Deck 17: Electric Potential

Question 1

A 3.6 μC charge is moved from a position where its electric potential energy is 7.2 mJ to a position where its potential energy is 1.8 mJ. What is the potential at the first position?

A) 1500 V
B) 2000 V
C) −2000 V
D) 3500 V
E) −1500 V

Answer 1

2000 V

Question 2

A 3.6 μC charge is moved from a position where its electric potential energy is 7.2 mJ to a position where its potential energy is 1.8 mJ. What is the change in potential from the initial position to the final position?

A) 1500 V
B) 2000 V
C) −2000 V
D) 3500 V
E) −1500 V

Answer 2

−1500 V

Question 3

A hollow conducting sphere of radius 12 cm has a net charge of 18 μC. What is the potential 20 cm from the center of the sphere?

A) 0 V
B) 15 V
C) 73 V
D) 8.1 × 10⁵ V
E) 4.1 × 10⁵ V

Answer 3

8.1 × 10⁵ V

Question 4

A charge q₁ is placed on the y-axis at y = 4.0 m and the resulting potential at the position (3.0 m, 4.0 m) is 3.0 V. The charge q₁ is removed and a charge q₂ is placed on the x-axis at x = 3.0 m and the resulting potential at the position (3.0 m, 4.0 m) is 4.0 V. If both charges are in place simultaneously, what is the potential at (3.0 m, 4.0 m)?

A) 1.0 V
B) 3.5 V
C) 5.0 V
D) 7.0 V
E) 12 V

Question 5

The SI unit for electric potential energy is equivalent to

A) N·m².
B) V·C.
C) N/m.
D) C·m².
E) none of these choices are correct

Question 6

A hollow conducting sphere of radius 12 cm has a net charge of 18 μC. What is the potential at the surface of the sphere?

A) 0 V
B) 24 V
C) 2.7 × 10⁵ V
D) 1.3 × 10⁶ V
E) 1.6 × 10⁶ V

Question 7

Three point charges, q₁, q₂, and q₃, are located at the vertices of an equilateral triangle. If q₁ = q₂, what value must q₃ have so that the total potential energy of the arrangement is zero?

A) q₁
B) 0.5 q₁
C) −0.5 q₁
D) (q₁ + q₂)/2
E) no value will have this result

Question 8

Three point charges, q₁, q₂, and q₃, are arranged so the potential energy for the pair q₁ and q₂ is 0.12 J and for the pair q₂ and q₃ is 0.23 J. If the total potential energy of the arrangement is 0.60 J, what is the potential energy of the pair q₁ and q₃?

A) 0.11 J
B) 0.35 J
C) 0.25 J
D) 0.95 J
E) Insufficient information is given for a unique answer

Question 9

A 2.5-mC charge is on the y-axis at y = 3.0 m, and a 6.3-mC charge is on the x-axis at x = 3.0 m. What is the direction of the electric potential at the origin?

A) 22.0°
B) 168°
C) 292°
D) 332°
E) potential has no direction

Question 10

What is the potential at a distance of 0.0529 nm from a proton?

A) 13.6 V
B) −13.6 V
C) 27.2 V
D) −27.2 V
E) 9.11 pC

Question 11

Three point charges, q₁, q₂, and q₃, are arranged so the potential energy for the pair q₁ and q₂ is 0.12 J and for the pair q₂ and q₃ is 0.23 J. What is the potential energy for the pair q₁ and q₃?

A) 0.11 J
B) −0.11J
C) 0.35 J
D) −0.35 J
E) Insufficient information is given for a unique answer

Question 12

Three point charges, q₁ = 2.0 μC, q₂ = 2.0 μC, and q₃ = −1.0 μC, are located at the vertices of an equilateral triangle of side length 30 cm. What is the potential energy of this arrangement?

A) 0.24 J
B) 0.12 J
C) −0.24 J
D) −0.12 J
E) 0

Question 13

Tripling the separation between charges changes the potential energy of a pair of point charges by a factor of

A) 3.
B) 9.
C) 1/3.
D) 1/9.
E) 1 (no change).

Question 14

Doubling both charges changes the potential energy for a pair of point charges by a factor of

A) 2.
B) 4.
C) 1/2.
D) 1/4.
E) 1 (no change).

