Deck 18: Electric Potential

Question 1

A free electron is in an electric field. With respect to the field, it experiences a force acting:

A) perpendicular.
B) along a constant potential line.
C) parallel.
D) anti-parallel (opposite in direction).

Answer 1

anti-parallel (opposite in direction).

Question 2

The unit of electrical potential, the volt, is dimensionally equivalent to:

A) J/C.
B) J.C.
C) F.C.
D) C/J.

Answer 2

J/C.

Question 3

Two protons, each of charge 1.60 *10 ^{- 19} C, are 3.00 *10 ^{- 5} m apart. What is the change in potential energy if they are brought 1.00 *10 ^{- 5} m closer together? (k_e = 8.99 *10⁹ N·m²/C²)

A) 3.84 *10 ^{- 24} J
B) 3.20 *10 ^{- 16} J
C) 1.15 *10 ^{- 23} J
D) 3.20 *10 ^{- 19} J

Answer 3

3.84 *10 ^{- 24} J

Question 4

Which of the following characteristics are held in common by both gravitational and electrostatic forces when dealing with either point masses or charges?

A) potential energy is a function of distance of separation
B) forces are conservative
C) inverse square distance law applies
D) all of the above choices are valid

Question 5

A proton (+1.6 *10 ^{- 19} C) moves 10 cm along the direction of an electric field of strength 4.0 N/C. The electrical potential difference between the proton's initial and ending points is:

A) 4.8 *10 ^{- 19} V.
B) 0.40 V.
C) 0.044 V.
D) 6.4 *10 ^{- 19} V.

Question 6

A uniform electric field, with a magnitude of 600 N/C, is directed parallel to the positive x axis. If the potential at x = 4.0 m is 1000 V, what is the potential at x = 2.0 m?

A) "-800 V"
B) "2200 V"
C) "2800 V"
D) "1600 V"

Question 7

Two point charges of values +3.4 $\mu$ C and +6.6 $\mu$ C, respectively, are separated by 0.20 m. What is the potential energy of this 2-charge system? (k_e = 8.99* 10⁹ N.m²/C²)

A) "+1.0 J"
B) "-5.0 J"
C) "-0.75 J"
D) "+0.50 J"

Question 8

An electron and a proton are each released from rest in the same uniform electric field. The electron moves a distance d_electron and the proton moves a distance d_proton as each particle's kinetic energy increases by 1.6 eV. How do d_electron and d_proton compare?

A) d_electron > d_proton
B) d_electron = d_proton
C) d_electron < d_proton
D) The answer depends on the direction of the electric field.

Question 9

If an electron is accelerated from rest through a potential difference of 300 V, find its approximate speed at the end of this process. (e = 1.6 * 10 ^{- 19} C; m_e = 9.1 *10 ^{- 31} kg)

A) 2.5 * 10⁷ m/s
B) 2.1 * 10⁷ m/s
C) 1.0 *10⁷ m/s
D) 1.4 * 10⁷ m/s

Question 10

If the distance between two isolated parallel plates that are oppositely charged is doubled, the electric field between the plates is essentially unchanged. However, the:

A) charge on each plate will double.
B) force on a charged particle halfway between the plates will get twice as small.
C) potential difference between the plates will double.
D) force on a charged particle halfway between the plates will get four times as small.

Question 11

An electron is released from rest at the negative plate of a parallel-plate capacitor. If the distance across the plates is 5.0 mm and the potential difference across the plates is 20 V, with what velocity does the electron hit the positive plate? (m_e = 9.1 * 10 ^{- 31} kg, e = 1.6 *10 ^{- 19} C)

A) 1.3 * 10⁶ m/s
B) 1.0 * 10⁶ m/s
C) 2.7 *10⁶ m/s
D) 5.3 * 10⁶ m/s

Question 12

The quantity of electrical potential, the volt, is dimensionally equivalent to:

A) force/charge.
B) electric field/distance.
C) force * charge.
D) electric field * distance.

