# Quizbank/Electricity and Magnetism (calculus) Exams/T1(5-10)

calcPhyEMt/T1(5-10) ID153290827354 (Study guide)

Exams:

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.

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### T1(5-10) A0

1)
A ring is uniformly charged with a net charge of 5 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) 5.581E+09 N/C2
b) 6.139E+09 N/C2
c) 6.753E+09 N/C2
d) 7.428E+09 N/C2
e) 8.171E+09 N/C2
2)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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

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,
${\displaystyle {\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}}$

a) 9.027E+03 V·m
b) 9.930E+03 V·m
c) 1.092E+04 V·m
d) 1.202E+04 V·m
e) 1.322E+04 V·m

4) 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 ρ(r)=ar1.2 (r≤R) where a=2 nC·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

5) When a 3.8 V battery operates a 1.67 W bulb, how many electrons pass through it each second?

a) 1.873E+18 electrons
b) 2.061E+18 electrons
c) 2.267E+18 electrons
d) 2.494E+18 electrons
e) 2.743E+18 electrons
6)
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 μC, q2=5 μC, q3=7 μC, and q4=10 μC. 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

7) 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 μC
b) 1.505E+01 μC
c) 1.655E+01 μC
d) 1.820E+01 μC
e) 2.003E+01 μC

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.94 Ω at a temperature of 30°C and that the temperature coefficient of expansion is 5.900E-03 (°C)−1). What is the resistance at a temperature of 445 °C?

a) 1.014E+01 Ω
b) 1.065E+01 Ω
c) 1.118E+01 Ω
d) 1.174E+01 Ω
e) 1.232E+01 Ω
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 351 V. If the combined external and internal resistance is 148 &Omega and the capacitance is 60 mF, how long will it take for the capacitor's voltage to reach 227.0 V?
a) 9.240E+00 s
b) 1.016E+01 s
c) 1.118E+01 s
d) 1.230E+01 s
e) 1.353E+01 s
10)
Two sources of emf ε1=49.6 V, and ε2=19.3 V are oriented as shownin the circuit. The resistances are R1=4.87 kΩ and R2=2.81 kΩ. 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

#### T1(5-10) A1

1)
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 μC, q2=6 μC, q3=9 μC, and q4=10 μC. 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
2)
Two sources of emf ε1=43.0 V, and ε2=13.8 V are oriented as shownin the circuit. The resistances are R1=3.97 kΩ and R2=1.12 kΩ. 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
3)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=3e}$?
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

4) 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 μC
b) 2.586E+01 μC
c) 2.844E+01 μC
d) 3.129E+01 μC
e) 3.442E+01 μC
5)
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

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=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m

7) 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

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.89 Ω at a temperature of 89°C and that the temperature coefficient of expansion is 5.340E-03 (°C)−1). What is the resistance at a temperature of 566 °C?

a) 9.763E+00 Ω
b) 1.025E+01 Ω
c) 1.076E+01 Ω
d) 1.130E+01 Ω
e) 1.187E+01 Ω
9)
A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 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=1.3 m (on axis) away from the loop's center?
a) 1.764E+09 N/C2
b) 1.941E+09 N/C2
c) 2.135E+09 N/C2
d) 2.348E+09 N/C2
e) 2.583E+09 N/C2

10) 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 ρ(r)=ar1.6 (r≤R) where a=3 nC·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

#### T1(5-10) A2

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 130 V. If the combined external and internal resistance is 109 &Omega and the capacitance is 59 mF, how long will it take for the capacitor's voltage to reach 69.9 V?
a) 3.728E+00 s
b) 4.101E+00 s
c) 4.511E+00 s
d) 4.962E+00 s
e) 5.458E+00 s
2)
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 μC, q2=7 μC, q3=8 μC, and q4=11 μC. How much work was required to assemble these four charges from infinity?
a) 7.982E+01 J
b) 8.780E+01 J
c) 9.658E+01 J
d) 1.062E+02 J
e) 1.169E+02 J

3) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.61 Ω at a temperature of 92°C and that the temperature coefficient of expansion is 4.260E-03 (°C)−1). What is the resistance at a temperature of 422 °C?

a) 6.279E+00 Ω
b) 6.593E+00 Ω
c) 6.923E+00 Ω
d) 7.269E+00 Ω
e) 7.632E+00 Ω
4)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=6e}$?
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

5) When a 4.63 V battery operates a 2.26 W bulb, how many electrons pass through it each second?

a) 2.770E+18 electrons
b) 3.047E+18 electrons
c) 3.351E+18 electrons
d) 3.686E+18 electrons
e) 4.055E+18 electrons

6) 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 μC
b) 4.405E+01 μC
c) 4.846E+01 μC
d) 5.330E+01 μC
e) 5.864E+01 μC
7)
A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 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=1.4 m (on axis) away from the loop's center?
a) 7.119E+09 N/C2
b) 7.831E+09 N/C2
c) 8.614E+09 N/C2
d) 9.476E+09 N/C2
e) 1.042E+10 N/C2
8)
Two sources of emf ε1=24.9 V, and ε2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 kΩ and R2=2.31 kΩ. 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) 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=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m

10) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C
b) 1.522E+02 N/C
c) 1.674E+02 N/C
d) 1.841E+02 N/C
e) 2.025E+02 N/C

### T1(5-10) B0

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

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
2)
A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 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=1.3 m (on axis) away from the loop's center?
a) 1.764E+09 N/C2
b) 1.941E+09 N/C2
c) 2.135E+09 N/C2
d) 2.348E+09 N/C2
e) 2.583E+09 N/C2
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=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° 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·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C
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=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° 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) 7.876E+01 N·m2/C
b) 8.664E+01 N·m2/C
c) 9.531E+01 N·m2/C
d) 1.048E+02 N·m2/C
e) 1.153E+02 N·m2/C

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) Calculate the final speed of a free electron accelerated from rest through a potential difference of 12 V.

a) 1.698E+06 m/s
b) 1.868E+06 m/s
c) 2.055E+06 m/s
d) 2.260E+06 m/s
e) 2.486E+06 m/s

7) 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 μC
b) 2.586E+01 μC
c) 2.844E+01 μC
d) 3.129E+01 μC
e) 3.442E+01 μC

8) A device requires consumes 88 W of power and requires 11.3 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) 1.467E+06 A/m2
b) 1.614E+06 A/m2
c) 1.775E+06 A/m2
d) 1.953E+06 A/m2
e) 2.148E+06 A/m2
9)
Two sources of emf ε1=18.2 V, and ε2=6.59 V are oriented as shownin the circuit. The resistances are R1=5.47 kΩ and R2=2.81 kΩ. 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

10) A given battery has a 15 V emf and an internal resistance of 0.177 Ω. If it is connected to a 0.824 Ω 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

#### T1(5-10) B1

1) 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 μC
b) 1.505E+01 μC
c) 1.655E+01 μC
d) 1.820E+01 μC
e) 2.003E+01 μC
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=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.6 m, z=z0=1.4 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.959E+01 N·m2/C
b) 4.354E+01 N·m2/C
c) 4.790E+01 N·m2/C
d) 5.269E+01 N·m2/C
e) 5.796E+01 N·m2/C

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

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

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)
A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 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) 3.159E+09 N/C2
b) 3.475E+09 N/C2
c) 3.823E+09 N/C2
d) 4.205E+09 N/C2
e) 4.626E+09 N/C2

6) A given battery has a 13 V emf and an internal resistance of 0.159 Ω. If it is connected to a 0.617 Ω 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
7)
Two sources of emf ε1=20.6 V, and ε2=9.53 V are oriented as shownin the circuit. The resistances are R1=5.46 kΩ and R2=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=1.5 mA and I4=0.415 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.085E+00 mA
b) 1.194E+00 mA
c) 1.313E+00 mA
d) 1.444E+00 mA
e) 1.589E+00 mA
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=1.5 m, y=y1=5.8 m, z=z0=1.1 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 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° 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) 5.606E+01 N·m2/C
b) 6.167E+01 N·m2/C
c) 6.784E+01 N·m2/C
d) 7.462E+01 N·m2/C
e) 8.208E+01 N·m2/C

9) A device requires consumes 168 W of power and requires 11.0 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) 1.901E+06 A/m2
b) 2.091E+06 A/m2
c) 2.300E+06 A/m2
d) 2.530E+06 A/m2
e) 2.783E+06 A/m2

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 46 V.

a) 3.022E+06 m/s
b) 3.324E+06 m/s
c) 3.657E+06 m/s
d) 4.023E+06 m/s
e) 4.425E+06 m/s

#### T1(5-10) B2

1)
Two sources of emf ε1=40.6 V, and ε2=13.5 V are oriented as shownin the circuit. The resistances are R1=4.35 kΩ and R2=2.44 kΩ. 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

2) A device requires consumes 73 W of power and requires 9.14 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) 1.187E+06 A/m2
b) 1.306E+06 A/m2
c) 1.436E+06 A/m2
d) 1.580E+06 A/m2
e) 1.738E+06 A/m2

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

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

4) 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 μC
b) 3.041E+01 μC
c) 3.345E+01 μC
d) 3.679E+01 μC
e) 4.047E+01 μC
5)
A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 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=1.3 m (on axis) away from the loop's center?
a) 4.788E+09 N/C2
b) 5.267E+09 N/C2
c) 5.793E+09 N/C2
d) 6.373E+09 N/C2
e) 7.010E+09 N/C2
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=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C
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=2.1 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° 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·m2/C
b) 4.316E+01 N·m2/C
c) 4.748E+01 N·m2/C
d) 5.222E+01 N·m2/C
e) 5.745E+01 N·m2/C

8) 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

9) Calculate the final speed of a free electron accelerated from rest through a potential difference of 83 V.

a) 4.466E+06 m/s
b) 4.912E+06 m/s
c) 5.403E+06 m/s
d) 5.944E+06 m/s
e) 6.538E+06 m/s

10) A given battery has a 13 V emf and an internal resistance of 0.159 Ω. If it is connected to a 0.617 Ω 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

### T1(5-10) C0

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

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
2)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.6 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.
a) 2.955E+00 V/m2
b) 3.250E+00 V/m2
c) 3.575E+00 V/m2
d) 3.933E+00 V/m2
e) 4.326E+00 V/m2

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=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m

4) 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
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 μC, q2=6 μC, q3=8 μC, and q4=10 μC. How much work was required to assemble these four charges from infinity?
a) 3.819E+01 J
b) 4.201E+01 J
c) 4.621E+01 J
d) 5.083E+01 J
e) 5.591E+01 J

6) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=83 V is x2 + y2 + z2 = R2, where R=

a) 1.378E+00 m
b) 1.516E+00 m
c) 1.668E+00 m
d) 1.834E+00 m
e) 2.018E+00 m
7)
In the figure shown C1=16.0 μF, C2=2.27 μF, and C3=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C1?
a) 2.515E+01 μC
b) 2.766E+01 μC
c) 3.043E+01 μC
d) 3.347E+01 μC
e) 3.682E+01 μC

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.75 Ω at a temperature of 24°C and that the temperature coefficient of expansion is 4.300E-03 (°C)−1). What is the resistance at a temperature of 423 °C?

a) 1.018E+01 Ω
b) 1.069E+01 Ω
c) 1.123E+01 Ω
d) 1.179E+01 Ω
e) 1.238E+01 Ω
9)
Two sources of emf ε1=40.6 V, and ε2=13.5 V are oriented as shownin the circuit. The resistances are R1=4.35 kΩ and R2=2.44 kΩ. 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
10)
The resistances in the figure shown are R1= 1.54 Ω, R2= 0.927 Ω, and R2= 2.46 Ω. 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=−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

#### T1(5-10) C1

1) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.73 Ω at a temperature of 99°C and that the temperature coefficient of expansion is 5.260E-03 (°C)−1). What is the resistance at a temperature of 420 °C?

a) 1.267E+01 Ω
b) 1.331E+01 Ω
c) 1.397E+01 Ω
d) 1.467E+01 Ω
e) 1.540E+01 Ω
2)
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 μC, q2=5 μC, q3=7 μC, and q4=10 μC. 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

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=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

a) 3.337E+03 V·m
b) 3.670E+03 V·m
c) 4.037E+03 V·m
d) 4.441E+03 V·m
e) 4.885E+03 V·m
4)
The resistances in the figure shown are R1= 2.73 Ω, R2= 1.4 Ω, and R2= 2.35 Ω. V1 and V3 are text 0.549 V and 1.27 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=−0.584 V. What is the absolute value of the current through R1?
a) 1.213E-01 A
b) 1.334E-01 A
c) 1.468E-01 A
d) 1.614E-01 A
e) 1.776E-01 A
5)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ at x=0.83 m if a=0.7 m, b=1.8 m. The total charge on the rod is 9 nC.
a) 6.897E+00 V/m2
b) 7.587E+00 V/m2
c) 8.345E+00 V/m2
d) 9.180E+00 V/m2
e) 1.010E+01 V/m2