Question 15

A 2.00 nC charge is placed on the x-axis at x = −3.00 cm, another 2.00 nC charge is placed on the x-axis at x = 3.00 cm, and a third 2.00 nC charge is placed on the y-axis at y = 3.00 cm. What is the potential at the origin?

A) 1800 V
B) 2700 V
C) 3600 V
D) 5400 V
E) 108 V

Question 16

Three 1.0 μC charges are placed along the x-axis, one charge at x = −10 cm, another at the origin, and the last one at x = 10 cm. What is the total potential energy of this arrangement?

A) 0.27 J
B) −0.27 J
C) 0.72 J
D) 0.22 J
E) infinite (or indeterminate)

Question 17

A hollow conducting sphere of radius 12 cm has a net charge of 18 μC. What is the potential at the center of the sphere?

A) 0 V
B) 24 V
C) 1.3 × 10⁶ V
D) 1.6 × 10⁶ V
E) infinite

Question 18

The unit of electric potential, the volt, is equal to a

A) C·N.
B) C²·N/s.
C) J²/C.
D) J/C.
E) J/C².

Question 19

The potential energy of a 3.5 pC charge separated by 6.2 cm from a 1.6 μC charge is

A) 1.3 × 10⁻⁷ J.
B) 8.1 × 10⁻⁷ J.
C) 1.2 × 10⁻⁵ J.
D) 8.1 × 10⁻⁵ J.
E) 1.0 × 10⁻⁵ J.

Question 20

What is the distance between a −2.00 μC charge and a −3.00 μC charge if their potential energy is 0.491 J?

A) 25.0 cm
B) 15.5 cm
C) 11.0 cm
D) 3.14 cm
E) 0.911 cm

Question 21

If electrons are accelerated from rest in an electron gun by sending them through a potential difference of 1000 V, what is the resulting speed of the electrons?

A) 9.41 × 10⁶ m/s
B) 1.33 × 10⁶ m/s
C) 1.88 × 10⁷ m/s
D) 1.97 × 10⁶ m/s
E) 6.22 × 10⁶ m/s

Question 22

Which of the following statements is true?

A) Electric field lines stay inside equipotential surfaces.
B) Equipotential surfaces intersect in straight lines.
C) Equipotential surfaces intersect in curved lines.
D) Electric field lines are perpendicular to equipotential surfaces.
E) Equipotential surfaces are parallel to each other.

Question 23

How much charge is on a conducting sphere of diameter 20 μm if its surface potential is 50 mV?

A) 50 × 10⁻¹⁹ C
B) 56 × 10⁻¹⁸ C
C) 14 × 10⁻¹⁷ C
D) 32 × 10⁻¹⁶ C
E) 1.6 × 10⁻¹⁹ C

Question 24

If electrons are accelerated from rest in an electron gun by sending them through a potential difference of 11.0 kV, what is the resulting kinetic energy of each electron?

A) 11.0 kJ
B) 1.00 × 10⁻¹⁹ J
C) 1.45 × 10⁻²³ J
D) 11.0 mJ
E) 1.76 × 10⁻¹⁵ J

Question 25

A conducting sphere of radius 20 cm is charged to a potential of 1.0 × 10⁶ volts. What is the charge on its surface?

A) 22 μC
B) 4.4 μC
C) 4.7 mC
D) 9.0 nC
E) 16 mC

Question 26

If 500 electrons are placed on a conducting sphere of radius 10 μm, what is the potential at the surface of the sphere?

A) 100 V
B) −10,000 V
C) 32 V
D) −72 mV
E) −72 V

Question 27

Two large equipotential surfaces are flat and parallel, and they are separated by a relatively small distance compared to their size. One surface is at 25.0 V and the other is at 33.0 V. The surfaces are 1.25 cm apart. Assuming the electric field is uniform between the surfaces, what is the magnitude of the electric field midway between them?

A) 25.0 V/m
B) 29.0 V/m
C) 33.0 V/m
D) 6.40 × 10² V/m
E) 1.00 × 10³ V/m

Question 28

A helium nucleus is accelerated from rest through a potential difference V to a kinetic energy of 3.2 × 10⁻¹³ J. What is V?

