) 4.430E+00 mA
 * -d) 4.873E+00 mA
 * -e) 5.360E+00 mA

2) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?


 * -a) 4.142E+09 N/C2
 * -b) 4.556E+09 N/C2
 * +c) 5.012E+09 N/C2
 * -d) 5.513E+09 N/C2
 * -e) 6.064E+09 N/C2

3) What is the average current involved when a truck battery sets in motion 537 C of charge in 5.08 s while starting an engine?


 * -a) 8.736E+01 A
 * -b) 9.610E+01 A
 * +c) 1.057E+02 A
 * -d) 1.163E+02 A
 * -e) 1.279E+02 A

4) In the circuit shown V=13.5 V, R1=2.66 &Omega;, R2=7.29 &Omega;, and R3=14.5 &Omega;. What is the power dissipated by R2?


 * -a) 7.123E+00 W
 * -b) 7.835E+00 W
 * -c) 8.618E+00 W
 * -d) 9.480E+00 W
 * +e) 1.043E+01 W

5) Two large parallel conducting plates are separated by 7.14 mm. Equal and opposite surface charges of 7.660E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?


 * -a) 4.031E-01 mm
 * -b) 4.636E-01 mm
 * -c) 5.332E-01 mm
 * -d) 6.131E-01 mm
 * +e) 7.051E-01 mm

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 8.457E+01 N&middot;m2/C
 * +b) 9.303E+01 N&middot;m2/C
 * -c) 1.023E+02 N&middot;m2/C
 * -d) 1.126E+02 N&middot;m2/C
 * -e) 1.238E+02 N&middot;m2/C

7) An empty parallel-plate capacitor with metal plates has an area of 2.83 m2, separated by 1.14 mm. How much charge does it store if the voltage is 4.180E+03 V?


 * -a) 6.275E+01 &mu;C
 * -b) 6.903E+01 &mu;C
 * -c) 7.593E+01 &mu;C
 * -d) 8.352E+01 &mu;C
 * +e) 9.188E+01 &mu;C

8) If a 21 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=94 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.371E+00 m
 * -b) 1.509E+00 m
 * -c) 1.659E+00 m
 * -d) 1.825E+00 m
 * +e) 2.008E+00 m

9) A DC winch moter draws 18 amps at 126 volts as it lifts a 5.830E+03 N weight at a constant speed of 0.26 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 1.919E+00 &Omega;
 * -b) 2.111E+00 &Omega;
 * +c) 2.322E+00 &Omega;
 * -d) 2.554E+00 &Omega;
 * -e) 2.809E+00 &Omega;

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k$$


 * -a) 4.286E+03 V&middot;m
 * -b) 4.714E+03 V&middot;m
 * +c) 5.186E+03 V&middot;m
 * -d) 5.704E+03 V&middot;m
 * -e) 6.275E+03 V&middot;m

Key: Q2
1) Two sources of emf &epsilon;1=44.4 V, and  &epsilon;2=16.8 V are oriented as shownin the circuit. The resistances are R1=4.58 k&Omega; and  R2=1.2 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=8.43 mA and I4=1.46 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 6.970E+00 mA
 * -b) 7.667E+00 mA
 * -c) 8.434E+00 mA
 * -d) 9.277E+00 mA
 * -e) 1.020E+01 mA

2) What is the average current involved when a truck battery sets in motion 889 C of charge in 3.64 s while starting an engine?


 * +a) 2.442E+02 A
 * -b) 2.687E+02 A
 * -c) 2.955E+02 A
 * -d) 3.251E+02 A
 * -e) 3.576E+02 A

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 6.920E+01 N&middot;m2/C
 * -b) 7.612E+01 N&middot;m2/C
 * -c) 8.373E+01 N&middot;m2/C
 * +d) 9.210E+01 N&middot;m2/C
 * -e) 1.013E+02 N&middot;m2/C

4) In the circuit shown V=18.4 V, R1=1.64 &Omega;, R2=6.56 &Omega;, and R3=12.8 &Omega;. What is the power dissipated by R2?


 * -a) 2.470E+01 W
 * +b) 2.717E+01 W
 * -c) 2.989E+01 W
 * -d) 3.288E+01 W
 * -e) 3.617E+01 W

5) An empty parallel-plate capacitor with metal plates has an area of 1.81 m2, separated by 1.26 mm. How much charge does it store if the voltage is 4.610E+03 V?


 * -a) 4.005E+01 &mu;C
 * -b) 4.405E+01 &mu;C
 * -c) 4.846E+01 &mu;C
 * -d) 5.330E+01 &mu;C
 * +e) 5.864E+01 &mu;C

6) A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?


 * +a) 5.402E+09 N/C2
 * -b) 5.943E+09 N/C2
 * -c) 6.537E+09 N/C2
 * -d) 7.191E+09 N/C2
 * -e) 7.910E+09 N/C2

7) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is, $$\vec E=2y^{1.8}\hat i +3x^{1.9}\hat j +5y^{3.2}\hat k$$


 * -a) 9.952E+03 V&middot;m
 * -b) 1.095E+04 V&middot;m
 * -c) 1.204E+04 V&middot;m
 * +d) 1.325E+04 V&middot;m
 * -e) 1.457E+04 V&middot;m

8) Two large parallel conducting plates are separated by 7.01 mm. Equal and opposite surface charges of 7.330E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 55 V?


 * -a) 3.799E-01 mm
 * -b) 4.368E-01 mm
 * -c) 5.024E-01 mm
 * -d) 5.777E-01 mm
 * +e) 6.644E-01 mm

9) If a 21 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=94 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.371E+00 m
 * -b) 1.509E+00 m
 * -c) 1.659E+00 m
 * -d) 1.825E+00 m
 * +e) 2.008E+00 m

10) A DC winch moter draws 24 amps at 159 volts as it lifts a 4.120E+03 N weight at a constant speed of 0.657 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 1.447E+00 &Omega;
 * -b) 1.591E+00 &Omega;
 * -c) 1.751E+00 &Omega;
 * +d) 1.926E+00 &Omega;
 * -e) 2.118E+00 &Omega;

Key: R0
1) A large thin isolated square plate has an area of 9 m2. It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * -a) 2.571E+01 N/C
 * -b) 2.828E+01 N/C
 * -c) 3.111E+01 N/C
 * -d) 3.422E+01 N/C
 * +e) 3.765E+01 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?


 * -a) 9.144E+00 N/C
 * -b) 1.006E+01 N/C
 * -c) 1.106E+01 N/C
 * -d) 1.217E+01 N/C
 * +e) 1.339E+01 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.978E+01 N&middot;m2/C
 * -b) 6.576E+01 N&middot;m2/C
 * -c) 7.233E+01 N&middot;m2/C
 * -d) 7.957E+01 N&middot;m2/C
 * -e) 8.752E+01 N&middot;m2/C

4) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.31 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.47 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * +a) 8.672E+02 V
 * -b) 9.539E+02 V
 * -c) 1.049E+03 V
 * -d) 1.154E+03 V
 * -e) 1.270E+03 V

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 74 V.


 * -a) 4.638E+06 m/s
 * +b) 5.102E+06 m/s
 * -c) 5.612E+06 m/s
 * -d) 6.173E+06 m/s
 * -e) 6.791E+06 m/s

6) An empty parallel-plate capacitor with metal plates has an area of 2.04 m2, separated by 1.21 mm. How much charge does it store if the voltage is 7.730E+03 V?


 * -a) 1.049E+02 &mu;C
 * +b) 1.154E+02 &mu;C
 * -c) 1.269E+02 &mu;C
 * -d) 1.396E+02 &mu;C
 * -e) 1.536E+02 &mu;C

7) Calculate the drift speed of electrons in a copper wire with a diameter of 4.49 mm carrying a 11.6 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 4.120E-05 m/s
 * -b) 4.532E-05 m/s
 * -c) 4.985E-05 m/s
 * +d) 5.483E-05 m/s
 * -e) 6.032E-05 m/s

8) A make-believe metal has a density of 1.180E+04 kg/m3 and an atomic mass of 121.0 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 4.010E+28 e&minus;/m3
 * -b) 4.411E+28 e&minus;/m3
 * -c) 4.852E+28 e&minus;/m3
 * -d) 5.337E+28 e&minus;/m3
 * +e) 5.871E+28 e&minus;/m3

9) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.945E+00 V
 * +b) 9.840E+00 V
 * -c) 1.082E+01 V
 * -d) 1.191E+01 V
 * -e) 1.310E+01 V

10) A battery with a terminal voltage of 9.88 V is connected to a circuit consisting of 3 15.9 &Omega; resistors and one 10.8 &Omega; resistor. What is the voltage drop across the 10.8 &Omega; resistor?


 * -a) 1.370E+00 V
 * -b) 1.507E+00 V
 * -c) 1.658E+00 V
 * +d) 1.824E+00 V
 * -e) 2.006E+00 V

Key: R1
1) A make-believe metal has a density of 2.670E+03 kg/m3 and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 3.930E+28 e&minus;/m3
 * -b) 4.323E+28 e&minus;/m3
 * -c) 4.755E+28 e&minus;/m3
 * -d) 5.231E+28 e&minus;/m3
 * -e) 5.754E+28 e&minus;/m3

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.978E+01 N&middot;m2/C
 * -b) 6.576E+01 N&middot;m2/C
 * -c) 7.233E+01 N&middot;m2/C
 * -d) 7.957E+01 N&middot;m2/C
 * -e) 8.752E+01 N&middot;m2/C

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 27 V.


 * -a) 2.802E+06 m/s
 * +b) 3.082E+06 m/s
 * -c) 3.390E+06 m/s
 * -d) 3.729E+06 m/s
 * -e) 4.102E+06 m/s

4) Calculate the drift speed of electrons in a copper wire with a diameter of 3.3 mm carrying a 18.5 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.472E-04 m/s
 * +b) 1.619E-04 m/s
 * -c) 1.781E-04 m/s
 * -d) 1.959E-04 m/s
 * -e) 2.155E-04 m/s

5) A battery with a terminal voltage of 14.9 V is connected to a circuit consisting of 2 16.3 &Omega; resistors and one 9.8 &Omega; resistor. What is the voltage drop across the 9.8 &Omega; resistor?


 * -a) 2.352E+00 V
 * -b) 2.587E+00 V
 * -c) 2.846E+00 V
 * -d) 3.131E+00 V
 * +e) 3.444E+00 V

6) Two sources of emf &epsilon;1=57.0 V, and  &epsilon;2=18.1 V are oriented as shownin the circuit. The resistances are R1=4.95 k&Omega; and  R2=2.09 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.23 mA and I4=1.04 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 1.921E+01 V
 * +b) 2.114E+01 V
 * -c) 2.325E+01 V
 * -d) 2.557E+01 V
 * -e) 2.813E+01 V

7) A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.57 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.59 cm, y=1.78 cm)? Note that following the textbook's example, the y-value of the field point at 1.78 cm matches the disance of the positive charge above the x-axis.


 * -a) 2.727E+02 V
 * -b) 2.999E+02 V
 * -c) 3.299E+02 V
 * +d) 3.629E+02 V
 * -e) 3.992E+02 V

8) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?


 * -a) 2.837E+01 N/C
 * -b) 3.121E+01 N/C
 * -c) 3.433E+01 N/C
 * -d) 3.776E+01 N/C
 * +e) 4.154E+01 N/C

9) A large thin isolated square plate has an area of 6 m2. It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?