Question 13

A uniform electric field, with a magnitude of 600 N/C, is directed parallel to the positive x axis. If the potential at x = 4.0 m is 1000 V, what is the change in potential energy of a proton as it moves from x = 4.0 m to x = 1.0 m? (q_p = 1.6 *10 ^{- 19} C)

A) 500 J
B) 2.9 *10 ^{- 16} J
C) 1.9 *10 ^{- 16} J
D) 8.0 *10 ^{- 17} J

Question 14

Two particles each have the same mass but particle #1 has four times the charge of particle #2. Particle #1 is accelerated from rest through a potential difference of 10 V and attains speed v. Particle #2 is accelerated from rest also through a potential difference of 10 V. What speed does particle #2 attain?

A) 2v
B) v/2
C) v/4
D)

Question 15

Case 1: An electron is released from rest in a uniform electric field. Case 2: A proton is released from rest in a uniform electric field of the same magnitude as in case 1. How does the electric potential energy of the charge-field system behave in these cases?

A) In case 1 the potential energy increases, but in case 2 it decreases.
B) In both cases, the potential energy increases.
C) In case 1 the potential energy decreases, but in case 2 it increases.
D) In both cases, the potential energy decreases.

Question 16

An electron in a cathode ray tube is accelerated through a potential difference of 10 kV. What kinetic energy does the electron gain in the process? (e = 1.6 * 10 ^{- 19} C)

A) 8.0 *10 ^{- 16} J
B) 1.6 *10 ^{- 15} J
C) 8.0 * 10²² J
D) 1.6 *10 ^{- 16} J

Question 17

In which case does an electric field do positive work on a charged particle?

A) A negative charge moves opposite to the direction of the electric field.
B) A positive charge completes one circular path around a stationary positive charge.
C) A positive charge is moved to a point of higher potential energy.
D) A positive charge completes one elliptical path around a stationary positive charge.

Question 18

If the distance between two negative point charges is increased by a factor of two, the resultant potential energy is what factor times the initial potential energy?

A) 2
B) 1/2
C) 1/4
D) 4

Question 19

An electron (charge -1.6 *10 ^{- 19} C) moves on a path perpendicular to the direction of a uniform electric field of strength 3.0 N/C. How much work is done on the electron as it moves 20 cm?

A) "1.6 * 10 ^{- 20} J"
B) "-4.8 *10 ^{- 20} J"
C) "4.8 *10 ^{- 20} J"
D) "zero"

Question 20

A proton (+1.6 *10 ^{- 19} C) moves 10 cm on a path in the direction opposite to a uniform electric field of strength 3.0 N/C. How much work is done on the proton by the electrical field?

A) "4.8*10 ^{- 20} J"
B) "1.6 * 10 ^{- 20} J"
C) "zero"
D) "-4.8 *10 ^{- 20} J"

Question 21

If a doubly-ionized oxygen atom is accelerated from rest by going through a potential difference of 10 V, what will be the change in its kinetic energy?

A) 10 eV
B) 40 eV
C) 20 eV
D) none of the above

Question 22

A solid conducting sphere of 10 cm radius has a net charge of 40 nC. If the potential at infinity is taken as zero, what is the potential at the center of the sphere?

A) 360 $\mu$ V
B) 3.6 * 10³ V
C) >3.6 * 10⁴ V
D) 36 $\mu$ V

Question 23

An electron in a TV picture tube is accelerated through a potential difference of 20 kV before it hits the screen. What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 * 10 ^{- 19} J)

A) 6.25 * 10²² eV
B) 1.0 *10⁴ eV
C) 2.0 * 10⁴ eV
D) 3.2*10 ^{- 22} eV

Question 24

Which of the following were found from Millikan's oil drop experiment?

A) the weight, and hence the mass, of the electron
B) all of the above
C) that quarks have charges that are fractions of the electronic charge
D) the value of the electron's quantized charge

Question 25

An ion is released from rest and moves due to the force from an electric field from a position in the field having a potential of 14 V to a position having a potential of 8 V. The ion:

A) can have either a positive or a negative charge.
B) must be neutral.
C) must have a positive charge.
D) must have a negative charge.

Question 26

Four point charges are on the rim of a circle. The charges are (in $\mu$ C) +0.50, +3.0, -1.0, -0.50. If the electrical potential at the circle's center due to the +0.5 charge alone is 4.5 * 10⁴ V, what is the total potential at the center due to the four charges combined?