A) 1.0 MV
B) 2.0 MV
C) 1.6 MV
D) 3.2 MV
E) 0.51 MV

Question 29

A conducting sphere of radius 20 cm is charged so that the electric field reaches 3.0 × 10⁵ V/m at its surface. What is the potential at the surface of the sphere?

A) 3.0 × 10⁴ V
B) 1.5 × 10⁴ V
C) 4.5 × 10⁴ V
D) 6.0 × 10⁴ V
E) 2.7 × 10⁵ V

Question 30

If protons are accelerated from rest in a Van de Graff accelerator through a potential difference of 1.00 MV, what is their resulting speed?

A) 3.67 × 10⁸ m/s
B) 6.25 × 10⁷ m/s
C) 9.79 × 10⁶ m/s
D) 1.38 × 10⁷ m/s
E) 6.92 × 10⁶ m/s

Question 31

If helium nuclei and protons are each accelerated from rest through the same potential difference V, which gets the greatest kinetic energy and by what factor is it greater?

A) The protons get twice as much kinetic energy.
B) The helium nuclei get twice as much kinetic energy.
C) They both get the same kinetic energy.
D) The protons get four times as much kinetic energy.
E) The helium nuclei get four times as much kinetic energy.

Question 32

A parallel plate capacitor has plates of area 100 cm² and separation 0.25 mm. If this capacitor is charged with 25 pC, what is the average charge density on the positive plate?

A) 400 μC/m²
B) 40 × 10⁻¹² C/m²
C) 25 pC/m²
D) 2.5 nC/m²
E) 8.8 × 10⁻¹² C/m²

Question 33

An air-filled parallel plate capacitor has plates of area 100 cm² and separation 0.25 mm. What is its capacitance?

A) 40 nF
B) 0.35 nF
C) 4.4 μF
D) 88 pF
E) 88 μF

Question 34

If two equipotent planes differ in potential by 1.0 volt, and the electric field between them is 20 N/C, what is the separation of the planes?

A) 20 cm
B) 0.050 cm
C) 5.0 cm
D) 2.0 cm
E) 4.0 cm

Question 35

A conducting sphere of radius 20 cm has a charge Q placed on it producing a field of magnitude E₀ at its surface. More charge is added to the surface until the magnitude of the field at the surface is 2 E₀. How much charge was added to the surface?

A) Q/2
B) Q
C) 2 Q
D) 1.4 Q
E) 3 Q

Question 36

A conducting sphere of radius 20 cm has a charge Q placed on it producing a field of magnitude E₀ at its surface. More charge is added to the surface until the magnitude of the field at the surface is 2 E₀. If the potential at the surface was V₀ when the field was E₀, what is the potential when the field is 2 E₀?

A) V₀/2
B) 2 V₀
C) 4 V₀
D) 5 V₀
E) 16 V₀

Question 37

Two large equipotential surfaces are flat and parallel, and they are separated by a relatively small distance compared to their size. One surface is at 25 V and the other is at 33 V. The surfaces are 1.25 cm apart. Assuming the electric field is uniform between the surfaces, what is the direction of the electric field midway between them?

A) The field is parallel to the surfaces.
B) The field is perpendicular to the surfaces and points toward the 33 V surface.
C) The field is perpendicular to the surfaces and points toward the 25 V surface.
D) The field makes clockwise circles, viewed from the 33 V surface.
E) The field makes clockwise circles, viewed from the 25 V surface.

Question 38

Which of the following unit equations is correct?

A) N·C = V/m
B) N·m = V·C
C) N·V = N·m
D) N/m = V/C
E) N/V = m/C

Question 39

The unit V is the same as a

A) N/m.
B) J/N.
C) C/m.
D) N·m/C.
E) C/N.

Question 40

If helium nuclei and protons are each accelerated from rest through the same potential difference, how do the resulting speeds compare?

A) The protons attain twice the speed of the helium nuclei.
B) The protons attain 1.4 times the speed of the helium nuclei.
C) The helium nuclei attain twice the speed of the protons.
D) The helium nuclei attain 1.4 times the speed of the protons.
E) They both attain the same speed.