 * +a) 8.471E+01 N/C
 * -b) 9.318E+01 N/C
 * -c) 1.025E+02 N/C
 * -d) 1.127E+02 N/C
 * -e) 1.240E+02 N/C

10) An empty parallel-plate capacitor with metal plates has an area of 2.78 m2, separated by 1.16 mm. How much charge does it store if the voltage is 8.980E+03 V?


 * -a) 1.432E+02 &mu;C
 * -b) 1.575E+02 &mu;C
 * -c) 1.732E+02 &mu;C
 * +d) 1.906E+02 &mu;C
 * -e) 2.096E+02 &mu;C

Key: R2
1) A battery with a terminal voltage of 7.63 V is connected to a circuit consisting of 2 15.9 &Omega; resistors and one 10.4 &Omega; resistor. What is the voltage drop across the 10.4 &Omega; resistor?


 * -a) 1.709E+00 V
 * +b) 1.880E+00 V
 * -c) 2.068E+00 V
 * -d) 2.275E+00 V
 * -e) 2.503E+00 V

2) A make-believe metal has a density of 1.580E+04 kg/m3 and an atomic mass of 41.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 2.292E+29 e&minus;/m3
 * -b) 2.521E+29 e&minus;/m3
 * -c) 2.773E+29 e&minus;/m3
 * -d) 3.051E+29 e&minus;/m3
 * -e) 3.356E+29 e&minus;/m3

3) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.09 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.45 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * -a) 3.814E+02 V
 * -b) 4.195E+02 V
 * +c) 4.615E+02 V
 * -d) 5.077E+02 V
 * -e) 5.584E+02 V

4) Two sources of emf &epsilon;1=27.1 V, and  &epsilon;2=8.04 V are oriented as shownin the circuit. The resistances are R1=2.94 k&Omega; and  R2=1.61 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.87 mA and I4=0.57 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.482E+00 V
 * +b) 9.330E+00 V
 * -c) 1.026E+01 V
 * -d) 1.129E+01 V
 * -e) 1.242E+01 V

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.3 m, z=z0=1.3 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 5.7m2. An electric field has the xyz components (0, 5.7, 7.5) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 3.249E+01 N&middot;m2/C
 * -b) 3.574E+01 N&middot;m2/C
 * -c) 3.931E+01 N&middot;m2/C
 * -d) 4.324E+01 N&middot;m2/C
 * -e) 4.757E+01 N&middot;m2/C

6) A large thin isolated square plate has an area of 4 m2. It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?


 * -a) 9.546E+01 N/C
 * -b) 1.050E+02 N/C
 * -c) 1.155E+02 N/C
 * +d) 1.271E+02 N/C
 * -e) 1.398E+02 N/C

7) Calculate the final speed of a free electron accelerated from rest through a potential difference of 19 V.


 * -a) 1.942E+06 m/s
 * -b) 2.137E+06 m/s
 * -c) 2.350E+06 m/s
 * +d) 2.585E+06 m/s
 * -e) 2.844E+06 m/s

8) An empty parallel-plate capacitor with metal plates has an area of 2.78 m2, separated by 1.16 mm. How much charge does it store if the voltage is 8.980E+03 V?


 * -a) 1.432E+02 &mu;C
 * -b) 1.575E+02 &mu;C
 * -c) 1.732E+02 &mu;C
 * +d) 1.906E+02 &mu;C
 * -e) 2.096E+02 &mu;C

9) Calculate the drift speed of electrons in a copper wire with a diameter of 3.33 mm carrying a 13.8 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 8.910E-05 m/s
 * -b) 9.801E-05 m/s
 * -c) 1.078E-04 m/s
 * +d) 1.186E-04 m/s
 * -e) 1.305E-04 m/s

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?


 * +a) 1.017E+01 N/C
 * -b) 1.118E+01 N/C
 * -c) 1.230E+01 N/C
 * -d) 1.353E+01 N/C
 * -e) 1.488E+01 N/C

Key: S0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=6e$$?


 * -a) 5.767E+01 degrees
 * +b) 6.343E+01 degrees
 * -c) 6.978E+01 degrees
 * -d) 7.676E+01 degrees
 * -e) 8.443E+01 degrees

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?


 * -a) 5.297E+00 N/C
 * -b) 5.827E+00 N/C
 * -c) 6.409E+00 N/C
 * -d) 7.050E+00 N/C
 * +e) 7.755E+00 N/C

3) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=3 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?


 * -a) 2.039E+01 N/C
 * -b) 2.243E+01 N/C
 * +c) 2.467E+01 N/C
 * -d) 2.714E+01 N/C
 * -e) 2.985E+01 N/C

4) When a 8.6 V battery operates a 2.76 W bulb, how many electrons pass through it each second?


 * -a) 1.655E+18 electrons
 * -b) 1.821E+18 electrons
 * +c) 2.003E+18 electrons
 * -d) 2.203E+18 electrons
 * -e) 2.424E+18 electrons

5) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=7 &mu;C, and q4=9 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 2.300E+01 J
 * -b) 2.530E+01 J
 * -c) 2.783E+01 J
 * +d) 3.061E+01 J
 * -e) 3.367E+01 J

6) In the figure shown C1=16.1 &mu;F, C2=2.14 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * +a) 1.199E+01 &mu;J
 * -b) 1.319E+01 &mu;J
 * -c) 1.450E+01 &mu;J
 * -d) 1.595E+01 &mu;J
 * -e) 1.755E+01 &mu;J

7) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.631E-01 &Omega;
 * -b) 2.894E-01 &Omega;
 * -c) 3.184E-01 &Omega;
 * +d) 3.502E-01 &Omega;
 * -e) 3.852E-01 &Omega;

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.98 &Omega; at a temperature of 92&deg;C and that the temperature coefficient of expansion is 5.080E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 455 &deg;C?


 * -a) 5.363E+00 &Omega;
 * +b) 5.631E+00 &Omega;
 * -c) 5.913E+00 &Omega;
 * -d) 6.208E+00 &Omega;
 * -e) 6.519E+00 &Omega;

9) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.945E+00 V
 * +b) 9.840E+00 V
 * -c) 1.082E+01 V
 * -d) 1.191E+01 V
 * -e) 1.310E+01 V

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 301 V.  If the combined external and internal resistance is 245 &Omega and the capacitance is  63 mF, how long will it take for the capacitor's voltage to reach 192.0 V?


 * -a) 1.296E+01 s
 * -b) 1.425E+01 s
 * +c) 1.568E+01 s
 * -d) 1.725E+01 s
 * -e) 1.897E+01 s

Key: S1
1) Calculate the resistance of a 12-gauge copper wire that is 59 m long and carries a current of 26 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 2.995E-01 &Omega;
 * -b) 3.294E-01 &Omega;
 * -c) 3.623E-01 &Omega;
 * -d) 3.986E-01 &Omega;
 * -e) 4.384E-01 &Omega;

2) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 190 V.  If the combined external and internal resistance is 255 &Omega and the capacitance is  54 mF, how long will it take for the capacitor's voltage to reach 101.0 V?


 * +a) 1.044E+01 s
 * -b) 1.149E+01 s
 * -c) 1.264E+01 s
 * -d) 1.390E+01 s
 * -e) 1.529E+01 s

3) In the figure shown C1=16.9 &mu;F, C2=2.86 &mu;F, and C3=5.1 &mu;F. The voltage source provides &epsilon;=9.98 V. What is the energy stored in C2?


 * -a) 1.764E+01 &mu;J
 * +b) 1.940E+01 &mu;J
 * -c) 2.134E+01 &mu;J
 * -d) 2.348E+01 &mu;J
 * -e) 2.583E+01 &mu;J

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * -a) 5.243E+01 degrees
 * -b) 5.767E+01 degrees
 * +c) 6.343E+01 degrees
 * -d) 6.978E+01 degrees
 * -e) 7.676E+01 degrees

5) A non-conducting sphere of radius R=1.4 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=3 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 1.3 m from the center?


 * +a) 1.457E+02 N/C
 * -b) 1.603E+02 N/C
 * -c) 1.763E+02 N/C
 * -d) 1.939E+02 N/C
 * -e) 2.133E+02 N/C

6) Two sources of emf &epsilon;1=57.0 V, and  &epsilon;2=18.1 V are oriented as shownin the circuit. The resistances are R1=4.95 k&Omega; and  R2=2.09 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.23 mA and I4=1.04 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 1.921E+01 V
 * +b) 2.114E+01 V
 * -c) 2.325E+01 V
 * -d) 2.557E+01 V
 * -e) 2.813E+01 V

7) When a 8.6 V battery operates a 2.76 W bulb, how many electrons pass through it each second?


 * -a) 1.655E+18 electrons
 * -b) 1.821E+18 electrons
 * +c) 2.003E+18 electrons
 * -d) 2.203E+18 electrons
 * -e) 2.424E+18 electrons

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.74 &Omega; at a temperature of 89&deg;C and that the temperature coefficient of expansion is 4.990E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 366 &deg;C?


 * -a) 1.529E+01 &Omega;
 * +b) 1.606E+01 &Omega;
 * -c) 1.686E+01 &Omega;
 * -d) 1.770E+01 &Omega;
 * -e) 1.859E+01 &Omega;

9) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?


 * -a) 2.837E+01 N/C
 * -b) 3.121E+01 N/C
 * -c) 3.433E+01 N/C
 * -d) 3.776E+01 N/C
 * +e) 4.154E+01 N/C

10) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * +a) 1.241E+02 J
 * -b) 1.365E+02 J
 * -c) 1.501E+02 J
 * -d) 1.652E+02 J
 * -e) 1.817E+02 J

Key: S2
1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.58 &Omega; at a temperature of 24&deg;C and that the temperature coefficient of expansion is 5.520E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 349 &deg;C?


 * -a) 9.526E+00 &Omega;
 * +b) 1.000E+01 &Omega;
 * -c) 1.050E+01 &Omega;
 * -d) 1.103E+01 &Omega;
 * -e) 1.158E+01 &Omega;

2) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?


 * -a) 4.743E+01 degrees
 * -b) 5.217E+01 degrees
 * -c) 5.739E+01 degrees
 * -d) 6.313E+01 degrees
 * +e) 6.944E+01 degrees

3) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.631E-01 &Omega;
 * -b) 2.894E-01 &Omega;
 * -c) 3.184E-01 &Omega;
 * +d) 3.502E-01 &Omega;
 * -e) 3.852E-01 &Omega;

4) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 554 V.  If the combined external and internal resistance is 228 &Omega and the capacitance is  93 mF, how long will it take for the capacitor's voltage to reach 450.0 V?


 * -a) 3.224E+01 s
 * +b) 3.547E+01 s
 * -c) 3.902E+01 s
 * -d) 4.292E+01 s
 * -e) 4.721E+01 s

5) When a 2.59 V battery operates a 2.89 W bulb, how many electrons pass through it each second?


 * -a) 5.756E+18 electrons
 * -b) 6.331E+18 electrons
 * +c) 6.964E+18 electrons
 * -d) 7.661E+18 electrons
 * -e) 8.427E+18 electrons

6) In the figure shown C1=17.6 &mu;F, C2=2.12 &mu;F, and C3=4.72 &mu;F. The voltage source provides &epsilon;=5.35 V. What is the energy stored in C2?