A) "18 * 10⁴ V"
B) "4.5 * 10⁴ V"
C) "zero"
D) "-4.5 *10⁴ V"

Question 27

A point charge of +3.0 $\mu$ C is located at the origin of a coordinate system and a second point charge of -9.0 $\mu$ C is at x = 1.00 m. What is the electric potential at the x = 0.50 m point? (k_e = 8.99 *10⁹ N.m²/C²)

A) "-5.4 * 10⁴ V"
B) "11 * 10⁴ V"
C) "16 * 10⁴ V"
D) "-11 * 10⁴ V"

Question 28

Two point charges of values +3.4 $\mu$ C and +6.6 $\mu$ C are separated by 0.20 m. What is the electrical potential at the point midway between the two charges? (k_e = 8.99 * 10⁹ N.m²/C²)

A) "+1.8 * 10⁶ V"
B) "-0.90*10⁶ V"
C) "+0.90 * 10⁶ V"
D) "+3.6 *10⁶ V"

Question 29

When charges q_a, q_b, and q_c are placed respectively at the corners a, b, and c of a right triangle, the potential at the midpoint of the hypotenuse is 20 V. When the charge q_a is removed, the potential at the midpoint becomes 15 V. When, instead, the charge q_b is removed (q_a and q_c both in place), the potential at the midpoint becomes 13 V. What is the potential at the midpoint if only the charge q_c is removed from the array of charges?

A) 12 V
B) 8 V
C) 7 V
D) 5 V

Question 30

If the plane x = 4 m is an equipotential surface, in which of the following directions can the electric field be in the region immediately adjacent to this plane?

A) the positive y direction
B) both the positive and negative z directions
C) the positive x direction
D) more than one of these choices

Question 31

There is a hollow, conducting, uncharged sphere with a negative charge inside the sphere. Consider the electrical potential at the inner and outer surfaces of the sphere. Which of the following is true?

A) The potentials on both surfaces are equal but not zero.
B) The potentials on both surfaces are zero.
C) The potential on the inner surface is greater.
D) The potential on the outer surface is greater.

Question 32

Equipotential surfaces around a point charge are

A) spherical.
B) cylindrical.
C) planar.
D) none of these choices.

Question 33

A solid metal sphere of radius r is inside a metal concentric spherical shell of inner radius 2r and outer radius 3r. A charge is place on the solid metal sphere and it is found that the potential at its surface is (at r) and that the potential at the outer surface of the spherical shell is (at 3r). In terms of and , what is the potential at the inner surface of the metal shell (at 2r)?

A)
B)
C)
D)

Question 34

At what distance from a point charge of 14 $\mu$ C would the electrical potential be 4.2 *10⁴ V? (k_e = 8.99 * 10⁹ N.m²/C²)

A) 0.76 m
B) 0.58 m
C) 3.0 m
D) 1.7 m

Question 35

A 9.0-V battery moves 200 mC of charge through a circuit running from its positive terminal to its negative terminal. How much energy was delivered to the circuit?

A) 4.5 x 10³ J
B) 1.8 J
C) 2.2 mJ
D) 0.18 J

Question 36

When charges q_a, q_b, and q_c are placed respectively at the corners a, b, and c of a right triangle, the potential at the midpoint of the hypotenuse is 20 V. When the charge q_a is removed, the potential at the midpoint becomes 15 V. When, instead, the charge q_b is removed (q_a and q_c both in place), the potential at the midpoint becomes 13 V. What is the potential at the midpoint if both charges q_a and q_c are removed?

A) 13 V
B) 7 V
C) 5 V
D) 8 V

Question 37

Find the electrical potential at 0.055 m from a point charge of 6.0 $\mu$ C. (k_e = 8.99 *10⁹ N.m²/C²)

A) 1.5 * 10⁵ V
B) 1.2 * 10⁷ V
C) 9.8 * 10⁵ V
D) 3.6 *10⁵ V

Question 38

When charge Q₁ is placed at point P₁, the resulting potential at point P is V₁. When Q₂ is placed at point P₂ after Q₁ is in position at P₁, the resulting potential at P becomes V₂. What is the potential at point P if charge Q₁ is then removed?