6)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.2{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.2{\text{ m}}}$.

a) 3.228E+00 V/m2
b) 3.551E+00 V/m2
c) 3.906E+00 V/m2
d) 4.297E+00 V/m2
e) 4.727E+00 V/m2
7)
Two sources of emf ε1=24.9 V, and ε2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 kΩ and R2=2.31 kΩ. 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
8)
In the figure shown C1=17.1 μF, C2=2.87 μF, and C3=4.74 μF. The voltage source provides ε=6.63 V. What is the charge on C1?
a) 2.385E+01 μC
b) 2.623E+01 μC
c) 2.886E+01 μC
d) 3.174E+01 μC
e) 3.492E+01 μC

9) 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

10) If a 18 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=12 V is x2 + y2 + z2 = R2, where R=

a) 1.114E+01 m
b) 1.226E+01 m
c) 1.348E+01 m
d) 1.483E+01 m
e) 1.631E+01 m

#### T1(5-10) C2

1) 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

2) If a 18 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=12 V is x2 + y2 + z2 = R2, where R=

a) 1.114E+01 m
b) 1.226E+01 m
c) 1.348E+01 m
d) 1.483E+01 m
e) 1.631E+01 m
3)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.7 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.
a) 6.804E+00 V/m2
b) 7.485E+00 V/m2
c) 8.233E+00 V/m2
d) 9.056E+00 V/m2
e) 9.962E+00 V/m2
4)
Two sources of emf ε1=18.2 V, and ε2=6.59 V are oriented as shownin the circuit. The resistances are R1=5.47 kΩ and R2=2.81 kΩ. 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
5)
The resistances in the figure shown are R1= 1.1 Ω, R2= 1.55 Ω, and R2= 2.11 Ω. 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=−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

6)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=2.8{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =3{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=1.9{\text{ m}}}$.

a) 4.295E+00 V/m2
b) 4.724E+00 V/m2
c) 5.196E+00 V/m2
d) 5.716E+00 V/m2
e) 6.288E+00 V/m2
7)
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 μC, q2=6 μC, q3=9 μC, and q4=10 μC. 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

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=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m
9)
In the figure shown C1=19.9 μF, C2=2.25 μF, and C3=4.75 μF. The voltage source provides ε=6.93 V. What is the charge on C1?
a) 2.451E+01 μC
b) 2.696E+01 μC
c) 2.966E+01 μC
d) 3.262E+01 μC
e) 3.589E+01 μC

10) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.89 Ω at a temperature of 89°C and that the temperature coefficient of expansion is 5.340E-03 (°C)−1). What is the resistance at a temperature of 566 °C?

a) 9.763E+00 Ω
b) 1.025E+01 Ω
c) 1.076E+01 Ω
d) 1.130E+01 Ω
e) 1.187E+01 Ω

### T1(5-10) D0

1)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.4 m. Evaluate ${\displaystyle f(x,y)}$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.
a) 3.161E+00 V/m2
b) 3.477E+00 V/m2
c) 3.825E+00 V/m2
d) 4.208E+00 V/m2
e) 4.628E+00 V/m2
2)
A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 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=0.4 m (on axis) away from the loop's center?
a) 2.013E+09 N/C2
b) 2.214E+09 N/C2
c) 2.435E+09 N/C2
d) 2.679E+09 N/C2
e) 2.947E+09 N/C2
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=1.4 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·m2/C
b) 6.811E+01 N·m2/C
c) 7.492E+01 N·m2/C
d) 8.242E+01 N·m2/C
e) 9.066E+01 N·m2/C

4) 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 ρ(r)=ar1.6 (r≤R) where a=3 nC·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

5) If a 14 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=83 V is x2 + y2 + z2 = R2, where R=

a) 1.378E+00 m
b) 1.516E+00 m
c) 1.668E+00 m
d) 1.834E+00 m
e) 2.018E+00 m

6) A 12.0 V battery can move 12,000 C of charge. How many Joules does it deliver?

a) 1.190E+05 J
b) 1.309E+05 J
c) 1.440E+05 J
d) 1.584E+05 J
e) 1.742E+05 J

7) 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 μC
b) 1.505E+01 μC
c) 1.655E+01 μC
d) 1.820E+01 μC
e) 2.003E+01 μC

8) What is consumer cost to operate one 115−W incandescent bulb for 12 hours per day for 1 year (365 days) if the cost of electricity is $0.128 per kilowatt-hour? a)$5.328E+01
b) $5.861E+01 c)$6.447E+01
d) $7.092E+01 e)$7.801E+01
9)
The resistances in the figure shown are R1= 2.42 Ω, R2= 1.09 Ω, and R2= 3.89 Ω. 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=−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

10) A given battery has a 11 V emf and an internal resistance of 0.0998 Ω. If it is connected to a 0.417 Ω 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

#### T1(5-10) D1

1) An empty parallel-plate capacitor with metal plates has an area of 2.82 m2, separated by 1.29 mm. How much charge does it store if the voltage is 7.420E+03 V?

a) 1.187E+02 μC
b) 1.306E+02 μC
c) 1.436E+02 μC
d) 1.580E+02 μC
e) 1.738E+02 μC

2) A 12.0 V battery can move 19,000 C of charge. How many Joules does it deliver?

a) 1.713E+05 J
b) 1.884E+05 J
c) 2.073E+05 J
d) 2.280E+05 J
e) 2.508E+05 J

3) 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
4)
A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 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=1.4 m (on axis) away from the loop's center?
a) 7.119E+09 N/C2
b) 7.831E+09 N/C2
c) 8.614E+09 N/C2
d) 9.476E+09 N/C2
e) 1.042E+10 N/C2

5) A given battery has a 9 V emf and an internal resistance of 0.16 Ω. If it is connected to a 0.45 Ω resistor what is the power dissipated by that load?

a) 6.691E+01 W
b) 7.360E+01 W
c) 8.096E+01 W
d) 8.905E+01 W
e) 9.796E+01 W

6) 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 ρ(r)=ar1.4 (r≤R) where a=2 nC·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
7)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.6 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.
a) 2.955E+00 V/m2
b) 3.250E+00 V/m2
c) 3.575E+00 V/m2
d) 3.933E+00 V/m2
e) 4.326E+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=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·m2/C
b) 7.789E+01 N·m2/C
c) 8.568E+01 N·m2/C
d) 9.425E+01 N·m2/C
e) 1.037E+02 N·m2/C

9) What is consumer cost to operate one 74−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
10)
The resistances in the figure shown are R1= 2.41 Ω, R2= 1.74 Ω, and R2= 3.35 Ω. 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=−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

#### T1(5-10) D2

1) 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 μC
b) 2.473E+01 μC
c) 2.721E+01 μC
d) 2.993E+01 μC
e) 3.292E+01 μC
2)
A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 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=1.3 m (on axis) away from the loop's center?
a) 4.788E+09 N/C2
b) 5.267E+09 N/C2
c) 5.793E+09 N/C2
d) 6.373E+09 N/C2
e) 7.010E+09 N/C2
3)
The resistances in the figure shown are R1= 1.81 Ω, R2= 1.18 Ω, and R2= 2.62 Ω. 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=−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

4) A given battery has a 9 V emf and an internal resistance of 0.141 Ω. If it is connected to a 0.663 Ω resistor what is the power dissipated by that load?

a) 5.674E+01 W
b) 6.242E+01 W
c) 6.866E+01 W
d) 7.553E+01 W
e) 8.308E+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=1.4 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·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

6) A 12.0 V battery can move 44,000 C of charge. How many Joules does it deliver?

a) 4.800E+05 J
b) 5.280E+05 J
c) 5.808E+05 J
d) 6.389E+05 J
e) 7.028E+05 J

7) If a 13 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=84 V is x2 + y2 + z2 = R2, where R=

a) 1.391E+00 m
b) 1.530E+00 m
c) 1.683E+00 m
d) 1.851E+00 m
e) 2.036E+00 m

8) What is consumer cost to operate one 87−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)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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) 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 ρ(r)=ar1.5 (r≤R) where a=2 nC·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

### T1(5-10) E0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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
2)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.7 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.
a) 5.267E+00 V/m2
b) 5.794E+00 V/m2
c) 6.374E+00 V/m2
d) 7.011E+00 V/m2
e) 7.712E+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)
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° 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·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C
5)
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

6) Calculate the final speed of a free electron accelerated from rest through a potential difference of 83 V.

a) 4.466E+06 m/s
b) 4.912E+06 m/s
c) 5.403E+06 m/s
d) 5.944E+06 m/s
e) 6.538E+06 m/s
7)
What is the net capacitance if C1=4.13 μF, C2=3.56 μF, and C3=3.57 μF in the configuration shown?
a) 5.482E+00 μF
b) 6.030E+00 μF
c) 6.633E+00 μF
d) 7.296E+00 μF
e) 8.026E+00 μF

8) A DC winch moter draws 26 amps at 153 volts as it lifts a 4.100E+03 N weight at a constant speed of 0.609 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) 2.191E+00 Ω
b) 2.410E+00 Ω
c) 2.651E+00 Ω
d) 2.916E+00 Ω
e) 3.208E+00 Ω
9)
The resistances in the figure shown are R1= 1.54 Ω, R2= 0.927 Ω, and R2= 2.46 Ω. 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=−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
10)
Two sources of emf ε1=67.2 V, and ε2=18.7 V are oriented as shownin the circuit. The resistances are R1=3.45 kΩ and R2=1.2 kΩ. 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

#### T1(5-10) E1

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=3e}$?
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
2)
The resistances in the figure shown are R1= 2.38 Ω, R2= 1.87 Ω, and R2= 2.32 Ω. V1 and V3 are text 0.605 V and 3.8 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=−0.67 V. What is the absolute value of the current through R1?
a) 8.147E-02 A
b) 8.962E-02 A
c) 9.858E-02 A
d) 1.084E-01 A
e) 1.193E-01 A
3)
What is the net capacitance if C1=4.55 μF, C2=4.39 μF, and C3=3.32 μF in the configuration shown?
a) 4.173E+00 μF
b) 4.590E+00 μF
c) 5.049E+00 μF
d) 5.554E+00 μF
e) 6.110E+00 μF
4)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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
5)
Two sources of emf ε1=42.2 V, and ε2=17.8 V are oriented as shownin the circuit. The resistances are R1=4.2 kΩ and R2=2.83 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=2.5 mA and I4=0.749 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) 1.056E+01 V
b) 1.161E+01 V
c) 1.277E+01 V
d) 1.405E+01 V
e) 1.545E+01 V

6) 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
7)
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

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 Ω
b) 1.845E+00 Ω
c) 2.030E+00 Ω
d) 2.233E+00 Ω
e) 2.456E+00 Ω
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=2.1 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° 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·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 83 V.

a) 4.466E+06 m/s
b) 4.912E+06 m/s
c) 5.403E+06 m/s
d) 5.944E+06 m/s
e) 6.538E+06 m/s

#### T1(5-10) E2

1)
A diploe has a charge magnitude of q=8 nC and a separation distance of d=3.55 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=3.43 cm, y=1.77 cm)? Note that following the textbook's example, the y-value of the field point at 1.77 cm matches the disance of the positive charge above the x-axis.
a) 5.796E+02 V
b) 6.375E+02 V
c) 7.013E+02 V
d) 7.714E+02 V
e) 8.486E+02 V
2)
Two sources of emf ε1=27.9 V, and ε2=11.1 V are oriented as shownin the circuit. The resistances are R1=2.82 kΩ and R2=2.25 kΩ. 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
3)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.7 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.
a) 5.267E+00 V/m2
b) 5.794E+00 V/m2
c) 6.374E+00 V/m2
d) 7.011E+00 V/m2
e) 7.712E+00 V/m2

4) Calculate the final speed of a free electron accelerated from rest through a potential difference of 45 V.

a) 3.617E+06 m/s
b) 3.979E+06 m/s
c) 4.376E+06 m/s
d) 4.814E+06 m/s
e) 5.296E+06 m/s

5) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

a) 1.491E+01 N/C
b) 1.640E+01 N/C
c) 1.804E+01 N/C
d) 1.984E+01 N/C
e) 2.182E+01 N/C
6)
The resistances in the figure shown are R1= 1.57 Ω, R2= 1.25 Ω, and R2= 3.38 Ω. 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=−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
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=2.1 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° 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·m2/C
b) 4.316E+01 N·m2/C
c) 4.748E+01 N·m2/C
d) 5.222E+01 N·m2/C
e) 5.745E+01 N·m2/C
8)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
a) 4.091E+01 degrees
b) 4.500E+01 degrees
c) 4.950E+01 degrees
d) 5.445E+01 degrees
e) 5.990E+01 degrees

9) 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 Ω
b) 2.718E+00 Ω
c) 2.990E+00 Ω
d) 3.288E+00 Ω
e) 3.617E+00 Ω
10)
What is the net capacitance if C1=3.54 μF, C2=3.53 μF, and C3=3.65 μF in the configuration shown?
a) 3.700E+00 μF
b) 4.070E+00 μF
c) 4.477E+00 μF
d) 4.925E+00 μF
e) 5.417E+00 μF

### T1(5-10) F0

1)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=7.9{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=5.1{\text{ m}}}$.