Question 41

An air-filled parallel plate capacitor is attached to a voltage source and charged. The voltage source is removed, and then the plates are separated to double their previous distance. What happens to the potential difference between the plates when they are separated?

A) It doubles.
B) It quadruples.
C) It halves.
D) It is diminished by a factor of 4.
E) It stays the same.

Question 42

If a 0.20 pF capacitor has a voltage of 40 mV, how many more electrons are on the negative plate than on the positive plate?

A) 8.0 × 10¹⁴
B) 5.0 × 10⁴
C) 1.0 × 10⁵
D) 4.0 × 10³
E) none, the electrons are in equal numbers on the plates

Question 43

An air-filled parallel plate capacitor is attached to a voltage source and charged. The voltage source is removed, and then the plates are separated to double their previous distance. What happens to the energy stored in the capacitor when the plates are separated?

A) It doubles.
B) It quadruples.
C) It halves.
D) It is diminished by a factor of 4.
E) It stays the same.

Question 44

A parallel plate capacitor is charged to 12 V and the voltage source is then disconnected. When the air space between the plates is then filled with a dielectric of constant 6.0, what is the resulting voltage between the plates?

A) 72 V
B) 12 V
C) 6.0 V
D) 2.0 V
E) none of these choices are correct

Question 45

If the area of the plates of a parallel plate capacitor is tripled and the plate separation is halved, by what factor does the capacitance change?

A) It triples.
B) It doubles.
C) It increases by a factor of 6.
D) It increases 1.5 times.
E) It decreases to 2/3 the original.

Question 46

A parallel plate capacitor is attached to a voltage source providing 12 V. If an insulator of dielectric constant 6.0 is then inserted between the capacitor plates, what happens to the surface charge density on the plates, assuming the voltage source is still attached?

A) It increases by a factor of 6.0.
B) It increases by a factor of 2.0.
C) It decreases by a factor of 6.0.
D) It decreases by a factor of 2.0.
E) It stays the same.

Question 47

If the plate area, plate separation, and dielectric constant all are doubled for a parallel plate capacitor, what happens to the capacitance?

A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It quarters.

Question 48

The unit F, the farad, is equal to which of the following?

A) V/m
B) V/C
C) V²/C
D) C/V
E) C/V²

Question 49

An air-filled parallel plate capacitor is attached to a voltage source and charged. The voltage source is removed, and then the plates are separated to double their previous distance. What happens to the electric field between the plates when the plates are separated?

A) It doubles.
B) It quadruples.
C) It halves.
D) It is diminished by a factor of 4.
E) It stays the same.

Question 50

An air-filled parallel plate capacitor is charged until its surface charge density reaches σ0, and then the voltage source is removed. If an insulator with dielectric constant 5.0 is inserted between the plates, what happens to the electric field strength, assuming the surface charge density does not change?

A) It increases by a factor of 5.
B) It increases by a factor of 25.
C) It decreases by a factor of 5.
D) It decreases by a factor of 25.
E) It stays the same.

Question 51

To store 80 mJ of energy in a 100 μF capacitor, what voltage is necessary?

A) 10 V
B) 45 V
C) 4.0 V
D) 40 V
E) more than 120 V

Question 52

If the plate area, plate separation, dielectric strength, and dielectric constant all are doubled for a parallel plate capacitor, what happens to the maximum voltage before breakdown occurs for this capacitor?

A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It quarters.

Question 53

If the charge on a parallel plate capacitor doubles, which of the following also doubles?

A) the electric field between the plates
B) the capacitance
C) the dielectric constant
D) the energy stored
E) the permittivity

Question 54

If the potential difference across the plates of a capacitor is doubled, what happens to the energy stored?

A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It increases by a factor of 1.414.

Question 55

What area plates would a 1.0 F parallel plate capacitor have, with a plate separation of 0.10 mm and a dielectric of constant 10?

A) 1000 cm²
B) 5500 cm²
C) 130 m²
D) 1.1 × 10⁶ m²
E) 4.4 × 10⁹ m²

Question 56

A 22 μF capacitor is charged to 100 V. What is the energy stored in the capacitor?

