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Chapter 25

Electric Potential

Multiple Choice

1. A charged particle (q = –8.0 mC), which moves in a region where the only forceacting on the particle is an electric force, is released from rest at point A. At pointB the kinetic energy of the particle is equal to 4.8 J. What is the electric potentialdifference V ?AB V −

AB V −

BA V V −

a. –0.60 kVb. +0.60 kVc. +0.80 kVd. –0.80 kVe. +0.48 kV

2. A particle (charge = 50 μC) moves in a region where the only force on it is anelectric force. As the particle moves 25 cm from point A to point B, its kineticenergy increases by 1.5 mJ. Determine the electric potential difference, V .

a. –50 Vb. –40 Vc. –30 Vd. –60 Ve. +15 V

3. Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where the electric field isuniform and given by E = (4i + 3j) N/C. What is the potential difference

?

a. 33 Vb. 27 Vc. 30 Vd. 24 Ve. 11 V

4. A particle (charge = +2.0 mC) moving in a region where only electric forces acton it has a kinetic energy of 5.0 J at point A. The particle subsequently passesthrough point B which has an electric potential of +1.5 kV relative to point A.Determine the kinetic energy of the particle as it moves through point B.

a. 3.0 J

b. 2.0 Jc. 5.0 Jd. 8.0 Je. 10.0 J

49

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50 CHAPTER 25

5. A particle (mass = 6.7 × 10–27 kg, charge = 3.2 × 10–19 C) moves along the positivex axis with a speed of 4.8 × 105 m/s. It enters a region of uniform electric fieldparallel to its motion and comes to rest after moving 2.0 m into the field. What isthe magnitude of the electric field?

a. 2.0 kN/C

b. 1.5 kN/Cc. 1.2 kN/Cd. 3.5 kN/Ce. 2.4 kN/C

6. A proton (mass = 1.67 × 10–27 kg, charge = 1.60 × 10–19 C) moves from point A topoint B under the influence of an electrostatic force only. At point A the protonmoves with a speed of 50 km/s. At point B the speed of the proton is 80 km/s.Determine the potential difference AB V V − .

a. +20 Vb. –20 Vc. –27 V

d. +27 Ve. –40 V

7. A proton (mass = 1.67 × 10–27 kg, charge = 1.60 × 10–19 C) moves from point A topoint B under the influence of an electrostatic force only. At point A the protonmoves with a speed of 60 km/s. At point B the speed of the proton is 80 km/s.Determine the potential difference V AB V − .

a. +15 Vb. –15 Vc. –33 Vd. +33 Ve. –20 V

8. What is the speed of a proton that has been accelerated from rest through apotential difference of 4.0 kV?

a. 1.1 × 106 m/sb. 9.8 × 105 m/sc. 8.8 × 105 m/sd. 1.2 × 106 m/se. 6.2 × 105 m/s

9. An electron (m = 9.1 × 10–31 kg, q = –1.6 × 10–19 C) starts from rest at point A andhas a speed of 5.0 × 106 m/s at point B. Only electric forces act on it during this

motion. Determine the electric potential difference V BA V − .

a. –71 Vb. +71 Vc. –26 Vd. +26 Ve. –140 V

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Electric Potential 51

10. A proton (m = 1.7 × 10–27 kg, q = +1.6 × 10–19 C) starts from rest at point A and hasa speed of 40 km/s at point B. Only electric forces act on it during this motion.Determine the electric potential difference AB V V − .

a. +8.5 Vb. –8.5 V

c. –4.8 Vd. +4.8 Ve. –17 V

11. A particle (m = 2.0 μg, q = –5.0 nC) has a speed of 30 m/s at point A and moves(with only electric forces acting on it) to point B where its speed is 80 m/s.Determine the electric potential difference BA V V − .

a. –2.2 kVb. +1.1 kVc. –1.1 kVd. +2.2 kVe. +1.3 kV

12. An alpha particle (m = 6.7 × 10–27 kg, q = +3.2 × 10–19 C) has a speed of 20 km/s atpoint A and moves to point B where it momentarily stops. Only electric forces acton the particle during this motion. Determine the electric potential difference

.BA V V −

BA V V −

BA

a b a

a. +4.2 Vb. –4.2 Vc. –9.4 Vd. +9.4 Ve. –8.4 V

13. Points A [at (3, 6) m] and B [at (8, –3) m] are in a region where the electric field is

uniform and given by E = 12i N/C. What is the electric potential difference?