A) V₁ - V₂
B) (V₁ + V₂)/2
C) V₁ + V₂
D) V₂ - V₁

Question 39

Electrons in an x-ray machine are accelerated from rest through a potential difference of 80,000 V. What is the kinetic energy of each of these electrons in eV?

A) 128 eV
B) 40 eV
C) 80 eV
D) 80 keV

Question 40

A point charge of +3.0 $\mu$ C is located at the origin of a coordinate system and a second point charge of -9.0 $\mu$ C is at x = 1.0 m. At what point on the x axis is the electrical potential zero?

A) "+0.33 m"
B) "-0.25 m"
C) "+0.25 m"
D) "+0.75 m"

Question 41

Increasing the separation of the two charged parallel plates of a capacitor, which are disconnected from a battery, will produce what effect on the capacitor?

A) increase charge
B) decrease charge
C) decrease capacitance
D) increase capacitance

Question 42

Two capacitors with capacitances of 1.0 $\mu$ C and 0.50 $\mu$ F, respectively, are connected in series. The system is connected to a 150 V battery. What charge accumulates on the 1.0- $\mu$ F capacitor?

A) 50 $\mu$ C
B) 150 $\mu$ C
C) 100 $\mu$ C
D) 33 $\mu$ C

Question 43

If two parallel, conducting plates have equal positive charge, the electric field lines will:

A) leave one plate and go straight to the other plate.
B) enter both plates from infinity.
C) leave both plates and go to infinity.
D) none of the above.

Question 44

At which location will the electric field between the two parallel plates of a charged capacitor be the strongest in magnitude?

A) near the positive plate
B) near the negative plate
C) midway between the two plates nearest their center
D) midway between the two plates at their ends

Question 45

Three capacitors have capacitances C₁ < C₂ < C₃. If these capacitors are connected in series, which of the following is true for the resulting equivalent capacitance?

A) C_eq < C₁
B) C_eq > C₃
C) C_eq = (C₁ + C₂ + C₃)/3
D) None of the above is always correct.

Question 46

Decreasing the voltage across the two plates of a capacitor will produce what effect on the capacitor?

A) decrease charge
B) increase capacitance
C) decrease capacitance
D) increase charge

Question 47

A 20- $\mu$ F capacitor is attached across a 1000-V power supply. What is the net charge on the capacitor?

A) 20 mC
B) 40 mC
C) 10 mC
D) none of these choices

Question 48

The unit of capacitance, the farad, is dimensionally equivalent to which of the following?

A) J/V
B) C/V
C) V.C
D) V/C

Question 49

What is the equivalent capacitance between points a and b? All capacitors are 2.0 $\mu$ F.

A) 1.2 µF
B) 0.25 µF
C) 4.0 µF
D) 0.60 µF

Question 50

Doubling the voltage across a parallel-plate capacitor does not double which of the following?

A) the electric field between the plates
B) the charge
C) the energy stored
D) both a and b

Question 51

Two capacitors with capacitances of 1.5 $\mu$ C and 0.25 $\mu$ F, respectively, are connected in parallel. The system is connected to a 40-V battery. What charge accumulates on the 1.5- $\mu$ F capacitor?

A) 100 $\mu$ C
B) 75 $\mu$ C
C) 60 $\mu$ C
D) 33 $\mu$ C

Question 52

Three capacitors of 1.0, 1.5, and 3.0 $\mu$ F are connected in series. Find the combined capacitance.

A) 0.50 $\mu$ F
B) 1.0 $\mu$ F
C) 5.0 $\mu$ F
D) 5.5 $\mu$ F

Question 53

Two capacitors with C_A greater than C_B, are connected in parallel with a battery. Which of the following is true?

A) There is the same charge stored on each capacitor.
B) There is the same potential difference across both capacitors.
C) There is more potential difference across C_B.
D) There is more potential difference across C_A.

Question 54

If C = 48 µF, determine the equivalent capacitance for the combination shown.