A) 0.22 J
B) 0.11 J
C) 22 J
D) 11 J
E) 44 mJ

Question 57

A parallel plate capacitor has a paper dielectric having dielectric strength 8.0 kV/mm and dielectric constant 3.0. The plate area is 3000 cm² and the plate separation is 0.50 mm. What is the capacitance?

A) 16 nF
B) 4.2 nF
C) 5.3 nF
D) 1.6 nF
E) 4.2 pF

Question 58

A parallel plate capacitor has a paper dielectric having dielectric strength 8.0 kV/mm and dielectric constant 3.0. The plate area is 3000 cm² and the plate separation is 0.50 mm. What is the highest voltage that can be applied to this capacitor before breakdown occurs?

A) 15 V
B) 1.2 × 10² V
C) 4.0 × 10² V
D) 4.0 × 10³V
E) 1.2 × 10⁴ V

Question 59

An air-filled 3.0 nF capacitor is charged to 8.0 V. If the plate separation is 100 μm, what is the energy density in the electric field between the plates?

A) 57 J/m³
B) 280 J/m³
C) 57 mJ/m³
D) 28 mJ/m³
E) more than 100 J/m³

Question 60

A parallel plate capacitor has a paper dielectric having dielectric strength 8.00 kV/mm and dielectric constant 3.00. The plate area is 3000 cm² and the plate separation is 0.500 mm. If 10.0 V are applied to this capacitor, what is the charge on the capacitor?

A) 50.0 μC
B) 42.0 nC
C) 159 nC
D) 16.0 nC
E) 42.0 μC

Question 61

The electric field between two charged plates is 7.2 kN/C. If the plates are separated by 3.0 mm, what is the potential difference between them?

A) Need more information
B) 240 kV
C) 220 V
D) 22 V

Question 62

A parallel plate capacitor, filled with air, has circular plates with a separation gap of 1.5 mm. If it is desired to store 12 mJ in this capacitor, what must the plate area be for a voltage of 1.5 kV?

A) 1.10 m²
B) 0.55 m²
C) 0.90 m²
D) 1.8 m²

Question 63

A pair of parallel conducting plates have potentials of −17 V and 55 V, respectively. An electron is ejected from the plate at potential −17 V and travels to the plate at 55 V. What is the speed of the electron as it strikes the 55 V plate, assuming it left the −17 V plate starting from rest? The mass of the electron is 9.11 × 10⁻³¹ kg.

A) 2.2 × 10⁶ m/s.
B) 5.0 × 10⁶ m/s
C) 3.6 × 10⁶ m/s
D) 3.1 × 10⁶ m/s

Question 64

A parallel plate capacitor has a dielectric with constant 3.5. The plates are circular with radius 0.07 m, and the separation gap is 0.375 mm. What energy may be stored in this capacitor if 1250 V is the applied voltage?

A) 9.9 × 10⁻⁴ J
B) 2.8 × 10⁻⁴ J
C) 2.0 × 10⁻³ J
D) 3.5 × 10⁻³ J

Question 65

A pair of electric charges has a positive potential energy. This implies that

A) the charges have the same sign.
B) both charges are positive.
C) both charges are negative.
D) the charges have opposite signs.

Question 66

The electric potential at a distance d from a point charge is V. At a distance d', the potential is 2V. What is the ratio of electric field at d' to that at d?

A) 4
B) more information is necessary
C) 2
D) 1/2
E) 1/4

Question 67

The electric field in a given location points along the -x-axis. This means that

A) at that location, the potential is positive.
B) at that location, the potential decreases as one moves toward negative values of x.
C) at that location, the potential decreases as one moves toward positive values of x.
D) at that location, the potential is negative.

Question 68

One member of a pair of parallel conducting plates has potential 17 V. An electron is ejected from that plate and travels the other plate, attaining a velocity of 5.0 × 10⁶ m/s in the process. What is the potential of the second plate? The mass of the electron is 9.11 × 10⁻³¹ kg.

A) 157 V
B) 88 V
C) 72 V
D) −54 V
E) 142 V

Question 69

A pair of conductors are connected with a wire. Which of the following statements is necessarily true?

A) The conductors are at the same electric potential.
B) The electric field at the surface of each conductor is the same.
C) The conductors each have the same charge.
D) There is no net charge on the conductors and wire.