a. +60 Vb. –60 Vc. +80 Vd. –80 Ve. +50 V

14. If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = –3.0 nC in the figure, what is thepotential difference ?V V −

BAq Q

a. +60 Vb. +72 Vc. +84 Vd. +96 Ve. +48 V

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52 CHAPTER 25

15. Several charges in the neighborhood of point P produce an electric potential of6.0 kV (relative to zero at infinity) and an electric field of 36i N/C at point P.Determine the work required of an external agent to move a 3.0-μC charge alongthe x axis from infinity to point P without any net change in the kinetic energy ofthe particle.

a. 21 mJb. 18 mJc. 24 mJd. 27 mJe. 12 mJ

16. Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = –2.0 nC,a = 3.0 m, and b = 4.0 m, what is the electric potential difference, V ?BA V −

b

a

a 90°

B

A

Q

q

90°

a. 8.4 Vb. 6.0 Vc. 7.2 Vd. 4.8 Ve. 0 V

17. Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 mon the y axis, a –80-nC charge at x = –4 m on the x axis, and a 70-nc charge at y = –6 m on the y axis. What is the electric potential (relative to a zero at infinity)at the point x = 8 m on the x axis?

a. +81 Vb. +48 Vc. +5.8 Vd. –72 Ve. –18 V

18. Point charges of equal magnitudes (25 nC) and opposite signs are placed on(diagonally) opposite corners of a 60-cm × 80-cm rectangle. If point A is thecorner of this rectangle nearest the positive charge and point B is located at theintersection of the diagonals of the rectangle, determine the potential difference,V

B

– V A

.

a. –47 Vb. +94 Vc. zerod. –94 Ve. +47 V

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19. Identical 2.0-μC charges are located on the vertices of a square with sides that are2.0 m in length. Determine the electric potential (relative to zero at infinity) at thecenter of the square.

a. 38 kVb. 51 kVc. 76 kVd. 64 kVe. 13 kV

20. A +4.0-μC charge is placed on the x axis at x = +3.0 m, and a –2.0-μC charge islocated on the y axis at y = –1.0 m. Point A is on the y axis at y = +4.0 m.Determine the electric potential at point A (relative to zero at the origin).

a. 6.0 kVb. 8.4 kVc. 9.6 kVd. 4.8 kVe. 3.6 kV

21. Identical 4.0-μC charges are placed on the y axis at y = ±4.0 m. Point A is on the x axis at x = +3.0 m. Determine the electric potential of point A (relative to zero atthe origin).

a. –4.5 kVb. –2.7 kVc. –1.8 kVd. –3.6 kVe. –14 kV

22. Four identical point charges (+6.0 nC) are placed at the corners of a rectanglewhich measures 6.0 m × 8.0 m. If the electric potential is taken to be zero atinfinity, what is the potential at the geometric center of this rectangle?

a. 58 Vb. 63 Vc. 43 Vd. 84 Ve. 11 V

23. Three identical point charges (+2.0 nC) are placed at the corners of an equilateraltriangle with sides of 2.0-m length. If the electric potential is taken to be zero atinfinity, what is the potential at the midpoint of any one of the sides of thetriangle?

a. 16 V

b. 10 Vc. 70 Vd. 46 Ve. 44 V

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54 CHAPTER 25

24. A particle (charge = Q) is kept in a fixed position at point P, and a second particle(charge = q) is released from rest when it is a distance R from P. If Q = +2.0 mC,q = –1.5 mC, and R = 30 cm, what is the kinetic energy of the moving particleafter it has moved a distance of 10 cm?

a. 60 kJb. 45 kJc. 75 kJd. 90 kJe. 230 kJ

25. Particle A (mass = m , charge = Q) and B (mass = m , charge = 5 Q) are releasedfrom rest with the distance between them equal to 1.0 m. If Q = 12 μC, what is thekinetic energy of particle B at the instant when the particles are 3.0 m apart?

a. 8.6 Jb. 3.8 Jc. 6.0 Jd. 2.2 Je. 4.3 J

26. A particle (charge = 40 μC) moves directly toward a second particle(charge = 80 μC) which is held in a fixed position. At an instant when thedistance between the two particles is 2.0 m, the kinetic energy of the movingparticle is 16 J. Determine the distance separating the two particles when themoving particle is momentarily stopped.

a. 0.75 mb. 0.84 mc. 0.95 md. 0.68 me. 0.56 m

27. A particle (charge 7.5 μC) is released from rest at a point on the x axis, x = 10 cm.It begins to move due to the presence of a 2.0-μC charge which remains fixed atthe origin. What is the kinetic energy of the particle at the instant it passes thepoint x = 1.0 m?

