Question 1

Through what potential difference must an electron (starting from rest)be accelerated if it is to reach a speed of 3.0 *107 m/s?

Accepted Answer

A) 5.8 kV 
B) 2.6 kV 
C) 7.1 kV 
D) 8.6 kV 
E) 5.1 kV 
A) 5.8 kV 
B) 2.6 kV 
C) 7.1 kV 
D) 8.6 kV 
E) 5.1 kV

Question 2

A 15-$\mu$F capacitor and a 30-$\mu$F capacitor are connected in series,and charged to a potential difference of 50 V.What is the resulting charge on the 30-$\mu$F capacitor?

Accepted Answer

A) 0.70 mC 
B) 0.80 mC 
C) 0.50 mC 
D) 0.60 mC 
E) 0.40 mC 
A) 0.70 mC 
B) 0.80 mC 
C) 0.50 mC 
D) 0.60 mC 
E) 0.40 mC

Question 3

An infinite plane of charge with $\sigma = + 55.5 \frac { p C } { \mathrm {~m} ^ { 2 } }$ is tilted at a 45$\degree$ angle to the vertical direction as shown below.The potential difference,VA -VB,in volts,between points A and B,a 4.50 m distance apart,is

Accepted Answer

A) -7.06. 
B) -9.98. 
C) -14.11. 
D) +7.06. 
E) +9.98. 
A) -7.06. 
B) -9.98. 
C) -14.11. 
D) +7.06. 
E) +9.98.

Question 4

A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the origin?

Accepted Answer

A)  $\int _ { 4 } ^ { 6 } \frac { 18 d x } { 4 - x }$ 
B)  $\int _ { 4 } ^ { 6 } \frac { 36 d x } { x }$ 
C)  $\int _ { 4 } ^ { 6 } \frac { 18 d x } { x }$ 
D)  $\int _ { 4 } ^ { 6 } \frac { 36 d x } { 6 - x }$ 
E)  $\int _ { 4 } ^ { 6 } \frac { 36 d x } { 4 + x }$ 
A)  $\int _ { 4 } ^ { 6 } \frac { 18 d x } { 4 - x }$ 
B)  $\int _ { 4 } ^ { 6 } \frac { 36 d x } { x }$ 
C)  $\int _ { 4 } ^ { 6 } \frac { 18 d x } { x }$ 
D)  $\int _ { 4 } ^ { 6 } \frac { 36 d x } { 6 - x }$ 
E)  $\int _ { 4 } ^ { 6 } \frac { 36 d x } { 4 + x }$

Question 5

A 30-$\mu$F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-$\mu$F capacitor.If the final potential difference across the 10-$\mu$F capacitor is 20 V,determine V0.

Accepted Answer

A) 13 V 
B) 27 V 
C) 20 V 
D) 29 V 
E) 60 V 
A) 13 V 
B) 27 V 
C) 20 V 
D) 29 V 
E) 60 V

Question 6

Can the lines in the figure below be equipotential lines?

Accepted Answer

A) No,because there are sharp corners. 
B) No,because they are isolated lines. 
C) Yes,because any lines within a charge distribution are equipotential lines. 
D) Yes,they might be boundary lines of the two surfaces of a conductor. 
E) It is not possible to say without further information. 
A) No,because there are sharp corners. 
B) No,because they are isolated lines. 
C) Yes,because any lines within a charge distribution are equipotential lines. 
D) Yes,they might be boundary lines of the two surfaces of a conductor. 
E) It is not possible to say without further information.

Question 7

A charged particle (q = -8.0 mC),which moves in a region where the only force acting on the particle is an electric force,is released from rest at point A.At point B the kinetic energy of the particle is equal to 4.8 J.What is the electric potential difference VB- VA?

Accepted Answer

A) -0.60 kV 
B) +0.60 kV 
C) +0.80 kV 
D) -0.80 kV 
E) +0.48 kV 
A) -0.60 kV 
B) +0.60 kV 
C) +0.80 kV 
D) -0.80 kV 
E) +0.48 kV

Question 8

Determine the equivalent capacitance of the combination shown when C = 12 pF.