 * -a) 6.750E+00 &mu;J
 * -b) 7.425E+00 &mu;J
 * +c) 8.168E+00 &mu;J
 * -d) 8.984E+00 &mu;J
 * -e) 9.883E+00 &mu;J

7) Two sources of emf &epsilon;1=39.2 V, and  &epsilon;2=12.6 V are oriented as shownin the circuit. The resistances are R1=3.86 k&Omega; and  R2=1.89 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.05 mA and I4=0.701 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.687E+00 V
 * -b) 9.555E+00 V
 * -c) 1.051E+01 V
 * -d) 1.156E+01 V
 * +e) 1.272E+01 V

8) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 5.178E+01 J
 * +b) 5.696E+01 J
 * -c) 6.266E+01 J
 * -d) 6.892E+01 J
 * -e) 7.582E+01 J

9) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?


 * +a) 2.285E+01 N/C
 * -b) 2.514E+01 N/C
 * -c) 2.765E+01 N/C
 * -d) 3.042E+01 N/C
 * -e) 3.346E+01 N/C

10) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?


 * -a) 3.251E+01 N/C
 * -b) 3.577E+01 N/C
 * -c) 3.934E+01 N/C
 * -d) 4.328E+01 N/C
 * +e) 4.760E+01 N/C

Key: T0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * -a) 9.958E-15 N
 * -b) 1.095E-14 N
 * -c) 1.205E-14 N
 * -d) 1.325E-14 N
 * +e) 1.458E-14 N

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.901E+01 N&middot;m2/C
 * -b) 3.192E+01 N&middot;m2/C
 * -c) 3.511E+01 N&middot;m2/C
 * -d) 3.862E+01 N&middot;m2/C
 * +e) 4.248E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 8.415E+01 N&middot;m2/C
 * -b) 9.256E+01 N&middot;m2/C
 * -c) 1.018E+02 N&middot;m2/C
 * +d) 1.120E+02 N&middot;m2/C
 * -e) 1.232E+02 N&middot;m2/C

4) Calculate the final speed of a free electron accelerated from rest through a potential difference of 6 V.


 * -a) 1.091E+06 m/s
 * -b) 1.201E+06 m/s
 * -c) 1.321E+06 m/s
 * +d) 1.453E+06 m/s
 * -e) 1.598E+06 m/s

5) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=12 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 7.789E+01 J
 * +b) 8.568E+01 J
 * -c) 9.425E+01 J
 * -d) 1.037E+02 J
 * -e) 1.140E+02 J

6) What is the net capacitance if C1=3.25 &mu;F, C2=4.87 &mu;F, and C3=2.19 &mu;F in the configuration shown?


 * +a) 4.139E+00 &mu;F
 * -b) 4.553E+00 &mu;F
 * -c) 5.008E+00 &mu;F
 * -d) 5.509E+00 &mu;F
 * -e) 6.060E+00 &mu;F

7) Calculate the drift speed of electrons in a copper wire with a diameter of 4.38 mm carrying a 5.79 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 2.615E-05 m/s
 * +b) 2.876E-05 m/s
 * -c) 3.164E-05 m/s
 * -d) 3.480E-05 m/s
 * -e) 3.828E-05 m/s

8) A DC winch moter draws 12 amps at 129 volts as it lifts a 4.210E+03 N weight at a constant speed of 0.318 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 9.924E-01 &Omega;
 * -b) 1.092E+00 &Omega;
 * -c) 1.201E+00 &Omega;
 * -d) 1.321E+00 &Omega;
 * +e) 1.453E+00 &Omega;

9) Two sources of emf &epsilon;1=24.4 V, and  &epsilon;2=6.73 V are oriented as shownin the circuit. The resistances are R1=5.7 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.36 mA and I4=0.418 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 5.418E+00 V
 * -b) 5.960E+00 V
 * -c) 6.556E+00 V
 * -d) 7.212E+00 V
 * +e) 7.933E+00 V

10) The resistances in the figure shown are R1= 2.74 &Omega;, R2= 1.63 &Omega;, and R2= 2.75 &Omega;. V1 and V3 are text 0.485 V and 2.01 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.555 V. What is the absolute value of the current through R1?


 * -a) 1.114E-01 A
 * +b) 1.225E-01 A
 * -c) 1.348E-01 A
 * -d) 1.483E-01 A
 * -e) 1.631E-01 A

Key: T1
1) Calculate the final speed of a free electron accelerated from rest through a potential difference of 69 V.


 * -a) 3.365E+06 m/s
 * -b) 3.701E+06 m/s
 * -c) 4.072E+06 m/s
 * -d) 4.479E+06 m/s
 * +e) 4.927E+06 m/s

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.756E+01 N&middot;m2/C
 * -b) 3.032E+01 N&middot;m2/C
 * -c) 3.335E+01 N&middot;m2/C
 * -d) 3.668E+01 N&middot;m2/C
 * +e) 4.035E+01 N&middot;m2/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.901E+01 N&middot;m2/C
 * -b) 3.192E+01 N&middot;m2/C
 * -c) 3.511E+01 N&middot;m2/C
 * -d) 3.862E+01 N&middot;m2/C
 * +e) 4.248E+01 N&middot;m2/C

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?


 * +a) 5.732E-15 N
 * -b) 6.305E-15 N
 * -c) 6.936E-15 N
 * -d) 7.629E-15 N
 * -e) 8.392E-15 N

5) What is the net capacitance if C1=3.54 &mu;F, C2=3.53 &mu;F, and C3=3.65 &mu;F in the configuration shown?


 * -a) 3.700E+00 &mu;F
 * -b) 4.070E+00 &mu;F
 * -c) 4.477E+00 &mu;F
 * -d) 4.925E+00 &mu;F
 * +e) 5.417E+00 &mu;F

6) The resistances in the figure shown are R1= 2.42 &Omega;, R2= 1.09 &Omega;, and R2= 3.89 &Omega;. V1 and V3 are text 0.677 V and 1.86 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.745 V. What is the absolute value of the current through R1?


 * -a) 2.089E-01 A
 * -b) 2.298E-01 A
 * +c) 2.528E-01 A
 * -d) 2.781E-01 A
 * -e) 3.059E-01 A

7) A DC winch moter draws 24 amps at 159 volts as it lifts a 4.120E+03 N weight at a constant speed of 0.657 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 1.447E+00 &Omega;
 * -b) 1.591E+00 &Omega;
 * -c) 1.751E+00 &Omega;
 * +d) 1.926E+00 &Omega;
 * -e) 2.118E+00 &Omega;

8) Two sources of emf &epsilon;1=54.9 V, and  &epsilon;2=19.8 V are oriented as shownin the circuit. The resistances are R1=3.93 k&Omega; and  R2=1.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=9.18 mA and I4=1.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.779E+01 V
 * -b) 1.957E+01 V
 * -c) 2.153E+01 V
 * -d) 2.368E+01 V
 * -e) 2.605E+01 V

9) Four charges lie at the corners of a 2 cm by 2 cm square as shown (i.e., a=b=2 cm.)  The charges are q1=4 &mu;C, q2=7 &mu;C, q3=8 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * +a) 1.241E+02 J
 * -b) 1.365E+02 J
 * -c) 1.501E+02 J
 * -d) 1.652E+02 J
 * -e) 1.817E+02 J

10) Calculate the drift speed of electrons in a copper wire with a diameter of 3.53 mm carrying a 2.8 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.947E-05 m/s
 * +b) 2.141E-05 m/s
 * -c) 2.355E-05 m/s
 * -d) 2.591E-05 m/s
 * -e) 2.850E-05 m/s

Key: T2
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=5e$$?


 * -a) 8.259E-15 N
 * -b) 9.085E-15 N
 * -c) 9.993E-15 N
 * -d) 1.099E-14 N
 * +e) 1.209E-14 N

2) Two sources of emf &epsilon;1=36.7 V, and  &epsilon;2=12.1 V are oriented as shownin the circuit. The resistances are R1=2.52 k&Omega; and  R2=1.22 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.14 mA and I4=1.19 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 7.805E+00 V
 * -b) 8.586E+00 V
 * -c) 9.444E+00 V
 * -d) 1.039E+01 V
 * +e) 1.143E+01 V

3) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=3 &mu;C, q2=5 &mu;C, q3=7 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * +a) 5.998E+01 J
 * -b) 6.598E+01 J
 * -c) 7.257E+01 J
 * -d) 7.983E+01 J
 * -e) 8.781E+01 J

4) Calculate the drift speed of electrons in a copper wire with a diameter of 2.17 mm carrying a 19.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 3.569E-04 m/s
 * +b) 3.926E-04 m/s
 * -c) 4.319E-04 m/s
 * -d) 4.750E-04 m/s
 * -e) 5.226E-04 m/s

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.777E+01 N&middot;m2/C
 * -b) 5.254E+01 N&middot;m2/C
 * -c) 5.780E+01 N&middot;m2/C
 * +d) 6.358E+01 N&middot;m2/C
 * -e) 6.993E+01 N&middot;m2/C

6) What is the net capacitance if C1=2.49 &mu;F, C2=4.24 &mu;F, and C3=2.96 &mu;F in the configuration shown?


 * -a) 4.117E+00 &mu;F
 * +b) 4.529E+00 &mu;F
 * -c) 4.982E+00 &mu;F
 * -d) 5.480E+00 &mu;F
 * -e) 6.028E+00 &mu;F

7) Calculate the final speed of a free electron accelerated from rest through a potential difference of 16 V.


 * -a) 2.157E+06 m/s
 * +b) 2.372E+06 m/s
 * -c) 2.610E+06 m/s
 * -d) 2.871E+06 m/s
 * -e) 3.158E+06 m/s

8) The resistances in the figure shown are R1= 1.33 &Omega;, R2= 1.72 &Omega;, and R2= 3.69 &Omega;. V1 and V3 are text 0.606 V and 3.31 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.608 V. What is the absolute value of the current through R1?


 * -a) 1.137E-01 A
 * -b) 1.251E-01 A
 * -c) 1.376E-01 A
 * +d) 1.514E-01 A
 * -e) 1.665E-01 A

9) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * +a) 3.551E+00 &Omega;
 * -b) 3.906E+00 &Omega;
 * -c) 4.297E+00 &Omega;
 * -d) 4.726E+00 &Omega;
 * -e) 5.199E+00 &Omega;

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.388E+01 N&middot;m2/C
 * +b) 1.526E+01 N&middot;m2/C
 * -c) 1.679E+01 N&middot;m2/C
 * -d) 1.847E+01 N&middot;m2/C
 * -e) 2.032E+01 N&middot;m2/C

Key: U0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * -a) 5.014E-14 N
 * -b) 5.515E-14 N
 * -c) 6.067E-14 N
 * -d) 6.674E-14 N
 * +e) 7.341E-14 N

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.8 (r&le;R) where a=2 nC&middot;m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?


 * +a) 2.079E+02 N/C
 * -b) 2.287E+02 N/C
 * -c) 2.516E+02 N/C
 * -d) 2.767E+02 N/C
 * -e) 3.044E+02 N/C

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.420E+01 N&middot;m2/C
 * -b) 4.862E+01 N&middot;m2/C
 * -c) 5.348E+01 N&middot;m2/C
 * -d) 5.882E+01 N&middot;m2/C
 * +e) 6.471E+01 N&middot;m2/C

4) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=19 V is x2 + y2 + z2 = R2, where R=


 * -a) 5.169E+00 m
 * -b) 5.686E+00 m
 * -c) 6.255E+00 m
 * -d) 6.880E+00 m
 * +e) 7.568E+00 m

5) A 12.0 V battery can move 26,000 C of charge. How many Joules does it deliver?