a. 3.0 Jb. 1.8 Jc. 2.4 Jd. 1.2 Je. 1.4 J

28. A particle (charge = 5.0 μC) is released from rest at a point x = 10 cm. If a 5.0-μCcharge is held fixed at the origin, what is the kinetic energy of the particle after it

has moved 90 cm?a. 1.6 Jb. 2.0 Jc. 2.4 Jd. 1.2 Je. 1.8 J

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29. A 60-μC charge is held fixed at the origin and a –20-μC charge is held fixed onthe x axis at a point x = 1.0 m. If a 10-μC charge is released from rest at a pointx = 40 cm, what is its kinetic energy the instant it passes the point x = 70 cm?

a. 9.8 Jb. 7.8 Jc. 8.8 Jd. 6.9 Je. 2.8 J

30. Two identical particles, each with a mass of 2.0 mg and a charge of 25 nC, arereleased simultaneously from rest when the two are 4.0 cm apart. What is thespeed of either particle at the instant when the two are separated by 10 cm?

a. 7.3 m/sb. 9.8 m/sc. 9.2 m/sd. 6.5 m/se. 4.6 m/s

31. Two particles, each having a mass of 3.0 mg and having equal but oppositecharges of magnitude 5.0 nC, are released simultaneously from rest when thetwo are 5.0 cm apart. What is the speed of either particle at the instant when thetwo are separated by 2.0 cm?

a. 2.1 m/sb. 1.5 m/sc. 1.8 m/sd. 2.4 m/se. 3.2 m/s

32. Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, aremoving directly toward each other with equal speeds of 4.0 m/s at an instant

when the distance separating the two is equal to 25 cm. How far apart will they be when closest to one another?

a. 9.8 cmb. 12 cmc. 7.8 cmd. 15 cme. 20 cm

33. Two particles, each having a mass of 3.0 mg and having equal but oppositecharges of magnitude of 6.0 nC, are released simultaneously from rest when theyare a very large distance apart. What distance separates the two at the instantwhen each has a speed of 5.0 m/s?

a. 4.3 mmb. 8.6 mmc. 7.3 mmd. 5.6 mme. 2.2 mm

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56 CHAPTER 25

34. A particle (q = +5.0 μC) is released from rest when it is 2.0 m from a chargedparticle which is held at rest. After the positively charged particle has moved1.0 m toward the fixed particle, it has a kinetic energy of 50 mJ. What is thecharge on the fixed particle?

a. –2.2 μCb. +6.7 μCc. –2.7 μCd. +8.0 μCe. –1.1 μC

35. Four identical point charges (+4.0 μC) are placed at the corners of a square whichhas 20-cm sides. How much work is required to assemble this chargearrangement starting with each of the charges a very large distance from any ofthe other charges?

a. +2.9 Jb. +3.9 Jc. +2.2 Jd. +4.3 J

e. +1.9 J

36. Identical 8.0-μC point charges are positioned on the x axis at x = ±1.0 m andreleased from rest simultaneously. What is the kinetic energy of either of thecharges after it has moved 2.0 m?

a. 84 mJb. 54 mJc. 96 mJd. 63 mJe. 48 mJ

37. 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. 5.8 kVb. 2.6 kVc. 7.1 kVd. 8.6 kVe. 5.1 kV

38. Identical point charges (+50 μC) are placed at the corners of a square with sidesof 2.0-m length. How much external energy is required to bring a fifth identicalcharge from infinity to the geometric center of the square?

a. 41 J

b. 16 Jc. 64 Jd. 10 Je. 80 J

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39. A charge of +3.0 μC is distributed uniformly along the circumference of a circlewith a radius of 20 cm. How much external energy is required to bring a chargeof 25μC from infinity to the center of the circle?

a. 5.4 Jb. 3.4 Jc. 4.3 Jd. 2.7 Je. 6.8 J

40. Identical point charges (+20 μC) are placed at the corners of an equilateraltriangle with sides of 2.0-m length. How much external energy is required to bring a charge of 45 μC from infinity to the midpoint of one side of the triangle?

a. 26 Jb. 16 Jc. 23 Jd. 21 Je. 12 J

41. Identical point charges (+30 μC) are placed at the corners of a rectangle(4.0 m × 6.0 m). How much external energy is required to bring a charge of 55 μCfrom infinity to the midpoint of one of the 6.0-m long sides of the rectangle?