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
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) 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 ρ(r)=ar1.2 (r≤R) where a=2 nC·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
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=2.3 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° 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·m2/C
b) 1.868E+01 N·m2/C
c) 2.055E+01 N·m2/C
d) 2.260E+01 N·m2/C
e) 2.486E+01 N·m2/C
5)
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 μC
b) 1.178E+01 μC
c) 1.296E+01 μC
d) 1.426E+01 μC
e) 1.568E+01 μC

6) Calculate the final speed of a free electron accelerated from rest through a potential difference of 46 V.

a) 3.022E+06 m/s
b) 3.324E+06 m/s
c) 3.657E+06 m/s
d) 4.023E+06 m/s
e) 4.425E+06 m/s

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 μC
b) 6.903E+01 μC
c) 7.593E+01 μC
d) 8.352E+01 μC
e) 9.188E+01 μC

8) A device requires consumes 73 W of power and requires 9.14 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) 1.187E+06 A/m2
b) 1.306E+06 A/m2
c) 1.436E+06 A/m2
d) 1.580E+06 A/m2
e) 1.738E+06 A/m2
9)
The resistances in the figure shown are R1= 2.04 Ω, R2= 1.19 Ω, and R2= 2.5 Ω. 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=−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)
Two sources of emf ε1=67.2 V, and ε2=18.7 V are oriented as shownin the circuit. The resistances are R1=3.45 kΩ and R2=1.2 kΩ. 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

#### T1(5-10) F1

1)
A Van de Graff generator has a 107 cm diameter metal sphere that produces 219 kV near its surface. What is the excess charge on the sphere?
a) 1.304E+01 μC
b) 1.434E+01 μC
c) 1.577E+01 μC
d) 1.735E+01 μC
e) 1.909E+01 μC

2) 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

3)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=2.8{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =3{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=1.9{\text{ m}}}$.

a) 4.295E+00 V/m2
b) 4.724E+00 V/m2
c) 5.196E+00 V/m2
d) 5.716E+00 V/m2
e) 6.288E+00 V/m2
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=1.5 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° 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·m2/C
b) 8.572E+01 N·m2/C
c) 9.429E+01 N·m2/C
d) 1.037E+02 N·m2/C
e) 1.141E+02 N·m2/C

5) A device requires consumes 168 W of power and requires 11.0 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) 1.901E+06 A/m2
b) 2.091E+06 A/m2
c) 2.300E+06 A/m2
d) 2.530E+06 A/m2
e) 2.783E+06 A/m2

6) 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 ρ(r)=ar1.5 (r≤R) where a=3 nC·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
7)
Two sources of emf ε1=40.9 V, and ε2=16.1 V are oriented as shownin the circuit. The resistances are R1=5.55 kΩ and R2=1.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=6.11 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 R2?
a) 8.754E+00 V
b) 9.630E+00 V
c) 1.059E+01 V
d) 1.165E+01 V
e) 1.282E+01 V
8)
A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 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) 3.159E+09 N/C2
b) 3.475E+09 N/C2
c) 3.823E+09 N/C2
d) 4.205E+09 N/C2
e) 4.626E+09 N/C2
9)
The resistances in the figure shown are R1= 1.1 Ω, R2= 1.55 Ω, and R2= 2.11 Ω. 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=−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

10) An empty parallel-plate capacitor with metal plates has an area of 2.82 m2, separated by 1.29 mm. How much charge does it store if the voltage is 7.420E+03 V?

a) 1.187E+02 μC
b) 1.306E+02 μC
c) 1.436E+02 μC
d) 1.580E+02 μC
e) 1.738E+02 μC

#### T1(5-10) F2

1) 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
2)
A ring is uniformly charged with a net charge of 9 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=0.73 m (on axis) away from the loop's center?
a) 7.415E+09 N/C2
b) 8.156E+09 N/C2
c) 8.972E+09 N/C2
d) 9.869E+09 N/C2
e) 1.086E+10 N/C2
3)
The resistances in the figure shown are R1= 1.81 Ω, R2= 1.18 Ω, and R2= 2.62 Ω. 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=−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
4)
A Van de Graff generator has a 85 cm diameter metal sphere that produces 235 kV near its surface. What is the excess charge on the sphere?
a) 9.184E+00 μC
b) 1.010E+01 μC
c) 1.111E+01 μC
d) 1.222E+01 μC
e) 1.345E+01 μC

5) 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 μC
b) 2.586E+01 μC
c) 2.844E+01 μC
d) 3.129E+01 μC
e) 3.442E+01 μC

6) 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 ρ(r)=ar1.2 (r≤R) where a=2 nC·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
7)
Two sources of emf ε1=17.3 V, and ε2=6.46 V are oriented as shownin the circuit. The resistances are R1=2.54 kΩ and R2=2.79 kΩ. 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

8) Calculate the final speed of a free electron accelerated from rest through a potential difference of 45 V.

a) 3.288E+06 m/s
b) 3.617E+06 m/s
c) 3.979E+06 m/s
d) 4.376E+06 m/s
e) 4.814E+06 m/s

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

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
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=1.4 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° 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·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C

### T1(5-10) G0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=4e}$?
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
2)
A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 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=0.33 m (on axis) away from the loop's center?
a) 1.353E+09 N/C2
b) 1.488E+09 N/C2
c) 1.637E+09 N/C2
d) 1.801E+09 N/C2
e) 1.981E+09 N/C2

3) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 6.411E+02 N/C
b) 7.052E+02 N/C
c) 7.757E+02 N/C
d) 8.533E+02 N/C
e) 9.386E+02 N/C
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=1.3 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° 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·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C

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

a) 2.408E-06 J
b) 2.649E-06 J
c) 2.914E-06 J
d) 3.205E-06 J
e) 3.526E-06 J
6)
A Van de Graff generator has a 72 cm diameter metal sphere that produces 285 kV near its surface. What is the excess charge on the sphere?
a) 1.038E+01 μC
b) 1.142E+01 μC
c) 1.256E+01 μC
d) 1.381E+01 μC
e) 1.519E+01 μC
7)
In the figure shown C1=16.9 μF, C2=2.86 μF, and C3=5.1 μF. The voltage source provides ε=9.98 V. What is the energy stored in C2?
a) 1.764E+01 μJ
b) 1.940E+01 μJ
c) 2.134E+01 μJ
d) 2.348E+01 μJ
e) 2.583E+01 μJ

8) What is the average current involved when a truck battery sets in motion 738 C of charge in 3.87 s while starting an engine?

a) 1.907E+02 A
b) 2.098E+02 A
c) 2.307E+02 A
d) 2.538E+02 A
e) 2.792E+02 A
9)
In the circuit shown V=15.8 V, R1=1.86 Ω, R2=7.66 Ω, and R3=12.9 Ω. 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
10)
The resistances in the figure shown are R1= 1.33 Ω, R2= 1.72 Ω, and R2= 3.69 Ω. 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=−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

#### T1(5-10) G1

1) 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 ρ(r)=ar1.6 (r≤R) where a=2 nC·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

2) A 4 C charge is separated from a 9 C charge by distance of 9 cm. What is the work done by increasing this separation to 14 cm?

a) 8.769E-07 J
b) 9.646E-07 J
c) 1.061E-06 J
d) 1.167E-06 J
e) 1.284E-06 J
3)
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=1.1 m (on axis) away from the loop's center?
a) 8.336E+09 N/C2
b) 9.170E+09 N/C2
c) 1.009E+10 N/C2
d) 1.110E+10 N/C2
e) 1.220E+10 N/C2

4) 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
5)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=5e}$?
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
6)
In the circuit shown V=15.4 V, R1=2.55 Ω, R2=5.12 Ω, and R3=12.7 Ω. What is the power dissipated by R2?
a) 1.096E+01 W
b) 1.206E+01 W
c) 1.326E+01 W
d) 1.459E+01 W
e) 1.605E+01 W
7)
A Van de Graff generator has a 114 cm diameter metal sphere that produces 275 kV near its surface. What is the excess charge on the sphere?
a) 1.744E+01 μC
b) 1.918E+01 μC
c) 2.110E+01 μC
d) 2.321E+01 μC
e) 2.554E+01 μC
8)
The resistances in the figure shown are R1= 2.41 Ω, R2= 1.74 Ω, and R2= 3.35 Ω. 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=−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
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=1.6 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° 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·m2/C
b) 4.862E+01 N·m2/C
c) 5.348E+01 N·m2/C
d) 5.882E+01 N·m2/C
e) 6.471E+01 N·m2/C
10)
In the figure shown C1=17.6 μF, C2=2.12 μF, and C3=4.72 μF. The voltage source provides ε=5.35 V. What is the energy stored in C2?
a) 6.750E+00 μJ
b) 7.425E+00 μJ
c) 8.168E+00 μJ
d) 8.984E+00 μJ
e) 9.883E+00 μJ

#### T1(5-10) G2

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

a) 2.408E-06 J
b) 2.649E-06 J
c) 2.914E-06 J
d) 3.205E-06 J
e) 3.526E-06 J
2)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
a) 9.750E-15 N
b) 1.072E-14 N
c) 1.180E-14 N
d) 1.298E-14 N
e) 1.427E-14 N
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° 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·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C
4)
In the figure shown C1=19.2 μF, C2=2.24 μF, and C3=4.93 μF. The voltage source provides ε=11.7 V. What is the energy stored in C2?
a) 1.303E+01 μJ
b) 1.434E+01 μJ
c) 1.577E+01 μJ
d) 1.735E+01 μJ
e) 1.908E+01 μJ

5) 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 ρ(r)=ar1.5 (r≤R) where a=3 nC·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
6)
The resistances in the figure shown are R1= 1.54 Ω, R2= 0.927 Ω, and R2= 2.46 Ω. 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=−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
7)
A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 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=0.4 m (on axis) away from the loop's center?
a) 2.013E+09 N/C2
b) 2.214E+09 N/C2
c) 2.435E+09 N/C2
d) 2.679E+09 N/C2
e) 2.947E+09 N/C2
8)
A Van de Graff generator has a 140 cm diameter metal sphere that produces 244 kV near its surface. What is the excess charge on the sphere?
a) 1.900E+01 μC
b) 2.090E+01 μC
c) 2.299E+01 μC
d) 2.529E+01 μC
e) 2.782E+01 μC

9) What is the average current involved when a truck battery sets in motion 701 C of charge in 4.98 s while starting an engine?

a) 1.280E+02 A
b) 1.408E+02 A
c) 1.548E+02 A
d) 1.703E+02 A
e) 1.874E+02 A
10)
In the circuit shown V=17.5 V, R1=2.34 Ω, R2=7.1 Ω, and R3=15.3 Ω. What is the power dissipated by R2?
a) 1.784E+01 W
b) 1.963E+01 W
c) 2.159E+01 W
d) 2.375E+01 W
e) 2.612E+01 W

### T1(5-10) H0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=6e}$?
a) 2.544E-14 N
b) 2.798E-14 N
c) 3.078E-14 N
d) 3.385E-14 N
e) 3.724E-14 N

2) A large thin isolated square plate has an area of 3 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) 1.694E+02 N/C
b) 1.864E+02 N/C
c) 2.050E+02 N/C
d) 2.255E+02 N/C
e) 2.480E+02 N/C

3) 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
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=2.3 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° 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·m2/C
b) 9.256E+01 N·m2/C
c) 1.018E+02 N·m2/C
d) 1.120E+02 N·m2/C
e) 1.232E+02 N·m2/C

5) Calculate the final speed of a free electron accelerated from rest through a potential difference of 12 V.