 * -a) 2.836E+05 J
 * +b) 3.120E+05 J
 * -c) 3.432E+05 J
 * -d) 3.775E+05 J
 * -e) 4.153E+05 J

6) In the figure shown C1=15.7 &mu;F, C2=2.87 &mu;F, and C3=5.46 &mu;F. The voltage source provides &epsilon;=5.38 V. What is the energy stored in C2?


 * -a) 6.890E+00 &mu;J
 * -b) 7.579E+00 &mu;J
 * -c) 8.337E+00 &mu;J
 * -d) 9.171E+00 &mu;J
 * +e) 1.009E+01 &mu;J

7) A make-believe metal has a density of 3.530E+03 kg/m3 and an atomic mass of 10.5 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 1.673E+29 e&minus;/m3
 * -b) 1.840E+29 e&minus;/m3
 * +c) 2.024E+29 e&minus;/m3
 * -d) 2.226E+29 e&minus;/m3
 * -e) 2.449E+29 e&minus;/m3

8) Calculate the drift speed of electrons in a copper wire with a diameter of 3.17 mm carrying a 12.0 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * +a) 1.138E-04 m/s
 * -b) 1.252E-04 m/s
 * -c) 1.377E-04 m/s
 * -d) 1.515E-04 m/s
 * -e) 1.666E-04 m/s

9) Two sources of emf &epsilon;1=40.7 V, and  &epsilon;2=12.3 V are oriented as shownin the circuit. The resistances are R1=3.5 k&Omega; and  R2=1.94 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.42 mA and I4=0.932 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * +a) 1.440E+01 V
 * -b) 1.584E+01 V
 * -c) 1.742E+01 V
 * -d) 1.916E+01 V
 * -e) 2.108E+01 V

10) The resistances in the figure shown are R1= 1.57 &Omega;, R2= 1.25 &Omega;, and R2= 3.38 &Omega;. V1 and V3 are text 0.585 V and 2.91 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.55 V. What is the absolute value of the current through R1?


 * -a) 1.427E-01 A
 * -b) 1.569E-01 A
 * +c) 1.726E-01 A
 * -d) 1.899E-01 A
 * -e) 2.089E-01 A

Key: U1
1) A make-believe metal has a density of 2.670E+03 kg/m3 and an atomic mass of 40.9 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 3.930E+28 e&minus;/m3
 * -b) 4.323E+28 e&minus;/m3
 * -c) 4.755E+28 e&minus;/m3
 * -d) 5.231E+28 e&minus;/m3
 * -e) 5.754E+28 e&minus;/m3

2) If a 24 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=97 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.838E+00 m
 * -b) 2.022E+00 m
 * +c) 2.224E+00 m
 * -d) 2.446E+00 m
 * -e) 2.691E+00 m

3) Calculate the drift speed of electrons in a copper wire with a diameter of 5.47 mm carrying a 3.48 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 1.008E-05 m/s
 * +b) 1.108E-05 m/s
 * -c) 1.219E-05 m/s
 * -d) 1.341E-05 m/s
 * -e) 1.475E-05 m/s

4) Two sources of emf &epsilon;1=36.7 V, and  &epsilon;2=12.1 V are oriented as shownin the circuit. The resistances are R1=2.52 k&Omega; and  R2=1.22 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.14 mA and I4=1.19 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 7.805E+00 V
 * -b) 8.586E+00 V
 * -c) 9.444E+00 V
 * -d) 1.039E+01 V
 * +e) 1.143E+01 V

5) The resistances in the figure shown are R1= 2.49 &Omega;, R2= 1.72 &Omega;, and R2= 3.58 &Omega;. V1 and V3 are text 0.417 V and 1.83 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.53 V. What is the absolute value of the current through R1?


 * -a) 8.220E-02 A
 * -b) 9.042E-02 A
 * -c) 9.946E-02 A
 * +d) 1.094E-01 A
 * -e) 1.203E-01 A

6) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?


 * +a) 4.782E+02 N/C
 * -b) 5.260E+02 N/C
 * -c) 5.787E+02 N/C
 * -d) 6.365E+02 N/C
 * -e) 7.002E+02 N/C

7) A 12.0 V battery can move 30,000 C of charge. How many Joules does it deliver?


 * -a) 3.273E+05 J
 * +b) 3.600E+05 J
 * -c) 3.960E+05 J
 * -d) 4.356E+05 J
 * -e) 4.792E+05 J

8) In the figure shown C1=16.7 &mu;F, C2=2.26 &mu;F, and C3=4.53 &mu;F. The voltage source provides &epsilon;=10.7 V. What is the energy stored in C2?


 * -a) 1.292E+01 &mu;J
 * -b) 1.421E+01 &mu;J
 * -c) 1.563E+01 &mu;J
 * +d) 1.719E+01 &mu;J
 * -e) 1.891E+01 &mu;J

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.214E+01 N&middot;m2/C
 * -b) 2.436E+01 N&middot;m2/C
 * -c) 2.679E+01 N&middot;m2/C
 * -d) 2.947E+01 N&middot;m2/C
 * +e) 3.242E+01 N&middot;m2/C

10) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=2e$$?


 * -a) 3.391E-14 N
 * -b) 3.731E-14 N
 * -c) 4.104E-14 N
 * +d) 4.514E-14 N
 * -e) 4.965E-14 N

Key: U2
1) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=3 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?


 * -a) 4.874E+01 N/C
 * +b) 5.362E+01 N/C
 * -c) 5.898E+01 N/C
 * -d) 6.488E+01 N/C
 * -e) 7.137E+01 N/C

2) A make-believe metal has a density of 5.880E+03 kg/m3 and an atomic mass of 87.4 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 3.347E+28 e&minus;/m3
 * -b) 3.682E+28 e&minus;/m3
 * +c) 4.050E+28 e&minus;/m3
 * -d) 4.455E+28 e&minus;/m3
 * -e) 4.901E+28 e&minus;/m3

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.695E+01 N&middot;m2/C
 * -b) 4.065E+01 N&middot;m2/C
 * -c) 4.472E+01 N&middot;m2/C
 * -d) 4.919E+01 N&middot;m2/C
 * +e) 5.411E+01 N&middot;m2/C

4) The resistances in the figure shown are R1= 1.81 &Omega;, R2= 1.18 &Omega;, and R2= 2.62 &Omega;. V1 and V3 are text 0.628 V and 2.54 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.748 V. What is the absolute value of the current through R1?


 * -a) 1.552E-01 A
 * -b) 1.707E-01 A
 * -c) 1.878E-01 A
 * -d) 2.065E-01 A
 * +e) 2.272E-01 A

5) In the figure shown C1=18.2 &mu;F, C2=2.44 &mu;F, and C3=5.0 &mu;F. The voltage source provides &epsilon;=7.78 V. What is the energy stored in C2?


 * -a) 1.225E+01 &mu;J
 * +b) 1.347E+01 &mu;J
 * -c) 1.482E+01 &mu;J
 * -d) 1.630E+01 &mu;J
 * -e) 1.793E+01 &mu;J

6) Calculate the drift speed of electrons in a copper wire with a diameter of 5.46 mm carrying a 8.19 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.


 * -a) 2.380E-05 m/s
 * +b) 2.618E-05 m/s
 * -c) 2.880E-05 m/s
 * -d) 3.168E-05 m/s
 * -e) 3.485E-05 m/s

7) Two sources of emf &epsilon;1=34.7 V, and  &epsilon;2=13.9 V are oriented as shownin the circuit. The resistances are R1=3.68 k&Omega; and  R2=1.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=5.68 mA and I4=0.933 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?


 * -a) 9.286E+00 V
 * -b) 1.021E+01 V
 * -c) 1.124E+01 V
 * +d) 1.236E+01 V
 * -e) 1.360E+01 V

8) If a 28 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=77 V is x2 + y2 + z2 = R2, where R=


 * -a) 2.701E+00 m
 * -b) 2.971E+00 m
 * +c) 3.268E+00 m
 * -d) 3.595E+00 m
 * -e) 3.955E+00 m

9) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=4e$$?


 * -a) 8.613E-15 N
 * -b) 9.474E-15 N
 * -c) 1.042E-14 N
 * +d) 1.146E-14 N
 * -e) 1.261E-14 N

10) A 12.0 V battery can move 29,000 C of charge. How many Joules does it deliver?


 * -a) 2.615E+05 J
 * -b) 2.876E+05 J
 * -c) 3.164E+05 J
 * +d) 3.480E+05 J
 * -e) 3.828E+05 J

Key: V0
1) A large thin isolated square plate has an area of 5 m2. It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?


 * -a) 6.534E+01 N/C
 * -b) 7.187E+01 N/C
 * +c) 7.906E+01 N/C
 * -d) 8.696E+01 N/C
 * -e) 9.566E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k$$


 * -a) 1.997E+03 V&middot;m
 * +b) 2.197E+03 V&middot;m
 * -c) 2.417E+03 V&middot;m
 * -d) 2.659E+03 V&middot;m
 * -e) 2.924E+03 V&middot;m

3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.420E+01 N&middot;m2/C
 * -b) 4.862E+01 N&middot;m2/C
 * -c) 5.348E+01 N&middot;m2/C
 * -d) 5.882E+01 N&middot;m2/C
 * +e) 6.471E+01 N&middot;m2/C

4) When a 6.24 V battery operates a 2.1 W bulb, how many electrons pass through it each second?


 * -a) 1.435E+18 electrons
 * -b) 1.578E+18 electrons
 * -c) 1.736E+18 electrons
 * -d) 1.910E+18 electrons
 * +e) 2.101E+18 electrons

5) Two large parallel conducting plates are separated by 9.58 mm. Equal and opposite surface charges of 7.360E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 84 V?


 * -a) 6.644E-01 mm
 * -b) 7.641E-01 mm
 * -c) 8.787E-01 mm
 * +d) 1.011E+00 mm
 * -e) 1.162E+00 mm

6) In the figure shown C1=17.7 &mu;F, C2=2.48 &mu;F, and C3=4.68 &mu;F. The voltage source provides &epsilon;=12.7 V. What is the energy stored in C2?


 * +a) 2.242E+01 &mu;J
 * -b) 2.467E+01 &mu;J
 * -c) 2.713E+01 &mu;J
 * -d) 2.985E+01 &mu;J
 * -e) 3.283E+01 &mu;J

7) A make-believe metal has a density of 8.060E+03 kg/m3 and an atomic mass of 19.7 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 1.850E+29 e&minus;/m3
 * -b) 2.036E+29 e&minus;/m3
 * -c) 2.239E+29 e&minus;/m3
 * +d) 2.463E+29 e&minus;/m3
 * -e) 2.709E+29 e&minus;/m3

8) What is consumer cost to operate one 79&minus;W incandescent bulb for 9 hours per day for 1 year (365 days) if the cost of electricity is $0.142 per kilowatt-hour?


 * -a) $2.517E+01
 * -b) $2.769E+01
 * -c) $3.046E+01
 * -d) $3.350E+01
 * +e) $3.685E+01

9) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 301 V.  If the combined external and internal resistance is 245 &Omega and the capacitance is  63 mF, how long will it take for the capacitor's voltage to reach 192.0 V?