Accepted Answer

A) 48 pF 
B) 12 pF 
C) 24 pF 
D) 6.0 pF 
E) 59 pF 
A) 48 pF 
B) 12 pF 
C) 24 pF 
D) 6.0 pF 
E) 59 pF

Question 9

Two spheres are made of conducting material.Sphere #2 has twice the radius of Sphere #1.What is the ratio of the capacitance of Sphere #2 to the capacitance of sphere #1?

Accepted Answer

A) 1,since all conducting spheres have the same capacitance. 
B) 2 
C) 4 
D) 8 
E) A single sphere has no capacitance since a second concentric spherical shell is necessary to make a spherical capacitor.Thus,none of the answers above is correct. 
A) 1,since all conducting spheres have the same capacitance. 
B) 2 
C) 4 
D) 8 
E) A single sphere has no capacitance since a second concentric spherical shell is necessary to make a spherical capacitor.Thus,none of the answers above is correct.

Question 10

Determine the energy stored in C1 when C1 = 10 $\mu$F,C2 = 12 $\mu$F,C3 = 15 $\mu$F,and V0 = 70 V.

Accepted Answer

A) 6.5 mJ 
B) 5.1 mJ 
C) 3.9 mJ 
D) 8.0 mJ 
E) 9.8 mJ 
A) 6.5 mJ 
B) 5.1 mJ 
C) 3.9 mJ 
D) 8.0 mJ 
E) 9.8 mJ

Question 11

Charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm).Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod)and point B (4.0 cm from the axis).

Accepted Answer

A) 2.7 V 
B) 2.0 V 
C) 2.4 V 
D) 1.7 V 
E) 3.4 V 
A) 2.7 V 
B) 2.0 V 
C) 2.4 V 
D) 1.7 V 
E) 3.4 V

Question 12

A system consisting of a positively-charged particle and an electric field

Accepted Answer

A) loses potential difference and kinetic energy when the charged particle moves in the direction of the field. 
B) loses electric potential energy when the charged particle moves in the direction of the field. 
C) loses kinetic energy when the charged particle moves in the direction of the field. 
D) gains electric potential energy when the charged particle moves in the direction of the field. 
E) gains potential difference and electric potential energy when the charged particle moves in the direction of the field. 
A) loses potential difference and kinetic energy when the charged particle moves in the direction of the field. 
B) loses electric potential energy when the charged particle moves in the direction of the field. 
C) loses kinetic energy when the charged particle moves in the direction of the field. 
D) gains electric potential energy when the charged particle moves in the direction of the field. 
E) gains potential difference and electric potential energy when the charged particle moves in the direction of the field.

Question 13

Which of the following statements is incorrect?

Accepted Answer

A) Capacitance is always positive. 
B) The symbol for potential difference between the plates of a capacitor is $\Delta V$ . 
C) Water is a polar molecule. 
D) When a dielectric is placed in a capacitor it serves to reduce the electric field. 
E) Nonpolar molecules cannot be used for dielectric material in a capacitor. 
A) Capacitance is always positive. 
B) The symbol for potential difference between the plates of a capacitor is $\Delta V$ . 
C) Water is a polar molecule. 
D) When a dielectric is placed in a capacitor it serves to reduce the electric field. 
E) Nonpolar molecules cannot be used for dielectric material in a capacitor.

Question 14

A parallel plate capacitor is charged to voltage V and then disconnected from the battery.Leopold says that the voltage will decrease if the plates are pulled apart.Gerhardt says that the voltage will remain the same.Which one,if either,is correct,and why?

Accepted Answer

A) Gerhardt,because the maximum voltage is determined by the battery. 
B) Gerhardt,because the charge per unit area on the plates does not change. 
C) Leopold,because charge is transferred from one plate to the other when the plates are separated. 
D) Leopold,because the force each plate exerts on the other decreases when the plates are pulled apart. 
E) Neither,because the voltage increases when the plates are pulled apart. 
A) Gerhardt,because the maximum voltage is determined by the battery. 
B) Gerhardt,because the charge per unit area on the plates does not change. 
C) Leopold,because charge is transferred from one plate to the other when the plates are separated. 
D) Leopold,because the force each plate exerts on the other decreases when the plates are pulled apart. 
E) Neither,because the voltage increases when the plates are pulled apart.