a. 22 Jb. 16 Jc. 13 Jd. 19 Je. 8.0 J

42. A charge per unit length given by λ (x) = bx , where b = 12 nC/m2 , is distributedalong the x axis from x = +9.0 cm to x = +16 cm. If the electric potential at infinityis taken to be zero, what is the electric potential at the point P on the y axis at y = 12 cm?

a. 5.4 Vb. 7.2 Vc. 9.0 Vd. 9.9 Ve. 16 V

43. A charge Q is uniformly distributed along the x axis from x = a to x = b. IfQ = 45 nC, a = –3.0 m, and b = 2.0 m, what is the electric potential (relative to zeroat infinity) at the point, x = 8.0 m, on the x axis?

a. 71 V

b. 60 Vc. 49 Vd. 82 Ve. 150 V

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58 CHAPTER 25

44. Charge of uniform density (3.5 nC/m) is distributed along the circular arcshown. Determine the electric potential (relative to zero at infinity) at point P.

660°

R

R

P+

+

+

+

+

+

+

+

+

+

+

a. 61 Vb. 42 Vc. 52 Vd. 33 Ve. 22 V

45. A charge of uniform density (0.80 nC/m) is distributed along the x axis from theorigin to the point x = 10 cm. What is the electric potential (relative to zero at

infinity) at a point, x = 18 cm, on the x axis?a. 7.1 Vb. 5.8 Vc. 9.0 Vd. 13 Ve. 16 V

46. A charge of 20 nC is distributed uniformly along the x axis from x = –2.0 m tox = +2.0 m. What is the electric potential (relative to zero at infinity) at the pointx = 5.0 m on the x axis?

a. 57 Vb. 48 Vc. 38 Vd. 67 Ve. 100 V

47. Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 mto x = 5.0 m. What is the electric potential (relative to zero at infinity) at the origin(x = 0)?

a. 91 Vb. 99 Vc. 82 Vd. 74 Ve. 140 V

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48. A linear charge of nonuniform density λ = bx , where b = 2.1 nC/m2 , is distributedalong the x axis from x = 2.0 m to x = 3.0 m. Determine the electric potential(relative to zero at infinity) of the point y = 4.0 m on the y axis.

a. 36 Vb. 95 Vc. 10 Vd. 17 Ve. 15 V

49. A nonuniform linear charge distribution given by λ (x) = bx , where b is a constant,is distributed along the x axis from x = 0 to x = +L. If b = 40 nC/m2 andL = 0.20 m, what is the electric potential (relative to a potential of zero at infinity)at the point y = 2L on the y axis?

a. 19 Vb. 17 Vc. 21 Vd. 23 V

e. 14 V50. A charge of 10 nC is distributed uniformly along the x axis from x = –2 m to

x = +3 m. Which of the following integrals is correct for the electric potential(relative to zero at infinity) at the point x = +5 m on the x axis?

∫−3

2

90

x

dxa.

∫− −3

2 5

90

x

dx b.

∫−3

2

18

x

dxc.

∫− −3

2 518

xdxd.

e. ∫− +3

2 5

90

x

dx

51. Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the electric potential(relative to zero at infinity) at the point x = +4 m on the x axis?

∫3 27dx

a. 0 x

∫ −3

0 4

9

x

dxb.

∫ −3

0 4

27

x

dxc.

d. ∫3

0

27

x

dx

e. ∫ +3

0 4

27

x

dx

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60 CHAPTER 25

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

a. ∫ −6

4 4

18

x

dx

b. ∫6

436xdx

c. ∫6

4

18

x

dx

d. ∫ −6

4 6

36

x

dx

e. ∫ +6

4 4

36

x

dx

53. A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m.Which of the following integrals is correct for the electric potential (relative to

zero at infinity) at the point x = +3 m on the x axis?

∫ +4 45dy

0 2/12 )9( y a.

∫ +4

0 2 )9(

180

y

dyb.

2/1

∫ +4

0 2 9

45

y

dyc.

∫ +4

0 2 9

180

y

dyd.

e. ∫ +4

0 2/32 )9(

45

y

dy

54. Charge of uniform linear density 6.0 nC/m is distributed along the x axis fromx = 0 to x = +3 m. Which of the following integrals is correct for the electricpotential (relative to zero at infinity) at the point y = +4 m on the y axis?

∫ +3

0 2/12 )16(

54

x

dxa.