 * -a) 1.296E+01 s
 * -b) 1.425E+01 s
 * +c) 1.568E+01 s
 * -d) 1.725E+01 s
 * -e) 1.897E+01 s

10) A battery with a terminal voltage of 14.6 V is connected to a circuit consisting of 2 21.7 &Omega; resistors and one 14.4 &Omega; resistor. What is the voltage drop across the 14.4 &Omega; resistor?


 * +a) 3.637E+00 V
 * -b) 4.001E+00 V
 * -c) 4.401E+00 V
 * -d) 4.841E+00 V
 * -e) 5.325E+00 V

Key: V1
1) A battery with a terminal voltage of 8.14 V is connected to a circuit consisting of 2 21.5 &Omega; resistors and one 13.1 &Omega; resistor. What is the voltage drop across the 13.1 &Omega; resistor?


 * -a) 1.298E+00 V
 * -b) 1.428E+00 V
 * -c) 1.571E+00 V
 * -d) 1.728E+00 V
 * +e) 1.901E+00 V

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is, $$\vec E=3y^{2.8}\hat i +1x^{2.3}\hat j +2y^{2.9}\hat k$$


 * -a) 2.210E+04 V&middot;m
 * +b) 2.431E+04 V&middot;m
 * -c) 2.674E+04 V&middot;m
 * -d) 2.941E+04 V&middot;m
 * -e) 3.235E+04 V&middot;m

3) A make-believe metal has a density of 1.050E+04 kg/m3 and an atomic mass of 58.8 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * +a) 1.075E+29 e&minus;/m3
 * -b) 1.183E+29 e&minus;/m3
 * -c) 1.301E+29 e&minus;/m3
 * -d) 1.431E+29 e&minus;/m3
 * -e) 1.574E+29 e&minus;/m3

4) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?


 * -a) 6.525E-01 mm
 * +b) 7.504E-01 mm
 * -c) 8.629E-01 mm
 * -d) 9.923E-01 mm
 * -e) 1.141E+00 mm

5) In the figure shown C1=16.7 &mu;F, C2=2.26 &mu;F, and C3=4.53 &mu;F. The voltage source provides &epsilon;=10.7 V. What is the energy stored in C2?


 * -a) 1.292E+01 &mu;J
 * -b) 1.421E+01 &mu;J
 * -c) 1.563E+01 &mu;J
 * +d) 1.719E+01 &mu;J
 * -e) 1.891E+01 &mu;J

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.698E+01 N&middot;m2/C
 * -b) 1.868E+01 N&middot;m2/C
 * -c) 2.055E+01 N&middot;m2/C
 * -d) 2.260E+01 N&middot;m2/C
 * +e) 2.486E+01 N&middot;m2/C

7) A large thin isolated square plate has an area of 4 m2. It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?


 * -a) 9.546E+01 N/C
 * -b) 1.050E+02 N/C
 * -c) 1.155E+02 N/C
 * +d) 1.271E+02 N/C
 * -e) 1.398E+02 N/C

8) What is consumer cost to operate one 89&minus;W incandescent bulb for 10 hours per day for 1 year (365 days) if the cost of electricity is $0.141 per kilowatt-hour?


 * -a) $3.785E+01
 * -b) $4.164E+01
 * +c) $4.580E+01
 * -d) $5.038E+01
 * -e) $5.542E+01

9) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?


 * -a) 1.439E+18 electrons
 * +b) 1.582E+18 electrons
 * -c) 1.741E+18 electrons
 * -d) 1.915E+18 electrons
 * -e) 2.106E+18 electrons

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 327 V.  If the combined external and internal resistance is 204 &Omega and the capacitance is  68 mF, how long will it take for the capacitor's voltage to reach 218.0 V?


 * -a) 1.385E+01 s
 * +b) 1.524E+01 s
 * -c) 1.676E+01 s
 * -d) 1.844E+01 s
 * -e) 2.028E+01 s

Key: V2
1) In the figure shown C1=16.5 &mu;F, C2=2.7 &mu;F, and C3=4.82 &mu;F. The voltage source provides &epsilon;=15.7 V. What is the energy stored in C2?


 * -a) 2.188E+01 &mu;J
 * -b) 2.407E+01 &mu;J
 * -c) 2.647E+01 &mu;J
 * +d) 2.912E+01 &mu;J
 * -e) 3.203E+01 &mu;J

2) What is consumer cost to operate one 73&minus;W incandescent bulb for 11 hours per day for 1 year (365 days) if the cost of electricity is $0.113 per kilowatt-hour?


 * +a) $3.312E+01
 * -b) $3.643E+01
 * -c) $4.007E+01
 * -d) $4.408E+01
 * -e) $4.849E+01

3) A large thin isolated square plate has an area of 8 m2. It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?


 * -a) 4.492E+01 N/C
 * +b) 4.941E+01 N/C
 * -c) 5.435E+01 N/C
 * -d) 5.979E+01 N/C
 * -e) 6.577E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is, $$\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k$$


 * -a) 8.731E+02 V&middot;m
 * -b) 9.604E+02 V&middot;m
 * -c) 1.056E+03 V&middot;m
 * +d) 1.162E+03 V&middot;m
 * -e) 1.278E+03 V&middot;m

5) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 8.457E+01 N&middot;m2/C
 * +b) 9.303E+01 N&middot;m2/C
 * -c) 1.023E+02 N&middot;m2/C
 * -d) 1.126E+02 N&middot;m2/C
 * -e) 1.238E+02 N&middot;m2/C

6) A make-believe metal has a density of 7.000E+03 kg/m3 and an atomic mass of 89.4 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.


 * -a) 3.219E+28 e&minus;/m3
 * -b) 3.541E+28 e&minus;/m3
 * -c) 3.896E+28 e&minus;/m3
 * -d) 4.285E+28 e&minus;/m3
 * +e) 4.714E+28 e&minus;/m3

7) A battery with a terminal voltage of 14.1 V is connected to a circuit consisting of 3 15.7 &Omega; resistors and one 10.2 &Omega; resistor. What is the voltage drop across the 10.2 &Omega; resistor?


 * -a) 2.074E+00 V
 * -b) 2.282E+00 V
 * +c) 2.510E+00 V
 * -d) 2.761E+00 V
 * -e) 3.037E+00 V

8) When a 7.1 V battery operates a 1.8 W bulb, how many electrons pass through it each second?


 * -a) 1.439E+18 electrons
 * +b) 1.582E+18 electrons
 * -c) 1.741E+18 electrons
 * -d) 1.915E+18 electrons
 * -e) 2.106E+18 electrons

9) Two large parallel conducting plates are separated by 6.67 mm. Equal and opposite surface charges of 7.080E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 60 V?


 * -a) 6.525E-01 mm
 * +b) 7.504E-01 mm
 * -c) 8.629E-01 mm
 * -d) 9.923E-01 mm
 * -e) 1.141E+00 mm

10) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 467 V.  If the combined external and internal resistance is 172 &Omega and the capacitance is  74 mF, how long will it take for the capacitor's voltage to reach 258.0 V?


 * -a) 7.688E+00 s
 * -b) 8.457E+00 s
 * -c) 9.303E+00 s
 * +d) 1.023E+01 s
 * -e) 1.126E+01 s

Key: W0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-8e$$, and $$q_3=6e$$?


 * -a) 5.243E+01 degrees
 * -b) 5.767E+01 degrees
 * +c) 6.343E+01 degrees
 * -d) 6.978E+01 degrees
 * -e) 7.676E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.134E+01 N&middot;m2/C
 * -b) 2.347E+01 N&middot;m2/C
 * +c) 2.582E+01 N&middot;m2/C
 * -d) 2.840E+01 N&middot;m2/C
 * -e) 3.124E+01 N&middot;m2/C

3) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=3 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?


 * -a) 4.874E+01 N/C
 * +b) 5.362E+01 N/C
 * -c) 5.898E+01 N/C
 * -d) 6.488E+01 N/C
 * -e) 7.137E+01 N/C

4) Two large parallel conducting plates are separated by 7.14 mm. Equal and opposite surface charges of 7.660E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?


 * -a) 4.031E-01 mm
 * -b) 4.636E-01 mm
 * -c) 5.332E-01 mm
 * -d) 6.131E-01 mm
 * +e) 7.051E-01 mm

5) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=61 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.107E+00 m
 * -b) 1.218E+00 m
 * -c) 1.339E+00 m
 * -d) 1.473E+00 m
 * +e) 1.621E+00 m

6) An empty parallel-plate capacitor with metal plates has an area of 2.16 m2, separated by 1.12 mm. How much charge does it store if the voltage is 1.530E+03 V?


 * -a) 2.375E+01 &mu;C
 * +b) 2.613E+01 &mu;C
 * -c) 2.874E+01 &mu;C
 * -d) 3.161E+01 &mu;C
 * -e) 3.477E+01 &mu;C

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.06 &Omega; at a temperature of 80&deg;C and that the temperature coefficient of expansion is 4.290E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 330 &deg;C?


 * -a) 1.196E+01 &Omega;
 * +b) 1.256E+01 &Omega;
 * -c) 1.319E+01 &Omega;
 * -d) 1.385E+01 &Omega;
 * -e) 1.454E+01 &Omega;

8) A DC winch moter draws 18 amps at 126 volts as it lifts a 5.830E+03 N weight at a constant speed of 0.26 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * -a) 1.919E+00 &Omega;
 * -b) 2.111E+00 &Omega;
 * +c) 2.322E+00 &Omega;
 * -d) 2.554E+00 &Omega;
 * -e) 2.809E+00 &Omega;

9) Two sources of emf &epsilon;1=28.6 V, and  &epsilon;2=11.1 V are oriented as shownin the circuit. The resistances are R1=3.73 k&Omega; and  R2=1.95 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.27 mA and I4=0.774 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 6.641E+00 V
 * +b) 7.305E+00 V
 * -c) 8.035E+00 V
 * -d) 8.839E+00 V
 * -e) 9.723E+00 V

10) A given battery has a 11 V emf and an internal resistance of 0.0998 &Omega;. If it is connected to a 0.417 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.419E+02 W
 * -b) 1.561E+02 W
 * -c) 1.717E+02 W
 * +d) 1.889E+02 W
 * -e) 2.078E+02 W

Key: W1
1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 3.750E+01 N&middot;m2/C
 * -b) 4.125E+01 N&middot;m2/C
 * -c) 4.537E+01 N&middot;m2/C
 * +d) 4.991E+01 N&middot;m2/C
 * -e) 5.490E+01 N&middot;m2/C

2) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=61 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.107E+00 m
 * -b) 1.218E+00 m
 * -c) 1.339E+00 m
 * -d) 1.473E+00 m
 * +e) 1.621E+00 m

3) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 &Omega; at a temperature of 82&deg;C and that the temperature coefficient of expansion is 4.530E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 390 &deg;C?


 * -a) 7.532E+00 &Omega;
 * -b) 7.908E+00 &Omega;
 * -c) 8.303E+00 &Omega;
 * +d) 8.719E+00 &Omega;
 * -e) 9.155E+00 &Omega;

4) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=8.29 V are oriented as shownin the circuit. The resistances are R1=3.43 k&Omega; and  R2=1.16 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.09 mA and I4=1.06 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 6.720E+00 V
 * -b) 7.392E+00 V
 * -c) 8.131E+00 V
 * -d) 8.944E+00 V
 * +e) 9.838E+00 V

5) A given battery has a 15 V emf and an internal resistance of 0.177 &Omega;. If it is connected to a 0.824 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.682E+02 W
 * +b) 1.850E+02 W
 * -c) 2.035E+02 W
 * -d) 2.239E+02 W
 * -e) 2.463E+02 W

6) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-8e$$, and $$q_3=6e$$?