Question 15

A proton (mass = 1.67*10 - 27 kg,charge = 1.60*10 - 19 C)moves from point A to point B under the influence of an electrostatic force only.At point A the proton moves with a speed of 60 km/s.At point B the speed of the proton is 80 km/s.Determine the potential difference VB- VA.

Accepted Answer

A) +15 V 
B) -15 V 
C) -33 V 
D) +33 V 
E) -20 V 
A) +15 V 
B) -15 V 
C) -33 V 
D) +33 V 
E) -20 V

Question 16

The plates of a parallel plate capacitor of capacitance $C _ { 0 }$ are horizontal.Into the gap a slab of dielectric material with $K = 2$ is placed,filling the bottom half of the gap between the plates.What is the resulting new capacitance?

Accepted Answer

A)  $\frac { 2 } { 5 } C _ { 0 }$ 
B)  $\frac { 3 } { 4 } C _ { 0 }$ 
C)  $4 C _ { 0 }$ 
D)  $\frac { 5 } { 2 } C _ { 0 }$ 
E)  $\frac { 4 } { 3 } C _ { 0 }$ 
A)  $\frac { 2 } { 5 } C _ { 0 }$ 
B)  $\frac { 3 } { 4 } C _ { 0 }$ 
C)  $4 C _ { 0 }$ 
D)  $\frac { 5 } { 2 } C _ { 0 }$ 
E)  $\frac { 4 } { 3 } C _ { 0 }$

Question 17

A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3.What is the magnitude of the potential difference between the center and a point 4.0 cm away?

Accepted Answer

A) 12 V 
B) 6.8 V 
C) 3.0 V 
D) 4.7 V 
E) 2.2 V 
A) 12 V 
B) 6.8 V 
C) 3.0 V 
D) 4.7 V 
E) 2.2 V

Question 18

What total energy is stored in the group of capacitors shown if the potential difference Vab is equal to 50 V?

Accepted Answer

A) 48 mJ 
B) 27 mJ 
C) 37 mJ 
D) 19 mJ 
E) 10 mJ 
A) 48 mJ 
B) 27 mJ 
C) 37 mJ 
D) 19 mJ 
E) 10 mJ

Question 19

Determine the equivalent capacitance of the combination shown when C = 45 $\mu$F.

Accepted Answer

A) 36 $\mu$F 
B) 32 $\mu$F 
C) 34 $\mu$F 
D) 30 $\mu$F 
E) 38 $\mu$F 
A) 36 $\mu$F 
B) 32 $\mu$F 
C) 34 $\mu$F 
D) 30 $\mu$F 
E) 38 $\mu$F

Question 20

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 * 107 positive charges of magnitude |e| are now placed on the positive plate of the capacitor,the voltage between the plates changes by

Accepted Answer

A) -5.0 V. 
B) -1.1 V. 
C) 0 V. 
D) +1.1 V. 
E) +5.0 V. 
A) -5.0 V. 
B) -1.1 V. 
C) 0 V. 
D) +1.1 V. 
E) +5.0 V.

Exam 20: Electric Potential and Capacitance

Through what potential difference must an electron (starting from rest)be accelerated if it is to reach a speed of 3.0 *107 m/s?

A 15- μ\muμ F capacitor and a 30- μ\muμ F capacitor are connected in series,and charged to a potential difference of 50 V.What is the resulting charge on the 30- μ\muμ F capacitor?

An infinite plane of charge with σ=+55.5pC m2\sigma = + 55.5 \frac { p C } { \mathrm {~m} ^ { 2 } }σ=+55.5 m2pC​ is tilted at a 45 °\degree° angle to the vertical direction as shown below.The potential difference,VA -VB,in volts,between points A and B,a 4.50 m distance apart,is

A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the origin?

A 30- μ\muμ F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10- μ\muμ F capacitor.If the final potential difference across the 10- μ\muμ F capacitor is 20 V,determine V0.

Can the lines in the figure below be equipotential lines?