A) 32 µF
B) 48 µF
C) 24 µF
D) 28 µF

Question 55

A parallel-plate capacitor has a capacitance of 20 µF. What potential difference across the plates is required to store 22 *10 ^{- 5} C on this capacitor?

A) 2.2 * 10^-2 V
B) 1.4 * 10 ^{- 8} V
C) 11 V
D) 70 V

Question 56

A 0.50- $\mu$ F capacitor is connected to a 400 V battery. Find the charge on the capacitor.

A) 2.0 *10 ^{- 4} C
B) 0.020 C
C) 1.0 *10 ^{- 4} C
D) 1.2 * 10 ^{- 12} C

Question 57

A capacitor is attached across a battery and charged. Then the battery is removed leaving the capacitor charged. The positive lead of the capacitor is then connected to one lead of a previously uncharged identical capacitor, and then the other lead of the charged capacitor is connected to the other lead of the second capacitor. How does the energy E₀ stored in the originally charged capacitor compare to the energy E_f stored in the connected capacitors?

A) E₀ = 2E_f
B) E₀ < E_f
C) E₀ = 4E_f
D) E₀ = E_f

Question 58

Suppose two equipotential surfaces are the planes x = 3 m and x = 5 m. If the potential at the x = 3 m surface is 10 V and the potential at the x = 5 m surface is 50 V, what is the magnitude of the electric field between the two surfaces?

A) 40 N/C
B) 20 N/C
C) 15 N/C
D) 10 N/C

Question 59

Two capacitors, with C_A greater than C_B, are connected in series with a battery. Which of the following is true?

A) There is more charge stored on C_B.
B) There is the same charge stored on each capacitor.
C) There is the same potential difference across both capacitors.
D) There is more charge stored on C_A.

Question 60

If three 3.0-µF capacitors are connected in parallel, what is the combined capacitance?

A) 0.46 $\mu$ F
B) 1.0 $\mu$ F
C) 9.0 $\mu$ F
D) 0.75 $\mu$ F

Question 61

Four identical 4-mF capacitors are connected together electrically. What is the greatest possible capacitance of the combination?

A) 16 mF
B) 8 mF
C) 4 mF
D) 1 mF

Question 62

If C₁ = 25 µF, C₂ = 20 µF, C₃ = 10 µF, and $\Delta$ V₀ = 42 V, determine the energy stored by C₃.

A) 3.6 mJ
B) 0.32 mJ
C) 1.8 mJ
D) 0.40 mJ

Question 63

What is the equivalent capacitance of the combination shown?

A) 25 µF
B) 10 µF
C) 29 µF
D) 40 µF

Question 64

Four identical 4-mF capacitors are connected together electrically. What is the least possible capacitance of the combination?

A) 4 mF
B) 1 mF
C) 1/8 mF
D) 1/4 mF

Question 65

How much charge can be placed on a capacitor of plate area 20 cm² with air between the plates before it reaches "atmospheric breakdown" where E = 3.0 *10⁶ V/m? ( $\varepsilon$ ₀ = 8.85 *10^-12 C²/N.m²)

A) 6.6 *10^-7 C
B) 2.7 * 10^-8 C
C) 5.3 *10 ^{- 8} C
D) 4.0 *10 ^{- 7} C

Question 66

Two capacitors with capacitances of 1.0 $\mu$ F and 0.50 $\mu$ F, respectively, are connected in series. The system is connected to a 50-V battery. What electrical potential energy is stored in the 1.0- $\mu$ F capacitor?

A) 5.6 * 10 ^{- 4} J
B) 4.3 * 10 ^{- 3} J
C) 0.065 *10 ^{- 3} J
D) 1.4 *10 ^{- 4} J

Question 67

Capacitor #1 has parallel plates of length L and width W, plate separation d, and is filled with dielectric with constant .Capacitor #2 has parallel plates of length 2L and width 2W, plate separation 2d, and is filled with dielectric with constant 2 . If a voltage V is applied to capacitor #1 and a voltage 2V is applied to capacitor #2, which capacitor stores more energy and by what factor?

A) Capacitor #2 by a factor of 8
B) Capacitor #2 by a factor of 16
C) Capacitor #1 by a factor of 4
D) Both capacitors store the same energy.