a) 1.698E+06 m/s
b) 1.868E+06 m/s
c) 2.055E+06 m/s
d) 2.260E+06 m/s
e) 2.486E+06 m/s
6)
An electron gun has parallel plates separated by 4.85 cm and gives electrons 36 keV of energy. What force would the field between the plates exert on a 0.663 μC charge that gets between the plates?
a) 3.697E-01 N
b) 4.067E-01 N
c) 4.474E-01 N
d) 4.921E-01 N
e) 5.413E-01 N
7)
What is the net capacitance if C1=3.06 μF, C2=3.09 μF, and C3=2.48 μF in the configuration shown?
a) 3.018E+00 μF
b) 3.320E+00 μF
c) 3.652E+00 μF
d) 4.017E+00 μF
e) 4.419E+00 μF

8) The charge passing a plane intersecting a wire is ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=27 C and ${\displaystyle \tau =}$0.0154 s. What is the current at ${\displaystyle 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 ε1=29.5 V, and ε2=11.0 V are oriented as shownin the circuit. The resistances are R1=2.45 kΩ and R2=1.96 kΩ. 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
10)
The resistances in the figure shown are R1= 1.81 Ω, R2= 1.18 Ω, and R2= 2.62 Ω. 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=−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

#### T1(5-10) H1

1) 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
2)
What is the net capacitance if C1=3.97 μF, C2=3.51 μF, and C3=2.18 μF in the configuration shown?
a) 3.038E+00 μF
b) 3.341E+00 μF
c) 3.675E+00 μF
d) 4.043E+00 μF
e) 4.447E+00 μF
3)
The resistances in the figure shown are R1= 1.54 Ω, R2= 0.927 Ω, and R2= 2.46 Ω. 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=−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
4)
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 μC 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
5)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=3e}$?
a) 2.036E-14 N
b) 2.240E-14 N
c) 2.464E-14 N
d) 2.710E-14 N
e) 2.981E-14 N
6)
Two sources of emf ε1=13.6 V, and ε2=6.53 V are oriented as shownin the circuit. The resistances are R1=2.89 kΩ and R2=2.12 kΩ. 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

7) 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

8) 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

9) The charge passing a plane intersecting a wire is ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=42 C and ${\displaystyle \tau =}$0.0166 s. What is the current at ${\displaystyle t=}$0.0156 s?

a) 9.886E+02 A
b) 1.087E+03 A
c) 1.196E+03 A
d) 1.316E+03 A
e) 1.447E+03 A
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=2.5 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=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

#### T1(5-10) H2

1) 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
2)
An electron gun has parallel plates separated by 4.25 cm and gives electrons 15 keV of energy. What force would the field between the plates exert on a 0.518 μC charge that gets between the plates?
a) 1.374E-01 N
b) 1.511E-01 N
c) 1.662E-01 N
d) 1.828E-01 N
e) 2.011E-01 N
3)
Two sources of emf ε1=40.3 V, and ε2=16.8 V are oriented as shownin the circuit. The resistances are R1=2.57 kΩ and R2=2.25 kΩ. 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

4) The charge passing a plane intersecting a wire is ${\displaystyle Q_{M}=\left(1-e^{t/\tau }\right)}$, where ${\displaystyle Q_{M}}$=38 C and ${\displaystyle \tau =}$0.0167 s. What is the current at ${\displaystyle 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
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=1.6 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° 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·m2/C
b) 3.544E+01 N·m2/C
c) 3.899E+01 N·m2/C
d) 4.289E+01 N·m2/C
e) 4.718E+01 N·m2/C

6) Calculate the final speed of a free electron accelerated from rest through a potential difference of 45 V.

a) 3.617E+06 m/s
b) 3.979E+06 m/s
c) 4.376E+06 m/s
d) 4.814E+06 m/s
e) 5.296E+06 m/s

7) 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 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C
b) 7.701E+01 N/C
c) 8.471E+01 N/C
d) 9.318E+01 N/C
e) 1.025E+02 N/C
8)
What is the net capacitance if C1=3.06 μF, C2=3.09 μF, and C3=2.48 μF in the configuration shown?
a) 3.018E+00 μF
b) 3.320E+00 μF
c) 3.652E+00 μF
d) 4.017E+00 μF
e) 4.419E+00 μF
9)
The resistances in the figure shown are R1= 2.34 Ω, R2= 1.34 Ω, and R2= 2.94 Ω. 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=−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)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=5e}$?
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

### T1(5-10) I0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.2{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.2{\text{ m}}}$.

a) 3.228E+00 V/m2
b) 3.551E+00 V/m2
c) 3.906E+00 V/m2
d) 4.297E+00 V/m2
e) 4.727E+00 V/m2

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,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

a) 1.128E+04 V·m
b) 1.241E+04 V·m
c) 1.365E+04 V·m
d) 1.502E+04 V·m
e) 1.652E+04 V·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=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° 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) 4.809E+01 N·m2/C
b) 5.290E+01 N·m2/C
c) 5.819E+01 N·m2/C
d) 6.401E+01 N·m2/C
e) 7.041E+01 N·m2/C

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)
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) 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 μC
b) 3.041E+01 μC
c) 3.345E+01 μC
d) 3.679E+01 μC
e) 4.047E+01 μC

8) A DC winch moter draws 25 amps at 119 volts as it lifts a 4.730E+03 N weight at a constant speed of 0.47 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) 1.094E+00 Ω
b) 1.203E+00 Ω
c) 1.323E+00 Ω
d) 1.456E+00 Ω
e) 1.601E+00 Ω
9)
Two sources of emf ε1=16.8 V, and ε2=6.85 V are oriented as shownin the circuit. The resistances are R1=4.43 kΩ and R2=1.24 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=2.68 mA and I4=0.758 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) 3.890E+00 V
b) 4.279E+00 V
c) 4.707E+00 V
d) 5.178E+00 V
e) 5.695E+00 V
10)
Two sources of emf ε1=29.5 V, and ε2=11.0 V are oriented as shownin the circuit. The resistances are R1=2.45 kΩ and R2=1.96 kΩ. 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

#### T1(5-10) I1

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=3e}$?
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
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° 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·m2/C
b) 9.303E+01 N·m2/C
c) 1.023E+02 N·m2/C
d) 1.126E+02 N·m2/C
e) 1.238E+02 N·m2/C

3) 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 Ω
b) 3.906E+00 Ω
c) 4.297E+00 Ω
d) 4.726E+00 Ω
e) 5.199E+00 Ω

4)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.2{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.2{\text{ m}}}$.

a) 3.228E+00 V/m2
b) 3.551E+00 V/m2
c) 3.906E+00 V/m2
d) 4.297E+00 V/m2
e) 4.727E+00 V/m2

5) An empty parallel-plate capacitor with metal plates has an area of 1.94 m2, separated by 1.36 mm. How much charge does it store if the voltage is 8.530E+03 V?

a) 7.359E+01 μC
b) 8.094E+01 μC
c) 8.904E+01 μC
d) 9.794E+01 μC
e) 1.077E+02 μC
6)
Two sources of emf ε1=39.2 V, and ε2=12.6 V are oriented as shownin the circuit. The resistances are R1=3.86 kΩ and R2=1.89 kΩ. 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) 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
8)
Two sources of emf ε1=29.3 V, and ε2=11.0 V are oriented as shownin the circuit. The resistances are R1=5.65 kΩ and R2=2.68 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=2.81 mA and I4=0.525 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.717E+00 mA
b) 1.888E+00 mA
c) 2.077E+00 mA
d) 2.285E+00 mA
e) 2.514E+00 mA
9)
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

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=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.0}{\hat {i}}+3x^{2.0}{\hat {j}}+3y^{3.0}{\hat {k}}}$

a) 4.820E+03 V·m
b) 5.302E+03 V·m
c) 5.832E+03 V·m
d) 6.415E+03 V·m
e) 7.057E+03 V·m

#### T1(5-10) I2

1)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=9.1{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=6.2{\text{ m}}}$.

a) 4.961E-01 V/m2
b) 5.457E-01 V/m2
c) 6.002E-01 V/m2
d) 6.603E-01 V/m2
e) 7.263E-01 V/m2

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) 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,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m
4)
A diploe has a charge magnitude of q=4 nC and a separation distance of d=3.79 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=3.2 cm, y=1.9 cm)? Note that following the textbook's example, the y-value of the field point at 1.9 cm matches the disance of the positive charge above the x-axis.
a) 2.731E+02 V
b) 3.004E+02 V
c) 3.304E+02 V
d) 3.634E+02 V
e) 3.998E+02 V

5) 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 Ω
b) 1.845E+00 Ω
c) 2.030E+00 Ω
d) 2.233E+00 Ω
e) 2.456E+00 Ω
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=1.3 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° 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·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C
7)
Two sources of emf ε1=26.2 V, and ε2=11.5 V are oriented as shownin the circuit. The resistances are R1=2.13 kΩ and R2=1.72 kΩ. 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
8)
Two sources of emf ε1=44.4 V, and ε2=16.8 V are oriented as shownin the circuit. The resistances are R1=4.58 kΩ and R2=1.2 kΩ. 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
9)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=4e}$?
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

10) An empty parallel-plate capacitor with metal plates has an area of 2.66 m2, separated by 1.18 mm. How much charge does it store if the voltage is 6.170E+03 V?

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

### T1(5-10) J0

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

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
2)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
a) 9.750E-15 N
b) 1.072E-14 N
c) 1.180E-14 N
d) 1.298E-14 N
e) 1.427E-14 N

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,
${\displaystyle {\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}}$

a) 9.027E+03 V·m
b) 9.930E+03 V·m
c) 1.092E+04 V·m
d) 1.202E+04 V·m
e) 1.322E+04 V·m

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C
b) 1.522E+02 N/C
c) 1.674E+02 N/C
d) 1.841E+02 N/C
e) 2.025E+02 N/C

5) When a 1.95 V battery operates a 2.8 W bulb, how many electrons pass through it each second?

a) 7.407E+18 electrons
b) 8.147E+18 electrons
c) 8.962E+18 electrons
d) 9.858E+18 electrons
e) 1.084E+19 electrons
6)
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 μC, q2=6 μC, q3=9 μC, and q4=12 μC. 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
7)
In the figure shown C1=19.9 μF, C2=2.25 μF, and C3=4.75 μF. The voltage source provides ε=6.93 V. What is the charge on C1?
a) 2.451E+01 μC
b) 2.696E+01 μC
c) 2.966E+01 μC
d) 3.262E+01 μC
e) 3.589E+01 μC

8) 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 Ω·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
9)
Two sources of emf ε1=30.6 V, and ε2=12.0 V are oriented as shownin the circuit. The resistances are R1=3.46 kΩ and R2=2.77 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=1.97 mA and I4=0.643 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) 4.986E+00 V
b) 5.484E+00 V
c) 6.033E+00 V
d) 6.636E+00 V
e) 7.299E+00 V
10)
Two sources of emf ε1=24.8 V, and ε2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 kΩ and R2=1.6 kΩ. 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

#### T1(5-10) J1

1) 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

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,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

a) 2.210E+04 V·m
b) 2.431E+04 V·m
c) 2.674E+04 V·m
d) 2.941E+04 V·m
e) 3.235E+04 V·m
3)
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 μC, q2=6 μC, q3=9 μC, and q4=10 μC. 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
4)
Two sources of emf ε1=38.9 V, and ε2=16.9 V are oriented as shownin the circuit. The resistances are R1=3.3 kΩ and R2=2.51 kΩ. 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

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

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) 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 ρ(r)=ar1.5 (r≤R) where a=2 nC·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
7)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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
8)
Two sources of emf ε1=20.6 V, and ε2=9.53 V are oriented as shownin the circuit. The resistances are R1=5.46 kΩ and R2=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=1.5 mA and I4=0.415 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.085E+00 mA
b) 1.194E+00 mA
c) 1.313E+00 mA
d) 1.444E+00 mA
e) 1.589E+00 mA
9)
In the figure shown C1=15.4 μF, C2=2.22 μF, and C3=4.77 μF. The voltage source provides ε=6.8 V. What is the charge on C1?
a) 2.702E+01 μC
b) 2.972E+01 μC
c) 3.269E+01 μC
d) 3.596E+01 μC
e) 3.956E+01 μC

10) Calculate the electric field in a 12-gauge copper wire that is 44 m long and carries a current of 78 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 2.704E-04 V/m
b) 2.974E-04 V/m
c) 3.272E-04 V/m
d) 3.599E-04 V/m
e) 3.959E-04 V/m

#### T1(5-10) J2

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

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)
Two sources of emf ε1=16.8 V, and ε2=7.15 V are oriented as shownin the circuit. The resistances are R1=3.12 kΩ and R2=1.51 kΩ. 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

3) Calculate the electric field in a 12-gauge copper wire that is 78 m long and carries a current of 24 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 1.218E-04 V/m
b) 1.340E-04 V/m
c) 1.474E-04 V/m
d) 1.621E-04 V/m
e) 1.783E-04 V/m