∫ +3

0 2 )16(

18

x

dx b. 2/1

∫

3 54dx

c. +0 2 16x

∫ +3

0 2 16

18

x

dxd.

e. ∫ +3

0 2/12 )16(

108

x

dx

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55. A rod (length = 2.0 m) is uniformly charged and has a total charge of 5.0 nC.What is the electric potential (relative to zero at infinity) at a point which liesalong the axis of the rod and is 3.0 m from the center of the rod?

a. 22 Vb. 19 Vc. 16 Vd. 25 Ve. 12 V

56. A charge of 18 nC is uniformly distributed along the y axis from y = 3 m to y = 5 m. Which of the following integrals is correct for the electric potential(relative to zero at infinity) at the point x = +2 m on the x axis?

∫ +5 81dy

a. 3 2/12 )4( y

∫ +5

3 2 )4(

162

y

dyb.

2/1

∫ +5

3 2 481 ydyc.

∫ +5

3 2 4

162

y

dyd.

e. ∫5

3

81

y

dy

57. Two large parallel conducting plates are 8.0 cm apart and carry equal butopposite charges on their facing surfaces. The magnitude of the surface chargedensity on either of the facing surfaces is 2.0 nC/m2. Determine the magnitude ofthe electric potential difference between the plates.

a. 36 Vb. 27 Vc. 18 Vd. 45 Ve. 16 V

58. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributeduniformly on its surface. If point A is located at the center of the sphere and pointB is 15 cm from the center, what is the magnitude of the electric potentialdifference between these two points?

a. 23 Vb. 30 Vc. 15 Vd. 45 Ve. 60 V

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62 CHAPTER 25

59. Charge of uniform density 50 nC/m3 is distributed throughout the inside of along nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitudeof 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. 2.7 Vb. 2.0 Vc. 2.4 Vd. 1.7 Ve. 3.4 V

60. Charge of uniform density 90 nC/m3 is distributed throughout the inside of along nonconducting cylindrical rod (radius = 2.0 cm). Determine the magnitudeof 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. 1.9 Vb. 1.4 Vc. 2.2 Vd. 2.8 Ve. 4.0 V

61. A nonconducting sphere of radius 10 cm is charged uniformly with a density of100 nC/m3. What is the magnitude of the potential difference between the centerand a point 4.0 cm away?

a. 12 Vb. 6.8 Vc. 3.0 Vd. 4.7 Ve. 2.2 V

62. A charge of 40 pC is distributed on an isolated spherical conductor that has a4.0-cm radius. Point A is 1.0 cm from the center of the conductor and point B is5.0 cm from the center of the conductor. Determine the electric potentialdifference V A – V B.

a. +1.8 Vb. +29 Vc. +27 Vd. +7.2 Ve. +9.0 V

63. Two flat conductors are placed with their inner faces separated by 6.0 mm. If thesurface charge density on one of the inner faces is 40 pC/m2 , what is the

magnitude of the electric potential differences between the two conductors?a. 36 mVb. 18 mVc. 32 mVd. 27 mVe. 14 mV

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64. The electric field in a region of space is given by Ex = (3.0x) N/C, Ey = Ez = 0,where x is in m. Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m.Determine the potential difference V B – V A.

a. –24 Vb. +24 V

c. –18 Vd. +30 Ve. –6.0 V

65. Equipotentials are lines along which

a. the electric field is constant in magnitude and direction.b. the electric charge is constant in magnitude and direction.c. maximum work against electrical forces is required to move a charge at

constant speed.d. a charge may be moved at constant speed without work against electrical

forces.e. charges move by themselves.

66. When a charged particle is moved along an electric field line,

a. the electric field does no work on the charge.b. the electrical potential energy of the charge does not change.c. the electrical potential energy of the charge undergoes the maximum change

in magnitude.d. the voltage changes, but there is no change in electrical potential energy.e. the electrical potential energy undergoes the maximum change, but there is

no change in voltage.

67. When a positive charge is released and moves along an electric field line, itmoves to a position of

a. lower potential and lower potential energy.b. lower potential and higher potential energy.c. higher potential and lower potential energy.d. higher potential and higher potential energy.e. greater magnitude of the electric field.

68. When a negative charge is released and moves along an electric field line, itmoves to a position of

a. lower potential and lower potential energy.b. lower potential and higher potential energy.c. higher potential and lower potential energy.d. higher potential and higher potential energy.

e. decreasing magnitude of the electric field.