Question 68

A 6.0- $\mu$ F capacitor is attached to a 20-V power supply. How much energy is stored in the capacitor?

A) 2.0 *10 ^{- 3} J
B) 5.2 * 10 ^{- 4} J
C) 2.0 *10 ^{- 4} J
D) 1.2 * 10 ^{- 3} J

Question 69

What is the equivalent capacitance of the combination shown?

A) 4.6 µF
B) 100 µF
C) 12 µF
D) 24 µF

Question 70

Two capacitors with capacitances of 1.5 $\mu$ F and 0.25 $\mu$ F, respectively, are connected in parallel. The system is connected to a 100-V battery. What electrical potential energy is stored in the 1.5- $\mu$ F capacitor?

A) 1.2 *10 ^{- 3} J
B) 1.9 *10 ^{- 3} J
C) 0.50 *10 ^{- 3} J
D) 7.5 *10 ^{- 3} J

Question 71

A parallel plate capacitor has the voltage applied to it doubled. Is the force between the plates attractive or repulsive, and what happens to the force between the plates when the voltage is doubled?

A) The force is attractive and it quadruples.
B) The force is attractive and it doubles.
C) The force is repulsive and it halves.
D) There is no force between the plates since the net charge is zero on the capacitor.

Question 72

If C = 14 µF, what is the equivalent capacitance for the combination shown?

A) 5.8 µF
B) 6.5 µF
C) 8.2 µF
D) 7.0 µF

Question 73

A pair of parallel plates, forming a capacitor, are charged. The plates are pulled apart to triple the original separation, the charges on the plates remaining the same. What is the ratio of the final energy stored to the original energy stored?

A) 1/9
B) 1.5
C) 1/3
D) 3

Question 74

The dielectric strength of rutile is 6.0 *10⁶ V/m, which corresponds to the maximum electric field that the dielectric can sustain before breakdown. What is the maximum charge that a 10 ^{- 10}-F capacitor with a 0.50-mm thickness of Rutile can hold?

A) 0.30 $\mu$ C
B) 6.0 C
C) 0.60 µC
D) 1.7 nC

Question 75

A pair of parallel plates, forming a capacitor, are connected to a battery. While the capacitor is still connected to the battery maintaining a constant voltage, the plates are pulled apart to triple their original distance. What is the ratio of the final energy stored to the original energy stored?

A) 1/9
B) 1/3
C) 3
D) 1

Question 76

Using a 1-mF capacitor, a 2-mF capacitor, and a 3-mF capacitor, which of the following capacitances cannot be made by a combination that uses all three? (Hint: At most only 2 combinations must be considered to determine the correct answer.)

A) 6/11 mF
B) 6 mF
C) 11/3 mF
D) 7 mF

Question 77

A parallel-plate capacitor has dimensions 4.0 cm * 5.0 cm. The plates are separated by a 1.0-mm thickness of paper (dielectric constant $\kappa$ = 3.7). What is the charge that can be stored on this capacitor, when connected to a 6.0-V battery? ( $\varepsilon$ ₀ = 8.85 * 10^-12 C²/N.m²)

A) 4.8 *10 ^{- 9} C
B) 4.8 *10 ^{- 11} C
C) 9.8 *10 ^{- 11} C
D) 3.9 *10 ^{- 10} C

Question 78

A "sandwich" is constructed of two flat pieces of metal (2.00 cm on a side) with a 3.00-mm thick piece of a dielectric called rutile ( $\kappa$ = 100) in between them. What is the capacitance? ( $\varepsilon$ ₀ = 8.85 * 10^-12 C²/N.m²)

A) 177 pF
B) 118 pF
C) 100 µF
D) 8.85 µF

Question 79

A 0.50- $\mu$ F capacitor is connected to a 400-V battery. What potential energy is stored in the capacitor?

A) 0.020 J
B) 0.040 J
C) 1.0 *10 ^{- 4} J
D) 1.2 *10 ^{- 12} J

Question 80

Inserting a dielectric material between two charged parallel conducting plates, originally separated by air and disconnected from a battery, will produce what effect on the capacitor?

A) increase voltage
B) increase charge
C) increase capacitance
D) decrease capacitance