4) 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
5)
In the figure shown C1=17.5 μF, C2=2.63 μF, and C3=5.76 μF. The voltage source provides ε=15.9 V. What is the charge on C1?
a) 8.197E+01 μC
b) 9.017E+01 μC
c) 9.919E+01 μC
d) 1.091E+02 μC
e) 1.200E+02 μC

6) 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 ρ(r)=ar1.8 (r≤R) where a=2 nC·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
7)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=6e}$?
a) 2.544E-14 N
b) 2.798E-14 N
c) 3.078E-14 N
d) 3.385E-14 N
e) 3.724E-14 N

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=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}}$

a) 2.694E+03 V·m
b) 2.963E+03 V·m
c) 3.259E+03 V·m
d) 3.585E+03 V·m
e) 3.944E+03 V·m
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 μC, q2=7 μC, q3=8 μC, and q4=10 μC. 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)
Two sources of emf ε1=29.5 V, and ε2=11.0 V are oriented as shownin the circuit. The resistances are R1=2.45 kΩ and R2=1.96 kΩ. 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

### T1(5-10) K0

1)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.7 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.
a) 5.267E+00 V/m2
b) 5.794E+00 V/m2
c) 6.374E+00 V/m2
d) 7.011E+00 V/m2
e) 7.712E+00 V/m2
2)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
a) 5.377E+01 degrees
b) 5.914E+01 degrees
c) 6.506E+01 degrees
d) 7.157E+01 degrees
e) 7.872E+01 degrees

3) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.579E+02 N/C
b) 2.837E+02 N/C
c) 3.121E+02 N/C
d) 3.433E+02 N/C
e) 3.776E+02 N/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

a) 1.491E+01 N/C
b) 1.640E+01 N/C
c) 1.804E+01 N/C
d) 1.984E+01 N/C
e) 2.182E+01 N/C
5)
A diploe has a charge magnitude of q=6 nC and a separation distance of d=4.06 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=3.28 cm, y=2.03 cm)? Note that following the textbook's example, the y-value of the field point at 2.03 cm matches the disance of the positive charge above the x-axis.
a) 4.590E+02 V
b) 5.049E+02 V
c) 5.554E+02 V
d) 6.109E+02 V
e) 6.720E+02 V

6) 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,φ) of P1 are (9 cm, 0°) and P2 is at (13 cm, 31°).

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
7)
What is the net capacitance if C1=3.25 μF, C2=4.87 μF, and C3=2.19 μF in the configuration shown?
a) 4.139E+00 μF
b) 4.553E+00 μF
c) 5.008E+00 μF
d) 5.509E+00 μF
e) 6.060E+00 μF

8) 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/m3
b) 6.798E+28 e/m3
c) 7.478E+28 e/m3
d) 8.226E+28 e/m3
e) 9.049E+28 e/m3
9)
Two sources of emf ε1=20.6 V, and ε2=9.53 V are oriented as shownin the circuit. The resistances are R1=5.46 kΩ and R2=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=1.5 mA and I4=0.415 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.085E+00 mA
b) 1.194E+00 mA
c) 1.313E+00 mA
d) 1.444E+00 mA
e) 1.589E+00 mA
10)
The resistances in the figure shown are R1= 1.54 Ω, R2= 0.927 Ω, and R2= 2.46 Ω. 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=−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

#### T1(5-10) K1

1)
A diploe has a charge magnitude of q=4 nC and a separation distance of d=3.79 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=3.2 cm, y=1.9 cm)? Note that following the textbook's example, the y-value of the field point at 1.9 cm matches the disance of the positive charge above the x-axis.
a) 2.731E+02 V
b) 3.004E+02 V
c) 3.304E+02 V
d) 3.634E+02 V
e) 3.998E+02 V
2)
Two sources of emf ε1=24.9 V, and ε2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.32 kΩ and R2=2.31 kΩ. 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

3) 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
4)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
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
5)
The resistances in the figure shown are R1= 2.73 Ω, R2= 1.4 Ω, and R2= 2.35 Ω. V1 and V3 are text 0.549 V and 1.27 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=−0.584 V. What is the absolute value of the current through R1?
a) 1.213E-01 A
b) 1.334E-01 A
c) 1.468E-01 A
d) 1.614E-01 A
e) 1.776E-01 A
6)
What is the net capacitance if C1=3.13 μF, C2=2.28 μF, and C3=2.59 μF in the configuration shown?
a) 3.231E+00 μF
b) 3.554E+00 μF
c) 3.909E+00 μF
d) 4.300E+00 μF
e) 4.730E+00 μF

7) 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 ρ(r)=ar1.5 (r≤R) where a=2 nC·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

8) Assume that a 29 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,φ) of P1 are (6 cm, 0°) and P2 is at (12 cm, 77°).

a) 1.483E+03 V
b) 1.632E+03 V
c) 1.795E+03 V
d) 1.975E+03 V
e) 2.172E+03 V

9) A make-believe metal has a density of 8.690E+03 kg/m3 and an atomic mass of 48.4 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) 1.081E+29 e/m3
b) 1.189E+29 e/m3
c) 1.308E+29 e/m3
d) 1.439E+29 e/m3
e) 1.582E+29 e/m3
10)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.4 m. Evaluate ${\displaystyle f(x,y)}$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.
a) 3.161E+00 V/m2
b) 3.477E+00 V/m2
c) 3.825E+00 V/m2
d) 4.208E+00 V/m2
e) 4.628E+00 V/m2

#### T1(5-10) K2

1)
What is the net capacitance if C1=3.06 μF, C2=3.09 μF, and C3=2.48 μF in the configuration shown?
a) 3.018E+00 μF
b) 3.320E+00 μF
c) 3.652E+00 μF
d) 4.017E+00 μF
e) 4.419E+00 μF

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

a) 1.114E+01 N/C
b) 1.225E+01 N/C
c) 1.347E+01 N/C
d) 1.482E+01 N/C
e) 1.630E+01 N/C
3)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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
4)
A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.51 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=3.85 cm, y=1.75 cm)? Note that following the textbook's example, the y-value of the field point at 1.75 cm matches the disance of the positive charge above the x-axis.
a) 2.073E+02 V
b) 2.281E+02 V
c) 2.509E+02 V
d) 2.760E+02 V
e) 3.035E+02 V

5) 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 ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C

6) 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,φ) of P1 are (6 cm, 0°) and P2 is at (12 cm, 32°).

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
7)
The resistances in the figure shown are R1= 1.18 Ω, R2= 0.878 Ω, and R2= 2.11 Ω. 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=−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
8)
Two sources of emf ε1=49.6 V, and ε2=19.3 V are oriented as shownin the circuit. The resistances are R1=4.87 kΩ and R2=2.81 kΩ. 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

9) 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/m3
b) 2.036E+29 e/m3
c) 2.239E+29 e/m3
d) 2.463E+29 e/m3
e) 2.709E+29 e/m3
10)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=5e}$?
a) 5.062E+01 degrees
b) 5.569E+01 degrees
c) 6.125E+01 degrees
d) 6.738E+01 degrees
e) 7.412E+01 degrees

### T1(5-10) L0

1)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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

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

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

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=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

a) 1.206E+03 V·m
b) 1.326E+03 V·m
c) 1.459E+03 V·m
d) 1.605E+03 V·m
e) 1.765E+03 V·m

4) 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 ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C

5) 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
6)
A diploe has a charge magnitude of q=5 nC and a separation distance of d=3.85 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=3.18 cm, y=1.93 cm)? Note that following the textbook's example, the y-value of the field point at 1.93 cm matches the disance of the positive charge above the x-axis.
a) 3.866E+02 V
b) 4.253E+02 V
c) 4.678E+02 V
d) 5.146E+02 V
e) 5.661E+02 V

7) 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 μC
b) 1.188E+02 μC
c) 1.306E+02 μC
d) 1.437E+02 μC
e) 1.581E+02 μC

8) 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
9)
Two sources of emf ε1=38.9 V, and ε2=15.7 V are oriented as shownin the circuit. The resistances are R1=2.24 kΩ and R2=2.23 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=3.01 mA and I4=0.86 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.955E+00 mA
b) 2.150E+00 mA
c) 2.365E+00 mA
d) 2.601E+00 mA
e) 2.862E+00 mA
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 543 V. If the combined external and internal resistance is 201 &Omega and the capacitance is 82 mF, how long will it take for the capacitor's voltage to reach 281.0 V?
a) 9.024E+00 s
b) 9.927E+00 s
c) 1.092E+01 s
d) 1.201E+01 s
e) 1.321E+01 s

#### T1(5-10) L1

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 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

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,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

a) 1.128E+04 V·m
b) 1.241E+04 V·m
c) 1.365E+04 V·m
d) 1.502E+04 V·m
e) 1.652E+04 V·m
3)
Two sources of emf ε1=44.4 V, and ε2=16.8 V are oriented as shownin the circuit. The resistances are R1=4.58 kΩ and R2=1.2 kΩ. 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

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) 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

6) 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 ρ(r)=ar1.4 (r≤R) where a=2 nC·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
7)
A diploe has a charge magnitude of q=4 nC and a separation distance of d=4.16 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=2.08 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) 3.070E+02 V
b) 3.377E+02 V
c) 3.715E+02 V
d) 4.086E+02 V
e) 4.495E+02 V

8)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=2.8{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =3{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=1.9{\text{ m}}}$.

a) 4.295E+00 V/m2
b) 4.724E+00 V/m2
c) 5.196E+00 V/m2
d) 5.716E+00 V/m2
e) 6.288E+00 V/m2
9)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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=1.7 m. Evaluate ${\displaystyle f(x,y)}$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.
a) 6.804E+00 V/m2
b) 7.485E+00 V/m2
c) 8.233E+00 V/m2
d) 9.056E+00 V/m2
e) 9.962E+00 V/m2

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 μC
b) 1.188E+02 μC
c) 1.306E+02 μC
d) 1.437E+02 μC
e) 1.581E+02 μC

#### T1(5-10) L2

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 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

2) When a 4.63 V battery operates a 2.26 W bulb, how many electrons pass through it each second?

a) 2.770E+18 electrons
b) 3.047E+18 electrons
c) 3.351E+18 electrons
d) 3.686E+18 electrons
e) 4.055E+18 electrons

3)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=3.3{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =4{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=2.0{\text{ m}}}$.

a) 6.877E+00 V/m2
b) 7.565E+00 V/m2
c) 8.321E+00 V/m2
d) 9.153E+00 V/m2
e) 1.007E+01 V/m2

4) 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 ρ(r)=ar1.5 (r≤R) where a=2 nC·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

5) 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 μC
b) 3.041E+01 μC
c) 3.345E+01 μC
d) 3.679E+01 μC
e) 4.047E+01 μC
6)
${\displaystyle E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx}$
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 ${\displaystyle f(x,y)}$ 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
7)
A diploe has a charge magnitude of q=8 nC and a separation distance of d=3.55 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=3.43 cm, y=1.77 cm)? Note that following the textbook's example, the y-value of the field point at 1.77 cm matches the disance of the positive charge above the x-axis.
a) 5.796E+02 V
b) 6.375E+02 V
c) 7.013E+02 V
d) 7.714E+02 V
e) 8.486E+02 V
8)
Two sources of emf ε1=40.3 V, and ε2=16.8 V are oriented as shownin the circuit. The resistances are R1=2.57 kΩ and R2=2.25 kΩ. 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

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,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

a) 4.286E+03 V·m
b) 4.714E+03 V·m
c) 5.186E+03 V·m
d) 5.704E+03 V·m
e) 6.275E+03 V·m

10) 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

### T1(5-10) M0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=3e}$?
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
2)
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=1.0 m (on axis) away from the loop's center?
a) 5.352E+09 N/C2
b) 5.887E+09 N/C2
c) 6.476E+09 N/C2
d) 7.124E+09 N/C2
e) 7.836E+09 N/C2
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=1.3 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° 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·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/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=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m
b) 3.771E+03 V·m
c) 4.149E+03 V·m
d) 4.564E+03 V·m
e) 5.020E+03 V·m
5)
An electron gun has parallel plates separated by 2.36 cm and gives electrons 54 keV of energy. What force would the field between the plates exert on a 0.45 μC charge that gets between the plates?
a) 7.033E-01 N
b) 7.736E-01 N
c) 8.510E-01 N
d) 9.361E-01 N
e) 1.030E+00 N
6)
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
7)
In the figure shown C1=16.0 μF, C2=2.27 μF, and C3=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C1?
a) 2.515E+01 μC
b) 2.766E+01 μC
c) 3.043E+01 μC
d) 3.347E+01 μC
e) 3.682E+01 μC