 * -a) 5.243E+01 degrees
 * -b) 5.767E+01 degrees
 * +c) 6.343E+01 degrees
 * -d) 6.978E+01 degrees
 * -e) 7.676E+01 degrees

7) A DC winch moter draws 20 amps at 175 volts as it lifts a 5.180E+03 N weight at a constant speed of 0.541 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * +a) 1.744E+00 &Omega;
 * -b) 1.918E+00 &Omega;
 * -c) 2.110E+00 &Omega;
 * -d) 2.321E+00 &Omega;
 * -e) 2.553E+00 &Omega;

8) Two large parallel conducting plates are separated by 8.7 mm. Equal and opposite surface charges of 7.220E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 67 V?


 * -a) 4.698E-01 mm
 * -b) 5.402E-01 mm
 * -c) 6.213E-01 mm
 * -d) 7.145E-01 mm
 * +e) 8.216E-01 mm

9) An empty parallel-plate capacitor with metal plates has an area of 2.51 m2, separated by 1.44 mm. How much charge does it store if the voltage is 2.230E+03 V?


 * -a) 2.351E+01 &mu;C
 * -b) 2.586E+01 &mu;C
 * -c) 2.844E+01 &mu;C
 * -d) 3.129E+01 &mu;C
 * +e) 3.442E+01 &mu;C

10) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.2 (r&le;R) where a=2 nC&middot;m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?


 * +a) 4.782E+02 N/C
 * -b) 5.260E+02 N/C
 * -c) 5.787E+02 N/C
 * -d) 6.365E+02 N/C
 * -e) 7.002E+02 N/C

Key: W2
1) A DC winch moter draws 19 amps at 175 volts as it lifts a 4.230E+03 N weight at a constant speed of 0.483 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.


 * +a) 3.551E+00 &Omega;
 * -b) 3.906E+00 &Omega;
 * -c) 4.297E+00 &Omega;
 * -d) 4.726E+00 &Omega;
 * -e) 5.199E+00 &Omega;

2) A given battery has a 14 V emf and an internal resistance of 0.132 &Omega;. If it is connected to a 0.689 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.656E+02 W
 * -b) 1.821E+02 W
 * +c) 2.003E+02 W
 * -d) 2.204E+02 W
 * -e) 2.424E+02 W

3) Two large parallel conducting plates are separated by 6.86 mm. Equal and opposite surface charges of 7.540E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 79 V?


 * -a) 6.100E-01 mm
 * -b) 7.015E-01 mm
 * -c) 8.067E-01 mm
 * +d) 9.277E-01 mm
 * -e) 1.067E+00 mm

4) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=5e$$?


 * -a) 3.961E+01 degrees
 * -b) 4.357E+01 degrees
 * -c) 4.793E+01 degrees
 * -d) 5.272E+01 degrees
 * +e) 5.799E+01 degrees

5) Two sources of emf &epsilon;1=26.8 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.2 k&Omega; and  R2=2.55 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.29 mA and I4=0.464 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 3.436E+00 V
 * -b) 3.779E+00 V
 * -c) 4.157E+00 V
 * -d) 4.573E+00 V
 * +e) 5.030E+00 V

6) An empty parallel-plate capacitor with metal plates has an area of 2.21 m2, separated by 1.25 mm. How much charge does it store if the voltage is 1.580E+03 V?


 * -a) 2.249E+01 &mu;C
 * +b) 2.473E+01 &mu;C
 * -c) 2.721E+01 &mu;C
 * -d) 2.993E+01 &mu;C
 * -e) 3.292E+01 &mu;C

7) If a 11 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=43 V is x2 + y2 + z2 = R2, where R=


 * +a) 2.299E+00 m
 * -b) 2.529E+00 m
 * -c) 2.782E+00 m
 * -d) 3.060E+00 m
 * -e) 3.366E+00 m

8) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=2 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?


 * -a) 3.821E+02 N/C
 * -b) 4.203E+02 N/C
 * -c) 4.624E+02 N/C
 * +d) 5.086E+02 N/C
 * -e) 5.594E+02 N/C

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.777E+01 N&middot;m2/C
 * -b) 5.254E+01 N&middot;m2/C
 * -c) 5.780E+01 N&middot;m2/C
 * +d) 6.358E+01 N&middot;m2/C
 * -e) 6.993E+01 N&middot;m2/C

10) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.95 &Omega; at a temperature of 96&deg;C and that the temperature coefficient of expansion is 4.400E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 469 &deg;C?


 * -a) 4.449E+00 &Omega;
 * -b) 4.672E+00 &Omega;
 * -c) 4.905E+00 &Omega;
 * +d) 5.150E+00 &Omega;
 * -e) 5.408E+00 &Omega;

Key: X0
1) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=0.76 m, b=1.7 m.  The total charge on the rod is 8 nC.


 * -a) 1.399E+01 V/m2
 * +b) 1.539E+01 V/m2
 * -c) 1.693E+01 V/m2
 * -d) 1.862E+01 V/m2
 * -e) 2.049E+01 V/m2

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * -a) 1.969E+02 V&middot;m
 * -b) 2.166E+02 V&middot;m
 * -c) 2.383E+02 V&middot;m
 * -d) 2.621E+02 V&middot;m
 * +e) 2.883E+02 V&middot;m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?


 * -a) 3.251E+01 N/C
 * -b) 3.577E+01 N/C
 * -c) 3.934E+01 N/C
 * -d) 4.328E+01 N/C
 * +e) 4.760E+01 N/C

4) If a 23 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=62 V is x2 + y2 + z2 = R2, where R=


 * -a) 2.277E+00 m
 * -b) 2.505E+00 m
 * -c) 2.755E+00 m
 * -d) 3.031E+00 m
 * +e) 3.334E+00 m

5) A diploe has a charge magnitude of q=4 nC and a separation distance of d=4.07 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.88 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * -a) 2.164E+02 V
 * -b) 2.381E+02 V
 * -c) 2.619E+02 V
 * +d) 2.880E+02 V
 * -e) 3.168E+02 V

6) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * -a) 5.969E+01 &mu;C
 * -b) 6.566E+01 &mu;C
 * +c) 7.222E+01 &mu;C
 * -d) 7.944E+01 &mu;C
 * -e) 8.739E+01 &mu;C

7) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 &Omega; at a temperature of 82&deg;C and that the temperature coefficient of expansion is 4.530E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 390 &deg;C?


 * -a) 7.532E+00 &Omega;
 * -b) 7.908E+00 &Omega;
 * -c) 8.303E+00 &Omega;
 * +d) 8.719E+00 &Omega;
 * -e) 9.155E+00 &Omega;

8) Calculate the electric field in a 12-gauge copper wire that is 16 m long and carries a current of 58 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.212E-04 V/m
 * -b) 2.433E-04 V/m
 * -c) 2.676E-04 V/m
 * +d) 2.944E-04 V/m
 * -e) 3.238E-04 V/m

9) Two sources of emf &epsilon;1=38.8 V, and  &epsilon;2=14.9 V are oriented as shownin the circuit. The resistances are R1=5.83 k&Omega; and  R2=1.77 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.57 mA and I4=1.19 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 1.013E+01 V
 * -b) 1.115E+01 V
 * -c) 1.226E+01 V
 * +d) 1.349E+01 V
 * -e) 1.484E+01 V

10) A given battery has a 13 V emf and an internal resistance of 0.159 &Omega;. If it is connected to a 0.617 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.301E+02 W
 * -b) 1.431E+02 W
 * -c) 1.574E+02 W
 * +d) 1.732E+02 W
 * -e) 1.905E+02 W

Key: X1
1) A diploe has a charge magnitude of q=7 nC and a separation distance of d=4.08 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.16 cm, y=2.04 cm)? Note that following the textbook's example, the y-value of the field point at 2.04 cm matches the disance of the positive charge above the x-axis.


 * -a) 7.017E+02 V
 * +b) 7.718E+02 V
 * -c) 8.490E+02 V
 * -d) 9.339E+02 V
 * -e) 1.027E+03 V

2) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.73 m if a=0.52 m, b=1.6 m.  The total charge on the rod is 7 nC.


 * -a) 9.655E+00 V/m2
 * -b) 1.062E+01 V/m2
 * -c) 1.168E+01 V/m2
 * +d) 1.285E+01 V/m2
 * -e) 1.414E+01 V/m2

3) Two sources of emf &epsilon;1=26.2 V, and  &epsilon;2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.11 mA and I4=0.746 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 4.275E+00 V
 * -b) 4.703E+00 V
 * +c) 5.173E+00 V
 * -d) 5.691E+00 V
 * -e) 6.260E+00 V

4) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.52 &Omega; at a temperature of 45&deg;C and that the temperature coefficient of expansion is 4.330E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 479 &deg;C?


 * -a) 3.970E+00 &Omega;
 * -b) 4.168E+00 &Omega;
 * +c) 4.376E+00 &Omega;
 * -d) 4.595E+00 &Omega;
 * -e) 4.825E+00 &Omega;

5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?


 * -a) 1.096E+00 N/C
 * -b) 1.206E+00 N/C
 * -c) 1.327E+00 N/C
 * -d) 1.459E+00 N/C
 * +e) 1.605E+00 N/C

6) In the figure shown C1=19.0 &mu;F, C2=2.35 &mu;F, and C3=5.22 &mu;F. The voltage source provides &epsilon;=6.01 V. What is the charge on C1?


 * -a) 2.444E+01 &mu;C
 * -b) 2.689E+01 &mu;C
 * -c) 2.958E+01 &mu;C
 * +d) 3.253E+01 &mu;C
 * -e) 3.579E+01 &mu;C

7) A given battery has a 15 V emf and an internal resistance of 0.0536 &Omega;. If it is connected to a 0.64 &Omega; resistor what is the power dissipated by that load?


 * -a) 2.721E+02 W
 * +b) 2.993E+02 W
 * -c) 3.293E+02 W
 * -d) 3.622E+02 W
 * -e) 3.984E+02 W

8) Calculate the electric field in a 12-gauge copper wire that is 99 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 3.604E-04 V/m
 * -b) 3.964E-04 V/m
 * -c) 4.360E-04 V/m
 * -d) 4.796E-04 V/m
 * -e) 5.276E-04 V/m

9) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=19 V is x2 + y2 + z2 = R2, where R=


 * -a) 5.169E+00 m
 * -b) 5.686E+00 m
 * -c) 6.255E+00 m
 * -d) 6.880E+00 m
 * +e) 7.568E+00 m

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k$$


 * +a) 3.429E+03 V&middot;m
 * -b) 3.771E+03 V&middot;m
 * -c) 4.149E+03 V&middot;m
 * -d) 4.564E+03 V&middot;m
 * -e) 5.020E+03 V&middot;m

Key: X2
1) A diploe has a charge magnitude of q=5 nC and a separation distance of d=4.29 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.33 cm, y=2.15 cm)? Note that following the textbook's example, the y-value of the field point at 2.15 cm matches the disance of the positive charge above the x-axis.