Question 70

A parallel plate capacitor with circular plates having radius 0.07 m is filled with a dielectric of constant 2.2. If it is desired to store 12 × 10⁻⁶ J in this capacitor, what must the separation distance be for a voltage of 1.5 kV?

A) 2.8 cm
B) 5.5 cm
C) 1.3 cm
D) 0.90 cm
E) 1.4 cm

Question 71

At a given location in space, the potential is known to be greater when one moves in any direction. To be more specific, no matter which direction one goes, a small step in that direction results in an increase in the potential. This means that the electric field at this location is

A) Can take on any value at all.
B) zero
C) negative
D) positive

Question 72

Which of the following statements is true?

A) If the electric potential is zero at a point, then the electric field is zero at that point also.
B) If the electric field is zero throughout a region of space, then the electric potential is necessarily also zero there.
C) If the electric field is zero at a point, then the electric potential is zero at that point also.
D) If the electric potential is zero throughout a region of space, then the electric field is necessarily also zero there.
E) The electric field is large where the potential is large, and vice versa.

Question 73

What is the force on a proton sitting midway between a pair of parallel conducting plates that are at potentials of −17 V and 55 V, respectively? Their separation distance is 1.5 cm.

A) 1.5 × 10⁻¹⁵ N
B) 1.5 × 10⁻¹⁶ N
C) 7.7 × 10⁻¹⁶ N
D) 3.8 × 10⁻¹⁶ N
E) 3.0 × 10⁻¹⁶ N

Question 74

A pair of parallel conducting plates have potentials of −17 V and 55 V, respectively. How much work needs to be done on an electron in order to move it from the 55 V to the −17 V plate?

A) 6.1 × 10⁻¹⁸J
B) −6.1 × 10⁻¹⁸J
C) 1.2 × 10⁻¹⁷J
D) −1.2 × 10⁻¹⁷J

Question 75

The magnitude of the force on a proton sitting midway between a pair of parallel conducting plates that are at potentials of −17 V and 55 V, respectively, is 7.69 × 10⁻¹⁶ N. What is the separation distance between the plates?

A) 3.0 cm
B) 1.2 cm
C) 0.58 cm
D) 1.5 cm

Question 76

A parallel plate capacitor has air between the plates, which are circular with radius 0.07 m. The separation gap is 0.375 mm. What is the maximum energy that can be stored in this capacitor if air-breakdown is to be avoided? The breakdown threshold field is approximately 3 × 10⁶ N/C.

A) 7.3 × 10⁻⁶ J
B) 2.3 × 10⁻⁴ J
C) 4.6 × 10⁻⁵ J
D) 6.1 × 10⁻³ J

Question 77

An electron is projected horizontally with a speed of 5.0 × 10⁶ m exactly in the middle of two parallel plates at potentials of −40 V and 104 V, respectively. The plate separation is 3.0 cm. The plates are long enough that the electron, rather than passing completely between the plates, eventually strikes the plate sitting at 104 V potential. What is the speed of the electron when it strikes the plate? The mass of the electron is 9.11 × 10⁻³¹ kg.

A) 8.7 × 10⁶ m/s
B) 7.1 × 10⁶ m/s
C) 6.0 × 10⁶ m/s
D) 5.0 × 10⁶ m/s

Question 78

A pair of parallel conducting plates have potentials of −17 V and 55 V, respectively. An electron is ejected from the plate at potential −17 V and travels to the plate at 55 V. What is the change in the electron's potential energy as it makes this journey?

A) 6.1 × 10⁻¹⁸J
B) −6.1 × 10⁻¹⁸J
C) 1.2 × 10⁻¹⁷J
D) −1.2 × 10⁻¹⁷J

Question 79

An air-filled, parallel plate capacitor with circular plates of radius 0.07 m is used to store energy. If it is desired to store 12 × 10⁻⁶ J in this capacitor, what must the separation distance be for a voltage of 1.5 kV?

A) 0.64 cm
B) 0.41 cm
C) 2.5 cm
D) 1.3 cm

Question 80

The electric field in the dielectric-filled region between the plates of a capacitor is E. What is the charge density on the plates?

A) E·V
B) E² ε₀
C) V²·E
D) ε₀E
E) κε₀E