8) 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 Ω·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
9)
Two sources of emf ε1=24.8 V, and ε2=10.3 V are oriented as shownin the circuit. The resistances are R1=2.19 kΩ and R2=1.6 kΩ. 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
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

#### T1(5-10) M1

1)
In the figure shown C1=19.4 μF, C2=2.49 μF, and C3=4.17 μF. The voltage source provides ε=6.35 V. What is the charge on C1?
a) 2.602E+01 μC
b) 2.862E+01 μC
c) 3.148E+01 μC
d) 3.463E+01 μC
e) 3.809E+01 μC
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 505 V. If the combined external and internal resistance is 189 &Omega and the capacitance is 74 mF, how long will it take for the capacitor's voltage to reach 374.0 V?
a) 1.560E+01 s
b) 1.716E+01 s
c) 1.887E+01 s
d) 2.076E+01 s
e) 2.284E+01 s

3) Calculate the electric field in a 12-gauge copper wire that is 25 m long and carries a current of 43 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 2.182E-04 V/m
b) 2.401E-04 V/m
c) 2.641E-04 V/m
d) 2.905E-04 V/m
e) 3.195E-04 V/m
4)
Two sources of emf ε1=30.5 V, and ε2=12.0 V are oriented as shownin the circuit. The resistances are R1=3.79 kΩ and R2=1.86 kΩ. 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
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=1.2 m, y=y1=4.2 m, z=z0=1.2 m, and z=z1=4.1 m. The surfaces in the yz plane each have area 8.7m2. Those in the xy plane have area 7.2m2 ,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 58° 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) 4.024E+01 N·m2/C
b) 4.426E+01 N·m2/C
c) 4.868E+01 N·m2/C
d) 5.355E+01 N·m2/C
e) 5.891E+01 N·m2/C

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=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
7)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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
8)
A ring is uniformly charged with a net charge of 8 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=0.32 m (on axis) away from the loop's center?
a) 3.339E+09 N/C2
b) 3.673E+09 N/C2
c) 4.041E+09 N/C2
d) 4.445E+09 N/C2
e) 4.889E+09 N/C2
9)
A diploe has a charge magnitude of q=4 nC and a separation distance of d=4.16 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=2.08 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) 3.070E+02 V
b) 3.377E+02 V
c) 3.715E+02 V
d) 4.086E+02 V
e) 4.495E+02 V
10)
An electron gun has parallel plates separated by 2.98 cm and gives electrons 11 keV of energy. What force would the field between the plates exert on a 0.685 μC charge that gets between the plates?
a) 1.900E-01 N
b) 2.090E-01 N
c) 2.299E-01 N
d) 2.529E-01 N
e) 2.781E-01 N

#### T1(5-10) M2

1)
Two sources of emf ε1=40.3 V, and ε2=16.8 V are oriented as shownin the circuit. The resistances are R1=2.57 kΩ and R2=2.25 kΩ. 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
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 351 V. If the combined external and internal resistance is 148 &Omega and the capacitance is 60 mF, how long will it take for the capacitor's voltage to reach 227.0 V?
a) 9.240E+00 s
b) 1.016E+01 s
c) 1.118E+01 s
d) 1.230E+01 s
e) 1.353E+01 s
3)
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
4)
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
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=1.5 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° 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·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C

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=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

a) 1.997E+03 V·m
b) 2.197E+03 V·m
c) 2.417E+03 V·m
d) 2.659E+03 V·m
e) 2.924E+03 V·m
7)
In the figure shown C1=19.6 μF, C2=2.15 μF, and C3=5.36 μF. The voltage source provides ε=11.6 V. What is the charge on C1?
a) 6.298E+01 μC
b) 6.928E+01 μC
c) 7.621E+01 μC
d) 8.383E+01 μC
e) 9.221E+01 μC

8) Calculate the electric field in a 12-gauge copper wire that is 15 m long and carries a current of 85 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 2.947E-04 V/m
b) 3.241E-04 V/m
c) 3.565E-04 V/m
d) 3.922E-04 V/m
e) 4.314E-04 V/m
9)
An electron gun has parallel plates separated by 4.85 cm and gives electrons 36 keV of energy. What force would the field between the plates exert on a 0.663 μC charge that gets between the plates?
a) 3.697E-01 N
b) 4.067E-01 N
c) 4.474E-01 N
d) 4.921E-01 N
e) 5.413E-01 N
10)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-8e}$, and ${\displaystyle q_{3}=5e}$?
a) 5.062E+01 degrees
b) 5.569E+01 degrees
c) 6.125E+01 degrees
d) 6.738E+01 degrees
e) 7.412E+01 degrees

### T1(5-10) N0

1) A large thin isolated square plate has an area of 5 m2. It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C
b) 6.788E+01 N/C
c) 7.467E+01 N/C
d) 8.214E+01 N/C
e) 9.035E+01 N/C
2)
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
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=1.3 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·m2/C
b) 7.789E+01 N·m2/C
c) 8.568E+01 N·m2/C
d) 9.425E+01 N·m2/C
e) 1.037E+02 N·m2/C

4) 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
5)
An electron gun has parallel plates separated by 4.95 cm and gives electrons 13 keV of energy. What force would the field between the plates exert on a 0.516 μC charge that gets between the plates?
a) 1.355E-01 N
b) 1.491E-01 N
c) 1.640E-01 N
d) 1.804E-01 N
e) 1.984E-01 N

6) 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
7)
What is the net capacitance if C1=2.3 μF, C2=2.84 μF, and C3=3.41 μF in the configuration shown?
a) 4.255E+00 μF
b) 4.681E+00 μF
c) 5.149E+00 μF
d) 5.664E+00 μF
e) 6.230E+00 μF

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.88 Ω at a temperature of 87°C and that the temperature coefficient of expansion is 5.290E-03 (°C)−1). What is the resistance at a temperature of 547 °C?

a) 1.831E+01 Ω
b) 1.923E+01 Ω
c) 2.019E+01 Ω
d) 2.120E+01 Ω
e) 2.226E+01 Ω
9)
In the circuit shown V=16.2 V, R1=2.84 Ω, R2=7.06 Ω, and R3=13.1 Ω. 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

10) A battery with a terminal voltage of 14.6 V is connected to a circuit consisting of 2 21.7 Ω resistors and one 14.4 Ω resistor. What is the voltage drop across the 14.4 Ω 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

#### T1(5-10) N1

1)
What is the net capacitance if C1=4.13 μF, C2=3.56 μF, and C3=3.57 μF in the configuration shown?
a) 5.482E+00 μF
b) 6.030E+00 μF
c) 6.633E+00 μF
d) 7.296E+00 μF
e) 8.026E+00 μF
2)
An electron gun has parallel plates separated by 4.95 cm and gives electrons 13 keV of energy. What force would the field between the plates exert on a 0.516 μC charge that gets between the plates?
a) 1.355E-01 N
b) 1.491E-01 N
c) 1.640E-01 N
d) 1.804E-01 N
e) 1.984E-01 N

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

a) 5.647E+01 N/C
b) 6.212E+01 N/C
c) 6.833E+01 N/C
d) 7.516E+01 N/C
e) 8.268E+01 N/C
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=1.3 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·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C
5)
In the circuit shown V=11.8 V, R1=2.38 Ω, R2=5.11 Ω, and R3=14.6 Ω. 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

6) 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

7) A battery with a terminal voltage of 14.1 V is connected to a circuit consisting of 2 20.3 Ω resistors and one 13.1 Ω resistor. What is the voltage drop across the 13.1 Ω 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

8) 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

9) Imagine a substance could be made into a very hot filament. Suppose the resitance is 3.64 Ω at a temperature of 82°C and that the temperature coefficient of expansion is 4.530E-03 (°C)−1). What is the resistance at a temperature of 390 °C?

a) 7.532E+00 Ω
b) 7.908E+00 Ω
c) 8.303E+00 Ω
d) 8.719E+00 Ω
e) 9.155E+00 Ω
10)
A ring is uniformly charged with a net charge of 8 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=0.32 m (on axis) away from the loop's center?
a) 3.339E+09 N/C2
b) 3.673E+09 N/C2
c) 4.041E+09 N/C2
d) 4.445E+09 N/C2
e) 4.889E+09 N/C2

#### T1(5-10) N2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

a) 1.114E+01 N/C
b) 1.225E+01 N/C
c) 1.347E+01 N/C
d) 1.482E+01 N/C
e) 1.630E+01 N/C

2) 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
3)
In the circuit shown V=15.4 V, R1=2.77 Ω, R2=6.07 Ω, and R3=14.5 Ω. 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

4) Imagine a substance could be made into a very hot filament. Suppose the resitance is 4.08 Ω at a temperature of 26°C and that the temperature coefficient of expansion is 4.800E-03 (°C)−1). What is the resistance at a temperature of 388 °C?

a) 1.064E+01 Ω
b) 1.117E+01 Ω
c) 1.173E+01 Ω
d) 1.231E+01 Ω
e) 1.293E+01 Ω
5)
An electron gun has parallel plates separated by 4.24 cm and gives electrons 48 keV of energy. What force would the field between the plates exert on a 0.48 μC charge that gets between the plates?
a) 5.434E-01 N
b) 5.977E-01 N
c) 6.575E-01 N
d) 7.233E-01 N
e) 7.956E-01 N
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=1.5 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·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C

7) A battery with a terminal voltage of 12.4 V is connected to a circuit consisting of 3 21.6 Ω resistors and one 12.1 Ω resistor. What is the voltage drop across the 12.1 Ω 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
8)
What is the net capacitance if C1=3.27 μF, C2=2.87 μF, and C3=3.23 μF in the configuration shown?
a) 3.250E+00 μF
b) 3.575E+00 μF
c) 3.933E+00 μF
d) 4.326E+00 μF
e) 4.758E+00 μF
9)
A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 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) 3.159E+09 N/C2
b) 3.475E+09 N/C2
c) 3.823E+09 N/C2
d) 4.205E+09 N/C2
e) 4.626E+09 N/C2

10) A large thin isolated square plate has an area of 9 m2. It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C
b) 3.771E+01 N/C
c) 4.148E+01 N/C
d) 4.563E+01 N/C
e) 5.020E+01 N/C

### T1(5-10) O0

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

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

2) A large thin isolated square plate has an area of 4 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) 4.821E+01 N/C
b) 5.303E+01 N/C
c) 5.834E+01 N/C
d) 6.417E+01 N/C
e) 7.059E+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=2.3 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·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C

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 ρ(r)=ar1.6 (r≤R) where a=2 nC·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) Calculate the final speed of a free electron accelerated from rest through a potential difference of 46 V.

a) 3.022E+06 m/s
b) 3.324E+06 m/s
c) 3.657E+06 m/s
d) 4.023E+06 m/s
e) 4.425E+06 m/s

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)
In the figure shown C1=15.4 μF, C2=2.22 μF, and C3=4.77 μF. The voltage source provides ε=6.8 V. What is the charge on C1?
a) 2.702E+01 μC
b) 2.972E+01 μC
c) 3.269E+01 μC
d) 3.596E+01 μC
e) 3.956E+01 μC

8) Calculate the resistance of a 12-gauge copper wire that is 11 m long and carries a current of 94 mA. The resistivity of copper is 1.680E-08 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 3.813E-02 Ω
b) 4.195E-02 Ω
c) 4.614E-02 Ω
d) 5.076E-02 Ω
e) 5.583E-02 Ω
9)
The resistances in the figure shown are R1= 1.57 Ω, R2= 1.25 Ω, and R2= 3.38 Ω. 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=−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
10)
In the circuit shown V=16.2 V, R1=2.84 Ω, R2=7.06 Ω, and R3=13.1 Ω. 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

#### T1(5-10) O1

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

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

2) 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 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 1.384E-01 Ω
b) 1.523E-01 Ω
c) 1.675E-01 Ω
d) 1.842E-01 Ω
e) 2.027E-01 Ω
3)
The resistances in the figure shown are R1= 1.18 Ω, R2= 0.878 Ω, and R2= 2.11 Ω. 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=−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
4)
In the circuit shown V=16.2 V, R1=2.84 Ω, R2=7.06 Ω, and R3=13.1 Ω. 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

5) 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

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

a) 2.408E-06 J
b) 2.649E-06 J
c) 2.914E-06 J
d) 3.205E-06 J
e) 3.526E-06 J
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=1.3 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·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C

8) 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 ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C
9)
In the figure shown C1=16.0 μF, C2=2.27 μF, and C3=4.4 μF. The voltage source provides ε=7.11 V. What is the charge on C1?
a) 2.515E+01 μC
b) 2.766E+01 μC
c) 3.043E+01 μC
d) 3.347E+01 μC
e) 3.682E+01 μC