A charged particle (q = -8.0 mC),which moves in a region where the only force acting on the particle is an electric force,is released from rest at point A.At point B the kinetic energy of the particle is equal to 4.8 J.What is the electric potential difference VB- VA?

Determine the equivalent capacitance of the combination shown when C = 12 pF.

Two spheres are made of conducting material.Sphere #2 has twice the radius of Sphere #1.What is the ratio of the capacitance of Sphere #2 to the capacitance of sphere #1?

Determine the energy stored in C1 when C1 = 10 μ\muμ F,C2 = 12 μ\muμ F,C3 = 15 μ\muμ F,and V0 = 70 V.

Charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm).Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod)and point B (4.0 cm from the axis).

A system consisting of a positively-charged particle and an electric field

Which of the following statements is incorrect?

A parallel plate capacitor is charged to voltage V and then disconnected from the battery.Leopold says that the voltage will decrease if the plates are pulled apart.Gerhardt says that the voltage will remain the same.Which one,if either,is correct,and why?

A proton (mass = 1.67*10 - 27 kg,charge = 1.60*10 - 19 C)moves from point A to point B under the influence of an electrostatic force only.At point A the proton moves with a speed of 60 km/s.At point B the speed of the proton is 80 km/s.Determine the potential difference VB- VA.

The plates of a parallel plate capacitor of capacitance C0C _ { 0 }C0​ are horizontal.Into the gap a slab of dielectric material with K=2K = 2K=2 is placed,filling the bottom half of the gap between the plates.What is the resulting new capacitance?

A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3.What is the magnitude of the potential difference between the center and a point 4.0 cm away?

What total energy is stored in the group of capacitors shown if the potential difference Vab is equal to 50 V?

Determine the equivalent capacitance of the combination shown when C = 45 μ\muμ F.

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 * 107 positive charges of magnitude |e| are now placed on the positive plate of the capacitor,the voltage between the plates changes by

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Through what potential difference must an electron (starting from rest)be accelerated if it is to reach a speed of 3.0 *10⁷ m/s?

A 15- $\mu$ F capacitor and a 30- $\mu$ F capacitor are connected in series,and charged to a potential difference of 50 V.What is the resulting charge on the 30- $\mu$ F capacitor?

A 30- $\mu$ F capacitor is charged to an unknown potential V₀ and then connected across an initially uncharged 10- $\mu$ F capacitor.If the final potential difference across the 10- $\mu$ F capacitor is 20 V,determine V₀.

A charged particle (q = -8.0 mC),which moves in a region where the only force acting on the particle is an electric force,is released from rest at point A.At point B the kinetic energy of the particle is equal to 4.8 J.What is the electric potential difference V_B- V_A?

Determine the energy stored in C₁ when C₁ = 10 $\mu$ F,C₂ = 12 $\mu$ F,C₃ = 15 $\mu$ F,and V₀ = 70 V. $Determine the energy stored in C<sub>1</sub> when C<sub>1</sub> = 10 \mu F,C<sub>2</sub> = 12 \mu F,C<sub>3</sub> = 15 \mu F,and V<sub>0</sub> = 70 V.$

Charge of uniform density 50 nC/m³ is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm).Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod)and point B (4.0 cm from the axis).

A proton (mass = 1.6710 ^- ²⁷ kg,charge = 1.6010 ^- ¹⁹ C)moves from point A to point B under the influence of an electrostatic force only.At point A the proton moves with a speed of 60 km/s.At point B the speed of the proton is 80 km/s.Determine the potential difference V_B- V_A.

The plates of a parallel plate capacitor of capacitance $C _ { 0 }$ are horizontal.Into the gap a slab of dielectric material with $K = 2$ is placed,filling the bottom half of the gap between the plates.What is the resulting new capacitance?

A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m³.What is the magnitude of the potential difference between the center and a point 4.0 cm away?

What total energy is stored in the group of capacitors shown if the potential difference V_ab is equal to 50 V?

Determine the equivalent capacitance of the combination shown when C = 45 $\mu$ F. $Determine the equivalent capacitance of the combination shown when C = 45 \mu F.$

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 * 10⁷ positive charges of magnitude |e| are now placed on the positive plate of the capacitor,the voltage between the plates changes by