 * -a) 4.324E+02 V
 * -b) 4.757E+02 V
 * +c) 5.232E+02 V
 * -d) 5.755E+02 V
 * -e) 6.331E+02 V

2) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.61 m, b=1.7 m.  The total charge on the rod is 8 nC.


 * -a) 5.995E+00 V/m2
 * -b) 6.595E+00 V/m2
 * +c) 7.254E+00 V/m2
 * -d) 7.980E+00 V/m2
 * -e) 8.778E+00 V/m2

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?


 * -a) 3.251E+01 N/C
 * -b) 3.577E+01 N/C
 * -c) 3.934E+01 N/C
 * -d) 4.328E+01 N/C
 * +e) 4.760E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k$$


 * -a) 1.997E+03 V&middot;m
 * +b) 2.197E+03 V&middot;m
 * -c) 2.417E+03 V&middot;m
 * -d) 2.659E+03 V&middot;m
 * -e) 2.924E+03 V&middot;m

5) In the figure shown C1=17.9 &mu;F, C2=2.76 &mu;F, and C3=5.12 &mu;F. The voltage source provides &epsilon;=13.2 V. What is the charge on C1?


 * -a) 5.969E+01 &mu;C
 * -b) 6.566E+01 &mu;C
 * +c) 7.222E+01 &mu;C
 * -d) 7.944E+01 &mu;C
 * -e) 8.739E+01 &mu;C

6) Calculate the electric field in a 12-gauge copper wire that is 41 m long and carries a current of 71 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * +a) 3.604E-04 V/m
 * -b) 3.964E-04 V/m
 * -c) 4.360E-04 V/m
 * -d) 4.796E-04 V/m
 * -e) 5.276E-04 V/m

7) If a 16 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=76 V is x2 + y2 + z2 = R2, where R=


 * -a) 1.422E+00 m
 * -b) 1.564E+00 m
 * -c) 1.720E+00 m
 * +d) 1.892E+00 m
 * -e) 2.081E+00 m

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.74 &Omega; at a temperature of 89&deg;C and that the temperature coefficient of expansion is 4.990E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 366 &deg;C?


 * -a) 1.529E+01 &Omega;
 * +b) 1.606E+01 &Omega;
 * -c) 1.686E+01 &Omega;
 * -d) 1.770E+01 &Omega;
 * -e) 1.859E+01 &Omega;

9) A given battery has a 10 V emf and an internal resistance of 0.119 &Omega;. If it is connected to a 0.445 &Omega; resistor what is the power dissipated by that load?


 * -a) 1.272E+02 W
 * +b) 1.399E+02 W
 * -c) 1.539E+02 W
 * -d) 1.693E+02 W
 * -e) 1.862E+02 W

10) Two sources of emf &epsilon;1=52.7 V, and  &epsilon;2=17.5 V are oriented as shownin the circuit. The resistances are R1=5.86 k&Omega; and  R2=2.08 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.48 mA and I4=0.988 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * +a) 2.064E+01 V
 * -b) 2.270E+01 V
 * -c) 2.497E+01 V
 * -d) 2.747E+01 V
 * -e) 3.021E+01 V

Key: Y0
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?


 * -a) 3.629E+01 degrees
 * -b) 3.992E+01 degrees
 * -c) 4.391E+01 degrees
 * -d) 4.830E+01 degrees
 * +e) 5.313E+01 degrees

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 13.0m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.953E+01 N&middot;m2/C
 * -b) 5.449E+01 N&middot;m2/C
 * -c) 5.993E+01 N&middot;m2/C
 * -d) 6.593E+01 N&middot;m2/C
 * +e) 7.252E+01 N&middot;m2/C

3) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.5 (r&le;R) where a=2 nC&middot;m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?


 * +a) 2.285E+01 N/C
 * -b) 2.514E+01 N/C
 * -c) 2.765E+01 N/C
 * -d) 3.042E+01 N/C
 * -e) 3.346E+01 N/C

4) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=9 &mu;C, and q4=11 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 4.554E+01 J
 * -b) 5.009E+01 J
 * -c) 5.510E+01 J
 * +d) 6.061E+01 J
 * -e) 6.667E+01 J

5) When a 6.24 V battery operates a 2.1 W bulb, how many electrons pass through it each second?


 * -a) 1.435E+18 electrons
 * -b) 1.578E+18 electrons
 * -c) 1.736E+18 electrons
 * -d) 1.910E+18 electrons
 * +e) 2.101E+18 electrons

6) In the figure shown C1=17.7 &mu;F, C2=2.48 &mu;F, and C3=4.68 &mu;F. The voltage source provides &epsilon;=12.7 V. What is the energy stored in C2?


 * +a) 2.242E+01 &mu;J
 * -b) 2.467E+01 &mu;J
 * -c) 2.713E+01 &mu;J
 * -d) 2.985E+01 &mu;J
 * -e) 3.283E+01 &mu;J

7) A device requires consumes 196 W of power and requires 2.4 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * +a) 4.563E+05 A/m2
 * -b) 5.019E+05 A/m2
 * -c) 5.521E+05 A/m2
 * -d) 6.073E+05 A/m2
 * -e) 6.680E+05 A/m2

8) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 4.957E-02 &Omega;
 * -b) 5.453E-02 &Omega;
 * -c) 5.998E-02 &Omega;
 * +d) 6.598E-02 &Omega;
 * -e) 7.258E-02 &Omega;

9) Two sources of emf &epsilon;1=27.1 V, and  &epsilon;2=8.04 V are oriented as shownin the circuit. The resistances are R1=2.94 k&Omega; and  R2=1.61 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.87 mA and I4=0.57 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.482E+00 V
 * +b) 9.330E+00 V
 * -c) 1.026E+01 V
 * -d) 1.129E+01 V
 * -e) 1.242E+01 V

10) Two sources of emf &epsilon;1=29.5 V, and  &epsilon;2=11.0 V are oriented as shownin the circuit. The resistances are R1=2.45 k&Omega; and  R2=1.96 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.03 mA and I4=0.783 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 2.247E+00 mA
 * -b) 2.472E+00 mA
 * -c) 2.719E+00 mA
 * -d) 2.991E+00 mA
 * -e) 3.290E+00 mA

Key: Y1
1) A device requires consumes 72 W of power and requires 11.7 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * -a) 1.519E+06 A/m2
 * -b) 1.671E+06 A/m2
 * -c) 1.838E+06 A/m2
 * -d) 2.022E+06 A/m2
 * +e) 2.224E+06 A/m2

2) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=2 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?


 * +a) 2.406E+01 N/C
 * -b) 2.646E+01 N/C
 * -c) 2.911E+01 N/C
 * -d) 3.202E+01 N/C
 * -e) 3.522E+01 N/C

3) Calculate the resistance of a 12-gauge copper wire that is 13 m long and carries a current of 22 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 4.957E-02 &Omega;
 * -b) 5.453E-02 &Omega;
 * -c) 5.998E-02 &Omega;
 * +d) 6.598E-02 &Omega;
 * -e) 7.258E-02 &Omega;

4) Two sources of emf &epsilon;1=16.8 V, and  &epsilon;2=7.15 V are oriented as shownin the circuit. The resistances are R1=3.12 k&Omega; and  R2=1.51 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.95 mA and I4=0.603 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 4.108E+00 V
 * +b) 4.519E+00 V
 * -c) 4.970E+00 V
 * -d) 5.468E+00 V
 * -e) 6.014E+00 V

5) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?


 * -a) 4.766E+01 degrees
 * -b) 5.243E+01 degrees
 * -c) 5.767E+01 degrees
 * +d) 6.343E+01 degrees
 * -e) 6.978E+01 degrees

6) Four charges lie at the corners of a 4 cm by 4 cm square as shown (i.e., a=b=4 cm.)  The charges are q1=3 &mu;C, q2=6 &mu;C, q3=7 &mu;C, and q4=10 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 4.438E+01 J
 * +b) 4.882E+01 J
 * -c) 5.370E+01 J
 * -d) 5.907E+01 J
 * -e) 6.498E+01 J

7) When a 2.76 V battery operates a 2.71 W bulb, how many electrons pass through it each second?


 * -a) 5.571E+18 electrons
 * +b) 6.128E+18 electrons
 * -c) 6.741E+18 electrons
 * -d) 7.415E+18 electrons
 * -e) 8.157E+18 electrons

8) Two sources of emf &epsilon;1=24.9 V, and  &epsilon;2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 k&Omega; and  R2=2.31 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.74 mA and I4=0.444 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 1.725E+00 mA
 * -b) 1.898E+00 mA
 * -c) 2.087E+00 mA
 * +d) 2.296E+00 mA
 * -e) 2.526E+00 mA

9) In the figure shown C1=15.4 &mu;F, C2=2.6 &mu;F, and C3=5.17 &mu;F. The voltage source provides &epsilon;=9.6 V. What is the energy stored in C2?


 * -a) 1.508E+01 &mu;J
 * +b) 1.659E+01 &mu;J
 * -c) 1.825E+01 &mu;J
 * -d) 2.007E+01 &mu;J
 * -e) 2.208E+01 &mu;J

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 6.192E+01 N&middot;m2/C
 * -b) 6.811E+01 N&middot;m2/C
 * -c) 7.492E+01 N&middot;m2/C
 * -d) 8.242E+01 N&middot;m2/C
 * -e) 9.066E+01 N&middot;m2/C

Key: Y2
1) When a 6.32 V battery operates a 1.94 W bulb, how many electrons pass through it each second?


 * -a) 1.439E+18 electrons
 * -b) 1.583E+18 electrons
 * -c) 1.742E+18 electrons
 * +d) 1.916E+18 electrons
 * -e) 2.107E+18 electrons

2) A non-conducting sphere of radius R=2.2 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.4 (r&le;R) where a=3 nC&middot;m-1.6. What is the magnitude of the electric field at a distance of 0.86 m from the center?


 * -a) 4.874E+01 N/C
 * +b) 5.362E+01 N/C
 * -c) 5.898E+01 N/C
 * -d) 6.488E+01 N/C
 * -e) 7.137E+01 N/C

3) Four charges lie at the corners of a 3 cm by 3 cm square as shown (i.e., a=b=3 cm.)  The charges are q1=4 &mu;C, q2=5 &mu;C, q3=7 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?


 * -a) 3.910E+01 J
 * -b) 4.301E+01 J
 * -c) 4.731E+01 J
 * -d) 5.204E+01 J
 * +e) 5.725E+01 J

4) Calculate the resistance of a 12-gauge copper wire that is 69 m long and carries a current of 98 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.


 * -a) 2.631E-01 &Omega;
 * -b) 2.894E-01 &Omega;
 * -c) 3.184E-01 &Omega;
 * +d) 3.502E-01 &Omega;
 * -e) 3.852E-01 &Omega;

5) A device requires consumes 177 W of power and requires 6.82 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.


 * -a) 9.741E+05 A/m2
 * -b) 1.072E+06 A/m2
 * -c) 1.179E+06 A/m2
 * +d) 1.297E+06 A/m2
 * -e) 1.426E+06 A/m2

6) Two sources of emf &epsilon;1=43.7 V, and  &epsilon;2=13.1 V are oriented as shownin the circuit. The resistances are R1=5.21 k&Omega; and  R2=1.72 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.86 mA and I4=0.9 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * -a) 2.691E+00 mA
 * +b) 2.960E+00 mA
 * -c) 3.256E+00 mA
 * -d) 3.582E+00 mA
 * -e) 3.940E+00 mA

7) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=5e$$?