10) Calculate the final speed of a free electron accelerated from rest through a potential difference of 83 V.

a) 4.466E+06 m/s
b) 4.912E+06 m/s
c) 5.403E+06 m/s
d) 5.944E+06 m/s
e) 6.538E+06 m/s

#### T1(5-10) O2

1)
In the circuit shown V=17.8 V, R1=2.27 Ω, R2=6.79 Ω, and R3=15.1 Ω. 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

2) 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 ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C

3) Calculate the final speed of a free electron accelerated from rest through a potential difference of 45 V.

a) 3.617E+06 m/s
b) 3.979E+06 m/s
c) 4.376E+06 m/s
d) 4.814E+06 m/s
e) 5.296E+06 m/s
4)
The resistances in the figure shown are R1= 1.81 Ω, R2= 1.18 Ω, and R2= 2.62 Ω. 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=−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=19.9 μF, C2=2.25 μF, and C3=4.75 μF. The voltage source provides ε=6.93 V. What is the charge on C1?
a) 2.451E+01 μC
b) 2.696E+01 μC
c) 2.966E+01 μC
d) 3.262E+01 μC
e) 3.589E+01 μC

6)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=9.1{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =2{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=6.2{\text{ m}}}$.

a) 4.961E-01 V/m2
b) 5.457E-01 V/m2
c) 6.002E-01 V/m2
d) 6.603E-01 V/m2
e) 7.263E-01 V/m2

7) 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

8) A 7 C charge is separated from a 12 C charge by distance of 9 cm. What is the work done by increasing this separation to 15 cm?

a) 2.292E-06 J
b) 2.521E-06 J
c) 2.773E-06 J
d) 3.050E-06 J
e) 3.355E-06 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=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·m2/C
b) 3.660E+01 N·m2/C
c) 4.026E+01 N·m2/C
d) 4.429E+01 N·m2/C
e) 4.872E+01 N·m2/C

10) 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 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 1.983E-01 Ω
b) 2.181E-01 Ω
c) 2.399E-01 Ω
d) 2.639E-01 Ω
e) 2.903E-01 Ω

### T1(5-10) P0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=2e}$?
a) 3.426E-15 N
b) 3.768E-15 N
c) 4.145E-15 N
d) 4.560E-15 N
e) 5.015E-15 N
2)
A ring is uniformly charged with a net charge of 5 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) 5.581E+09 N/C2
b) 6.139E+09 N/C2
c) 6.753E+09 N/C2
d) 7.428E+09 N/C2
e) 8.171E+09 N/C2
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° 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·m2/C
b) 9.146E+01 N·m2/C
c) 1.006E+02 N·m2/C
d) 1.107E+02 N·m2/C
e) 1.217E+02 N·m2/C
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=1.4 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·m2/C
b) 6.811E+01 N·m2/C
c) 7.492E+01 N·m2/C
d) 8.242E+01 N·m2/C
e) 9.066E+01 N·m2/C

5) Two large parallel conducting plates are separated by 8.13 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 92 V?

a) 9.394E-01 mm
b) 1.080E+00 mm
c) 1.242E+00 mm
d) 1.429E+00 mm
e) 1.643E+00 mm

6) 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,φ) of P1 are (9 cm, 0°) and P2 is at (12 cm, 14°).

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

7) An empty parallel-plate capacitor with metal plates has an area of 2.66 m2, separated by 1.18 mm. How much charge does it store if the voltage is 6.170E+03 V?

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

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)
Two sources of emf ε1=38.8 V, and ε2=14.9 V are oriented as shownin the circuit. The resistances are R1=5.83 kΩ and R2=1.77 kΩ. 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) Three resistors, R1 = 1.52 Ω, and R2 = R2 = 3.38 Ω, are connected in parallel to a 5.82 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)

a) 1.842E+01 W
b) 2.026E+01 W
c) 2.228E+01 W
d) 2.451E+01 W
e) 2.696E+01 W

#### T1(5-10) P1

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

2) 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
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=2.9 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° 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·m2/C
b) 1.910E+01 N·m2/C
c) 2.101E+01 N·m2/C
d) 2.311E+01 N·m2/C
e) 2.543E+01 N·m2/C

4) Three resistors, R1 = 1.52 Ω, and R2 = R2 = 3.38 Ω, are connected in parallel to a 5.82 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)

a) 1.842E+01 W
b) 2.026E+01 W
c) 2.228E+01 W
d) 2.451E+01 W
e) 2.696E+01 W
5)
Two sources of emf ε1=30.3 V, and ε2=8.6 V are oriented as shownin the circuit. The resistances are R1=3.81 kΩ and R2=2.39 kΩ. 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
6)
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

7) 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

8) An empty parallel-plate capacitor with metal plates has an area of 1.94 m2, separated by 1.36 mm. How much charge does it store if the voltage is 8.530E+03 V?

a) 7.359E+01 μC
b) 8.094E+01 μC
c) 8.904E+01 μC
d) 9.794E+01 μC
e) 1.077E+02 μC

9) Assume that a 25 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,φ) of P1 are (5 cm, 0°) and P2 is at (13 cm, 70°).

a) 2.285E+03 V
b) 2.514E+03 V
c) 2.765E+03 V
d) 3.042E+03 V
e) 3.346E+03 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=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·m2/C
b) 3.660E+01 N·m2/C
c) 4.026E+01 N·m2/C
d) 4.429E+01 N·m2/C
e) 4.872E+01 N·m2/C

#### T1(5-10) P2

1)
Two sources of emf ε1=26.8 V, and ε2=10.1 V are oriented as shownin the circuit. The resistances are R1=2.2 kΩ and R2=2.55 kΩ. 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
2)
A ring is uniformly charged with a net charge of 2 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=0.99 m (on axis) away from the loop's center?
a) 2.429E+09 N/C2
b) 2.672E+09 N/C2
c) 2.939E+09 N/C2
d) 3.233E+09 N/C2
e) 3.556E+09 N/C2

3) Three resistors, R1 = 0.61 Ω, and R2 = R2 = 1.35 Ω, 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

4) Assume that a 17 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,φ) of P1 are (9 cm, 0°) and P2 is at (12 cm, 15°).

a) 4.244E+02 V
b) 4.669E+02 V
c) 5.135E+02 V
d) 5.649E+02 V
e) 6.214E+02 V
5)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=6e}$?
a) 1.308E-13 N
b) 1.439E-13 N
c) 1.583E-13 N
d) 1.741E-13 N
e) 1.915E-13 N

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 μC
b) 1.505E+01 μC
c) 1.655E+01 μC
d) 1.820E+01 μC
e) 2.003E+01 μC
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=1.5 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·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C

8) Two large parallel conducting plates are separated by 7.93 mm. Equal and opposite surface charges of 7.720E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 77 V?

a) 6.678E-01 mm
b) 7.679E-01 mm
c) 8.831E-01 mm
d) 1.016E+00 mm
e) 1.168E+00 mm

9) 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
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=2.5 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=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

### T1(5-10) Q0

1) 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
2)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=4e}$?
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

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,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

a) 8.731E+02 V·m
b) 9.604E+02 V·m
c) 1.056E+03 V·m
d) 1.162E+03 V·m
e) 1.278E+03 V·m

4) 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

5) A 12.0 V battery can move 35,000 C of charge. How many Joules does it deliver?

a) 4.200E+05 J
b) 4.620E+05 J
c) 5.082E+05 J
d) 5.590E+05 J
e) 6.149E+05 J
6)
A Van de Graff generator has a 95 cm diameter metal sphere that produces 190 kV near its surface. What is the excess charge on the sphere?
a) 9.129E+00 μC
b) 1.004E+01 μC
c) 1.105E+01 μC
d) 1.215E+01 μC
e) 1.337E+01 μC

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 μC
b) 6.903E+01 μC
c) 7.593E+01 μC
d) 8.352E+01 μC
e) 9.188E+01 μC

8) 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 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 3.737E-01 Ω
b) 4.111E-01 Ω
c) 4.522E-01 Ω
d) 4.975E-01 Ω
e) 5.472E-01 Ω
9)
Two sources of emf ε1=20.6 V, and ε2=9.53 V are oriented as shownin the circuit. The resistances are R1=5.46 kΩ and R2=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=1.5 mA and I4=0.415 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.085E+00 mA
b) 1.194E+00 mA
c) 1.313E+00 mA
d) 1.444E+00 mA
e) 1.589E+00 mA
10)
The resistances in the figure shown are R1= 2.54 Ω, R2= 1.15 Ω, and R2= 2.9 Ω. V1 and V3 are text 0.446 V and 3.39 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=−0.744 V. What is the absolute value of the current through R1?
a) 1.285E-01 A
b) 1.414E-01 A
c) 1.555E-01 A
d) 1.711E-01 A
e) 1.882E-01 A

#### T1(5-10) Q1

1)
The resistances in the figure shown are R1= 1.6 Ω, R2= 1.3 Ω, and R2= 2.22 Ω. 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=−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

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=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m
3)
Two sources of emf ε1=49.6 V, and ε2=19.3 V are oriented as shownin the circuit. The resistances are R1=4.87 kΩ and R2=2.81 kΩ. 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) 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 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 4.957E-02 Ω
b) 5.453E-02 Ω
c) 5.998E-02 Ω
d) 6.598E-02 Ω
e) 7.258E-02 Ω

5) 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 μC
b) 2.695E+01 μC
c) 2.965E+01 μC
d) 3.261E+01 μC
e) 3.587E+01 μC

6) 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

7) 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
8)
A Van de Graff generator has a 124 cm diameter metal sphere that produces 270 kV near its surface. What is the excess charge on the sphere?
a) 1.539E+01 μC
b) 1.693E+01 μC
c) 1.863E+01 μC
d) 2.049E+01 μC
e) 2.254E+01 μC

9) 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
10)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=2e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=5e}$?
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

#### T1(5-10) Q2

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 Ω·m and 12-gauge wire as a cross-sectional area of 3.31 mm2.

a) 2.995E-01 Ω
b) 3.294E-01 Ω
c) 3.623E-01 Ω
d) 3.986E-01 Ω
e) 4.384E-01 Ω

2) An empty parallel-plate capacitor with metal plates has an area of 2.66 m2, separated by 1.18 mm. How much charge does it store if the voltage is 6.170E+03 V?

a) 1.231E+02 μC
b) 1.355E+02 μC
c) 1.490E+02 μC
d) 1.639E+02 μC
e) 1.803E+02 μC
3)
A Van de Graff generator has a 116 cm diameter metal sphere that produces 246 kV near its surface. What is the excess charge on the sphere?
a) 1.193E+01 μC
b) 1.312E+01 μC
c) 1.443E+01 μC
d) 1.588E+01 μC
e) 1.746E+01 μC

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=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
5)
Two sources of emf ε1=29.5 V, and ε2=11.0 V are oriented as shownin the circuit. The resistances are R1=2.45 kΩ and R2=1.96 kΩ. 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
6)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=6\times 10^{-7}{\text{m}}}$.what angle does the force on ${\displaystyle q_{2}}$ make above the ${\displaystyle -x}$ axis if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
a) 5.377E+01 degrees
b) 5.914E+01 degrees
c) 6.506E+01 degrees
d) 7.157E+01 degrees
e) 7.872E+01 degrees

7) 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

8) A 12.0 V battery can move 24,000 C of charge. How many Joules does it deliver?

a) 1.967E+05 J
b) 2.164E+05 J
c) 2.380E+05 J
d) 2.618E+05 J
e) 2.880E+05 J

9) 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
10)
The resistances in the figure shown are R1= 1.1 Ω, R2= 1.55 Ω, and R2= 2.11 Ω. 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=−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

### T1(5-10) R0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=4e}$?
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 ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 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=1.4 m (on axis) away from the loop's center?
a) 7.119E+09 N/C2
b) 7.831E+09 N/C2
c) 8.614E+09 N/C2
d) 9.476E+09 N/C2
e) 1.042E+10 N/C2
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·m2/C
b) 3.192E+01 N·m2/C
c) 3.511E+01 N·m2/C
d) 3.862E+01 N·m2/C
e) 4.248E+01 N·m2/C

4) 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 ρ(r)=ar1.5 (r≤R) where a=2 nC·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
5)
A Van de Graff generator has a 105 cm diameter metal sphere that produces 210 kV near its surface. What is the excess charge on the sphere?
a) 9.216E+00 μC
b) 1.014E+01 μC
c) 1.115E+01 μC
d) 1.227E+01 μC
e) 1.349E+01 μC

6) 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
7)
What is the net capacitance if C1=3.25 μF, C2=4.87 μF, and C3=2.19 μF in the configuration shown?
a) 4.139E+00 μF
b) 4.553E+00 μF
c) 5.008E+00 μF
d) 5.509E+00 μF
e) 6.060E+00 μF

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 5.89 Ω at a temperature of 43°C and that the temperature coefficient of expansion is 4.400E-03 (°C)−1). What is the resistance at a temperature of 398 °C?

a) 1.369E+01 Ω
b) 1.437E+01 Ω
c) 1.509E+01 Ω
d) 1.584E+01 Ω
e) 1.664E+01 Ω

9) A battery with a terminal voltage of 14.6 V is connected to a circuit consisting of 2 21.7 Ω resistors and one 14.4 Ω resistor. What is the voltage drop across the 14.4 Ω 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

10) Three resistors, R1 = 1.43 Ω, and R2 = R2 = 3.25 Ω, 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

#### T1(5-10) R1

1)
What is the net capacitance if C1=4.7 μF, C2=4.82 μF, and C3=3.61 μF in the configuration shown?
a) 5.445E+00 μF
b) 5.990E+00 μF
c) 6.589E+00 μF
d) 7.247E+00 μF
e) 7.972E+00 μF
2)
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

3) 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 ρ(r)=ar1.2 (r≤R) where a=2 nC·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

4) A battery with a terminal voltage of 9.88 V is connected to a circuit consisting of 3 15.9 Ω resistors and one 10.8 Ω resistor. What is the voltage drop across the 10.8 Ω 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
5)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=2e}$?
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

6) Three resistors, R1 = 0.548 Ω, and R2 = R2 = 1.24 Ω, 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=1.1 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·m2/C
b) 2.287E+01 N·m2/C
c) 2.516E+01 N·m2/C
d) 2.768E+01 N·m2/C
e) 3.044E+01 N·m2/C
8)
A Van de Graff generator has a 95 cm diameter metal sphere that produces 190 kV near its surface. What is the excess charge on the sphere?
a) 9.129E+00 μC
b) 1.004E+01 μC
c) 1.105E+01 μC
d) 1.215E+01 μC
e) 1.337E+01 μC

9) 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

10) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.98 Ω at a temperature of 92°C and that the temperature coefficient of expansion is 5.080E-03 (°C)−1). What is the resistance at a temperature of 455 °C?

a) 5.363E+00 Ω
b) 5.631E+00 Ω
c) 5.913E+00 Ω
d) 6.208E+00 Ω
e) 6.519E+00 Ω

#### T1(5-10) R2

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=1.4 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·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

2) Imagine a substance could be made into a very hot filament. Suppose the resitance is 4.08 Ω at a temperature of 26°C and that the temperature coefficient of expansion is 4.800E-03 (°C)−1). What is the resistance at a temperature of 388 °C?

a) 1.064E+01 Ω
b) 1.117E+01 Ω
c) 1.173E+01 Ω
d) 1.231E+01 Ω
e) 1.293E+01 Ω
3)
What is the net capacitance if C1=4.55 μF, C2=4.39 μF, and C3=3.32 μF in the configuration shown?
a) 4.173E+00 μF
b) 4.590E+00 μF
c) 5.049E+00 μF
d) 5.554E+00 μF
e) 6.110E+00 μF
4)
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
5)
A Van de Graff generator has a 95 cm diameter metal sphere that produces 187 kV near its surface. What is the excess charge on the sphere?
a) 9.883E+00 μC
b) 1.087E+01 μC
c) 1.196E+01 μC
d) 1.315E+01 μC
e) 1.447E+01 μC
6)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=3e}$, ${\displaystyle q_{2}=-9e}$, and ${\displaystyle q_{3}=6e}$?
a) 1.308E-13 N
b) 1.439E-13 N
c) 1.583E-13 N
d) 1.741E-13 N
e) 1.915E-13 N

7) If a 19 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=73 V is x2 + y2 + z2 = R2, where R=

a) 1.598E+00 m
b) 1.757E+00 m
c) 1.933E+00 m
d) 2.127E+00 m
e) 2.339E+00 m

8) Three resistors, R1 = 0.87 Ω, and R2 = R2 = 2.0 Ω, are connected in parallel to a 8.57 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)

a) 6.977E+01 W
b) 7.674E+01 W
c) 8.442E+01 W
d) 9.286E+01 W
e) 1.021E+02 W

9) A battery with a terminal voltage of 7.63 V is connected to a circuit consisting of 3 20.9 Ω resistors and one 12.1 Ω resistor. What is the voltage drop across the 12.1 Ω 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) 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 ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C

### T1(5-10) S0

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)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=8.7{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =7{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=5.8{\text{ m}}}$.

a) 3.722E-01 V/m2
b) 4.094E-01 V/m2
c) 4.504E-01 V/m2
d) 4.954E-01 V/m2
e) 5.450E-01 V/m2

3) 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
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=1.3 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° 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·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C

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) Calculate the final speed of a free electron accelerated from rest through a potential difference of 12 V.

a) 1.544E+06 m/s
b) 1.698E+06 m/s
c) 1.868E+06 m/s
d) 2.055E+06 m/s
e) 2.260E+06 m/s
7)
In the figure shown C1=16.9 μF, C2=2.3 μF, and C3=4.67 μF. The voltage source provides ε=13.4 V. What is the charge on C1?
a) 6.011E+01 μC
b) 6.613E+01 μC
c) 7.274E+01 μC
d) 8.001E+01 μC
e) 8.801E+01 μC

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)
In the circuit shown V=10.8 V, R1=1.26 Ω, R2=5.65 Ω, and R3=14.8 Ω. What is the power dissipated by R2?
a) 8.240E+00 W
b) 9.064E+00 W
c) 9.970E+00 W
d) 1.097E+01 W
e) 1.206E+01 W
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 319 V. If the combined external and internal resistance is 231 &Omega and the capacitance is 64 mF, how long will it take for the capacitor's voltage to reach 175.0 V?
a) 9.718E+00 s
b) 1.069E+01 s
c) 1.176E+01 s
d) 1.293E+01 s
e) 1.423E+01 s

#### T1(5-10) S1

1)
In the circuit shown V=17.9 V, R1=1.68 Ω, R2=7.84 Ω, and R3=12.3 Ω. What is the power dissipated by R2?
a) 2.240E+01 W
b) 2.464E+01 W
c) 2.710E+01 W
d) 2.981E+01 W
e) 3.279E+01 W

2) 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

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

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

4) 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
5)
In the figure shown C1=17.1 μF, C2=2.87 μF, and C3=4.74 μF. The voltage source provides ε=6.63 V. What is the charge on C1?
a) 2.385E+01 μC
b) 2.623E+01 μC
c) 2.886E+01 μC
d) 3.174E+01 μC
e) 3.492E+01 μC

6) 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
7)
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=1.1 m (on axis) away from the loop's center?
a) 8.336E+09 N/C2
b) 9.170E+09 N/C2
c) 1.009E+10 N/C2
d) 1.110E+10 N/C2
e) 1.220E+10 N/C2
8)
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 543 V. If the combined external and internal resistance is 201 &Omega and the capacitance is 82 mF, how long will it take for the capacitor's voltage to reach 281.0 V?
a) 9.024E+00 s
b) 9.927E+00 s
c) 1.092E+01 s
d) 1.201E+01 s
e) 1.321E+01 s

9) 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
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=1.7 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° 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·m2/C
b) 7.612E+01 N·m2/C
c) 8.373E+01 N·m2/C
d) 9.210E+01 N·m2/C
e) 1.013E+02 N·m2/C

#### T1(5-10) S2

1)
In the circuit shown V=18.4 V, R1=1.64 Ω, R2=6.56 Ω, and R3=12.8 Ω. 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
2)
In the figure shown C1=19.9 μF, C2=2.25 μF, and C3=4.75 μF. The voltage source provides ε=6.93 V. What is the charge on C1?
a) 2.451E+01 μC
b) 2.696E+01 μC
c) 2.966E+01 μC
d) 3.262E+01 μC
e) 3.589E+01 μC

3) 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
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=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° 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) 4.809E+01 N·m2/C
b) 5.290E+01 N·m2/C
c) 5.819E+01 N·m2/C
d) 6.401E+01 N·m2/C
e) 7.041E+01 N·m2/C

5) 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

6) What is the average current involved when a truck battery sets in motion 738 C of charge in 3.87 s while starting an engine?

a) 1.907E+02 A
b) 2.098E+02 A
c) 2.307E+02 A
d) 2.538E+02 A
e) 2.792E+02 A
7)
A ring is uniformly charged with a net charge of 2 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=0.99 m (on axis) away from the loop's center?
a) 2.429E+09 N/C2
b) 2.672E+09 N/C2
c) 2.939E+09 N/C2
d) 3.233E+09 N/C2
e) 3.556E+09 N/C2

8) Calculate the final speed of a free electron accelerated from rest through a potential difference of 81 V.

a) 4.411E+06 m/s
b) 4.853E+06 m/s
c) 5.338E+06 m/s
d) 5.872E+06 m/s
e) 6.459E+06 m/s

9)  ${\displaystyle E(z)=\int _{0}^{R}f(r',z)dr'}$
is an integral that calculates the magnitude of the electric field at a distance ${\displaystyle z}$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is ${\displaystyle R=6.9{\text{ m}}}$ and the surface charge density is ${\displaystyle \sigma =9{\text{ nC/m}}^{3}}$. Evaluate ${\displaystyle f(r',z)}$ at ${\displaystyle r'=4.3{\text{ m}}}$.

a) 8.924E-01 V/m2
b) 9.816E-01 V/m2
c) 1.080E+00 V/m2
d) 1.188E+00 V/m2
e) 1.307E+00 V/m2
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 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

### T1(5-10) T0

1)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=4\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=4e}$?
a) 9.750E-15 N
b) 1.072E-14 N
c) 1.180E-14 N
d) 1.298E-14 N
e) 1.427E-14 N

2) A large thin isolated square plate has an area of 3 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) 1.694E+02 N/C
b) 1.864E+02 N/C
c) 2.050E+02 N/C
d) 2.255E+02 N/C
e) 2.480E+02 N/C

3) 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
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=1.4 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·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

5) Two large parallel conducting plates are separated by 7.42 mm. Equal and opposite surface charges of 7.760E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 61 V?

a) 3.979E-01 mm
b) 4.576E-01 mm
c) 5.263E-01 mm
d) 6.052E-01 mm
e) 6.960E-01 mm

6) 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
7)
In the figure shown C1=19.2 μF, C2=2.24 μF, and C3=4.93 μF. The voltage source provides ε=11.7 V. What is the energy stored in C2?
a) 1.303E+01 μJ
b) 1.434E+01 μJ
c) 1.577E+01 μJ
d) 1.735E+01 μJ
e) 1.908E+01 μJ

8) Imagine a substance could be made into a very hot filament. Suppose the resitance is 1.52 Ω at a temperature of 45°C and that the temperature coefficient of expansion is 4.330E-03 (°C)−1). What is the resistance at a temperature of 479 °C?

a) 3.970E+00 Ω
b) 4.168E+00 Ω
c) 4.376E+00 Ω
d) 4.595E+00 Ω
e) 4.825E+00 Ω
9)
Two sources of emf ε1=45.3 V, and ε2=13.3 V are oriented as shownin the circuit. The resistances are R1=3.82 kΩ and R2=1.5 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=6.17 mA and I4=1.11 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) 1.177E+01 V
b) 1.295E+01 V
c) 1.424E+01 V
d) 1.567E+01 V
e) 1.723E+01 V
10)
Two sources of emf ε1=13.6 V, and ε2=6.53 V are oriented as shownin the circuit. The resistances are R1=2.89 kΩ and R2=2.12 kΩ. 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

#### T1(5-10) T1

1) A 8 C charge is separated from a 12 C charge by distance of 9 cm. What is the work done by increasing this separation to 18 cm?

a) 3.274E-06 J
b) 3.601E-06 J
c) 3.961E-06 J
d) 4.358E-06 J
e) 4.793E-06 J
2)
Three small charged objects are placed as shown, where ${\displaystyle b=2a}$, and ${\displaystyle a=2\times 10^{-7}{\text{m}}}$. What is the magnitude of the net force on ${\displaystyle q_{2}}$ if ${\displaystyle q_{1}=1e}$, ${\displaystyle q_{2}=-7e}$, and ${\displaystyle q_{3}=2e}$?
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
3)
Two sources of emf ε1=20.6 V, and ε2=9.53 V are oriented as shownin the circuit. The resistances are R1=5.46 kΩ and R2=2.55 kΩ. Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown. I3=1.5 mA and I4=0.415 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
a) 1.085E+00 mA
b) 1.194E+00 mA
c) 1.313E+00 mA
d) 1.444E+00 mA
e) 1.589E+00 mA

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)