 * -a) 4.357E+01 degrees
 * -b) 4.793E+01 degrees
 * -c) 5.272E+01 degrees
 * +d) 5.799E+01 degrees
 * -e) 6.379E+01 degrees

8) In the figure shown C1=16.1 &mu;F, C2=2.14 &mu;F, and C3=5.76 &mu;F. The voltage source provides &epsilon;=8.35 V. What is the energy stored in C2?


 * +a) 1.199E+01 &mu;J
 * -b) 1.319E+01 &mu;J
 * -c) 1.450E+01 &mu;J
 * -d) 1.595E+01 &mu;J
 * -e) 1.755E+01 &mu;J

9) Two sources of emf &epsilon;1=30.3 V, and  &epsilon;2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 k&Omega; and  R2=2.39 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.38 mA and I4=0.416 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?


 * -a) 8.945E+00 V
 * +b) 9.840E+00 V
 * -c) 1.082E+01 V
 * -d) 1.191E+01 V
 * -e) 1.310E+01 V

10) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 8.5m2. Those in the xy plane have area 2.8m2 ,and those in the zx plane have area 3.7m2. An electric field has the xyz components (0, 7.4, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 2.079E+01 N&middot;m2/C
 * -b) 2.287E+01 N&middot;m2/C
 * -c) 2.516E+01 N&middot;m2/C
 * +d) 2.768E+01 N&middot;m2/C
 * -e) 3.044E+01 N&middot;m2/C

Key: Z0
1) A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?


 * -a) 1.202E+09 N/C2
 * -b) 1.322E+09 N/C2
 * -c) 1.454E+09 N/C2
 * -d) 1.599E+09 N/C2
 * +e) 1.759E+09 N/C2

2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 4.730E+01 N&middot;m2/C
 * +b) 5.203E+01 N&middot;m2/C
 * -c) 5.723E+01 N&middot;m2/C
 * -d) 6.295E+01 N&middot;m2/C
 * -e) 6.925E+01 N&middot;m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.0}\hat i +2x^{2.1}\hat j +3y^{2.5}\hat k$$


 * -a) 9.027E+03 V&middot;m
 * +b) 9.930E+03 V&middot;m
 * -c) 1.092E+04 V&middot;m
 * -d) 1.202E+04 V&middot;m
 * -e) 1.322E+04 V&middot;m

4) An electron gun has parallel plates separated by 3.39 cm and gives electrons 57 keV of energy. What force would the field between the plates exert on a 0.218 &mu;C charge that gets between the plates?


 * -a) 3.029E-01 N
 * -b) 3.332E-01 N
 * +c) 3.665E-01 N
 * -d) 4.032E-01 N
 * -e) 4.435E-01 N

5) A 7 C charge is separated from a 15 C charge by distance of 14 cm.  What is the work done by increasing this separation to 20 cm?


 * -a) 1.519E-06 J
 * -b) 1.671E-06 J
 * -c) 1.838E-06 J
 * +d) 2.022E-06 J
 * -e) 2.224E-06 J

6) In the figure shown C1=16.7 &mu;F, C2=2.26 &mu;F, and C3=4.53 &mu;F. The voltage source provides &epsilon;=10.7 V. What is the energy stored in C2?


 * -a) 1.292E+01 &mu;J
 * -b) 1.421E+01 &mu;J
 * -c) 1.563E+01 &mu;J
 * +d) 1.719E+01 &mu;J
 * -e) 1.891E+01 &mu;J

7) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=16 C  and $$\tau=$$0.0214 s. What is the current at $$t=$$0.0207 s?


 * -a) 2.135E+02 A
 * -b) 2.349E+02 A
 * -c) 2.584E+02 A
 * +d) 2.842E+02 A
 * -e) 3.126E+02 A

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 &Omega; at a temperature of 82&deg;C and that the temperature coefficient of expansion is 4.530E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 390 &deg;C?


 * -a) 7.532E+00 &Omega;
 * -b) 7.908E+00 &Omega;
 * -c) 8.303E+00 &Omega;
 * +d) 8.719E+00 &Omega;
 * -e) 9.155E+00 &Omega;

9) In the circuit shown V=11.9 V, R1=2.75 &Omega;, R2=7.19 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * +a) 7.982E+00 W
 * -b) 8.780E+00 W
 * -c) 9.658E+00 W
 * -d) 1.062E+01 W
 * -e) 1.169E+01 W

10) Two sources of emf &epsilon;1=31.0 V, and  &epsilon;2=10.0 V are oriented as shownin the circuit. The resistances are R1=4.22 k&Omega; and  R2=1.37 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=3.32 mA and I4=1.03 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 2.290E+00 mA
 * -b) 2.519E+00 mA
 * -c) 2.771E+00 mA
 * -d) 3.048E+00 mA
 * -e) 3.353E+00 mA

Key: Z1
1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is, $$\vec E=2y^{2.7}\hat i +2x^{2.9}\hat j +2y^{2.0}\hat k$$


 * +a) 7.200E+01 V&middot;m
 * -b) 7.920E+01 V&middot;m
 * -c) 8.712E+01 V&middot;m
 * -d) 9.583E+01 V&middot;m
 * -e) 1.054E+02 V&middot;m

2) A 3 C charge is separated from a 7 C charge by distance of 10 cm.  What is the work done by increasing this separation to 15 cm?


 * -a) 5.199E-07 J
 * -b) 5.719E-07 J
 * +c) 6.291E-07 J
 * -d) 6.920E-07 J
 * -e) 7.612E-07 J

3) Imagine a substance could be made into a very hot filament. Suppose the resitance is 6.74 &Omega; at a temperature of 89&deg;C and that the temperature coefficient of expansion is 4.990E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 366 &deg;C?


 * -a) 1.529E+01 &Omega;
 * +b) 1.606E+01 &Omega;
 * -c) 1.686E+01 &Omega;
 * -d) 1.770E+01 &Omega;
 * -e) 1.859E+01 &Omega;

4) In the circuit shown V=11.8 V, R1=2.38 &Omega;, R2=5.11 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * -a) 8.489E+00 W
 * -b) 9.338E+00 W
 * +c) 1.027E+01 W
 * -d) 1.130E+01 W
 * -e) 1.243E+01 W

5) Two sources of emf &epsilon;1=18.2 V, and  &epsilon;2=6.59 V are oriented as shownin the circuit. The resistances are R1=5.47 k&Omega; and  R2=2.81 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=1.64 mA and I4=0.341 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 1.299E+00 mA
 * -b) 1.429E+00 mA
 * -c) 1.572E+00 mA
 * -d) 1.729E+00 mA
 * -e) 1.902E+00 mA

6) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * -a) 1.891E+01 N&middot;m2/C
 * -b) 2.080E+01 N&middot;m2/C
 * +c) 2.288E+01 N&middot;m2/C
 * -d) 2.517E+01 N&middot;m2/C
 * -e) 2.768E+01 N&middot;m2/C

7) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=27 C  and $$\tau=$$0.0154 s. What is the current at $$t=$$0.0177 s?


 * -a) 4.591E+02 A
 * -b) 5.050E+02 A
 * +c) 5.555E+02 A
 * -d) 6.111E+02 A
 * -e) 6.722E+02 A

8) In the figure shown C1=18.1 &mu;F, C2=2.13 &mu;F, and C3=5.48 &mu;F. The voltage source provides &epsilon;=14.6 V. What is the energy stored in C2?


 * -a) 1.645E+01 &mu;J
 * -b) 1.809E+01 &mu;J
 * -c) 1.990E+01 &mu;J
 * +d) 2.189E+01 &mu;J
 * -e) 2.408E+01 &mu;J

9) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?


 * -a) 6.925E+09 N/C2
 * -b) 7.617E+09 N/C2
 * +c) 8.379E+09 N/C2
 * -d) 9.217E+09 N/C2
 * -e) 1.014E+10 N/C2

10) An electron gun has parallel plates separated by 5.38 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.427 &mu;C charge that gets between the plates?


 * -a) 3.542E-01 N
 * -b) 3.896E-01 N
 * +c) 4.286E-01 N
 * -d) 4.714E-01 N
 * -e) 5.186E-01 N

Key: Z2
1) An electron gun has parallel plates separated by 3.02 cm and gives electrons 39 keV of energy. What force would the field between the plates exert on a 0.699 &mu;C charge that gets between the plates?


 * -a) 8.206E-01 N
 * +b) 9.027E-01 N
 * -c) 9.930E-01 N
 * -d) 1.092E+00 N
 * -e) 1.201E+00 N

2) In the figure shown C1=20.7 &mu;F, C2=2.79 &mu;F, and C3=5.18 &mu;F. The voltage source provides &epsilon;=15.0 V. What is the energy stored in C2?


 * -a) 2.064E+01 &mu;J
 * -b) 2.270E+01 &mu;J
 * -c) 2.497E+01 &mu;J
 * -d) 2.747E+01 &mu;J
 * +e) 3.022E+01 &mu;J

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is, $$\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k$$


 * -a) 1.969E+02 V&middot;m
 * -b) 2.166E+02 V&middot;m
 * -c) 2.383E+02 V&middot;m
 * -d) 2.621E+02 V&middot;m
 * +e) 2.883E+02 V&middot;m

4) In the circuit shown V=11.9 V, R1=2.75 &Omega;, R2=7.19 &Omega;, and R3=14.6 &Omega;. What is the power dissipated by R2?


 * +a) 7.982E+00 W
 * -b) 8.780E+00 W
 * -c) 9.658E+00 W
 * -d) 1.062E+01 W
 * -e) 1.169E+01 W

5) Two sources of emf &epsilon;1=24.8 V, and  &epsilon;2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 k&Omega; and  R2=1.6 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.49 mA and I4=0.83 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?


 * +a) 1.660E+00 mA
 * -b) 1.826E+00 mA
 * -c) 2.009E+00 mA
 * -d) 2.209E+00 mA
 * -e) 2.430E+00 mA

6) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.95 &Omega; at a temperature of 96&deg;C and that the temperature coefficient of expansion is 4.400E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 469 &deg;C?


 * -a) 4.449E+00 &Omega;
 * -b) 4.672E+00 &Omega;
 * -c) 4.905E+00 &Omega;
 * +d) 5.150E+00 &Omega;
 * -e) 5.408E+00 &Omega;

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?


 * +a) 5.978E+01 N&middot;m2/C
 * -b) 6.576E+01 N&middot;m2/C
 * -c) 7.233E+01 N&middot;m2/C
 * -d) 7.957E+01 N&middot;m2/C
 * -e) 8.752E+01 N&middot;m2/C

8) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=23 C  and $$\tau=$$0.0204 s. What is the current at $$t=$$0.0106 s?


 * -a) 6.096E+02 A
 * +b) 6.706E+02 A
 * -c) 7.376E+02 A
 * -d) 8.114E+02 A
 * -e) 8.925E+02 A

9) A 8 C charge is separated from a 13 C charge by distance of 7 cm.  What is the work done by increasing this separation to 13 cm?


 * -a) 4.209E-06 J
 * -b) 4.630E-06 J
 * -c) 5.093E-06 J
 * -d) 5.603E-06 J
 * +e) 6.163E-06 J

10) A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?


 * -a) 6.925E+09 N/C2
 * -b) 7.617E+09 N/C2
 * +c) 8.379E+09 N/C2
 * -d) 9.217E+09 N/C2
 * -e) 1.014E+10 N/C2