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64 CHAPTER 25

69. A charge is placed on a spherical conductor of radius r1. This sphere is thenconnected to a distant sphere of radius r2 (not equal to r1) by a conducting wire.After the charges on the spheres are in equilibrium,

a. the electric fields at the surfaces of the two spheres are equal.b. the amount of charge on each sphere is q/2.

c. both spheres are at the same potential.d. the potentials are in the ratio

1

2

1

2

q

q

V

V = .

e. the potentials are in the ratio1

2

1

2

r

r

V

V = .

70. The electric potential inside a charged solid spherical conductor in equilibrium

a. is always zero.b. is constant and equal to its value at the surface.c. decreases from its value at the surface to a value of zero at the center.d. increases from its value at the surface to a value at the center that is a

multiple of the potential at the surface.e. is equal to the charge passing through the surface per unit time divided bythe resistance.

71. Which statement is always correct when applied to a charge distribution locatedin a finite region of space?

a. Electric potential is always zero at infinity.b. Electric potential is always zero at the origin.c. Electric potential is always zero at a boundary surface to a charge

distribution.d. Electric potential is always infinite at a boundary surface to a charge

distribution.

e. The location where electric potential is zero may be chosen arbitrarily.72. Which of the following represents the equipotential lines of a dipole?

(a) (b) (c) (d) (e)

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73. Can the lines in the figure below be equipotential lines?

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.

74. A series of n uncharged concentric shells surround a small central charge q. Thecharge distributed on the outside of the nth shell is

a. .nq−

b. .qn)(ln−

c. + q .

d. .qn)(ln+

+

q)3

q)3(ln+

q3+

0

e. .nq

75. A series of 3 uncharged concentric shells surround a small central charge q. Thecharge distributed on the outside of the third shell is

a. .q3−

b. .(ln−

c. + q .

d. .

e. .

76. A series of n uncharged concentric spherical conducting shells surround a smallcentral charge q. The potential at a point outside the nth shell, at distance r fromthe center, and relative to =V at ∞ , is

r

qnke−a. .

r

qkn e)(ln− .b.

r

qke+c. .

d. r

qkn e)(ln+ .

e. r

qnke+ .

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66 CHAPTER 25

77. A series of 3 uncharged concentric spherical conducting shells surround a smallcentral charge q. The potential at a point outside the third shell, at distance r fromthe center, and relative to 0=V at ∞ , is

a. r

qke3− .

b. r

qke)3(ln− .

c. r

qke+ .

d. r

qke)3(ln+ .

e. r

qke3+ .

78. The electric field in the region defined by the y-z plane and the negative x axis isgiven by , where a is a constant. (There is no field for positive values of

x.) As increases in magnitude, relative to

axE −=

x− 0=V at the origin, the electricpotential in the region defined above is

a. a decreasing function proportional to 2x− .

b. a decreasing function proportional to x− .

c. constant.d. an increasing function proportional to x+ .

e. an increasing function proportional to 2x+ .

79. The electric field in the region defined by the y-z plane and the positive x axis isgiven by , where a is a constant. (There is no field for negative values of x.)

As increases in magnitude, relative to

axE

x

=

0=V at the origin, the electric potentialin the region defined above is

a. a decreasing function proportional to 2x− .

x−b. a decreasing function proportional to .

c. constant.x+d. an increasing function proportional to .

e. an increasing function proportional to 2x+

q3

.

+ at the origin, and80. Two charges lie on the x axis, q2− at = m0.5x . The point

on the x axis where the electric potential has a zero value (when the value atinfinity is also zero) is

a. 1.0 m.b. 2.0 m.c. 2.5 m.d. 3.0 m.e. 4.0 m.

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81. Two charges lie on the x axis, q2+ at the origin, and q3− at m0.5=x . The point

on the x axis where the electric potential has a zero value (when the value atinfinity is also zero) is

a. 1.0 m.b. 2.0 m.

c. 2.5 m.d. 3.0 m.e. 4.0 m.

82. When introduced into a region where an electric field is present, an electron withinitial velocity

v will always move

a. along an electric field line, in the positive direction of the line.b. along an electric field line, in the negative direction of the line.c. from a point at a positive potential to a point at a negative potential.d. from a point at a negative potential to a point at a positive potential.e. as described in both (b) and (d).

83. When introduced into a region where an electric field is present, an proton withinitial velocity

v will always move

a. along an electric field line, in the positive direction of the line.b. along an electric field line, in the negative direction of the line.c. from a point at a positive potential to a point at a negative potential.d. from a point at a negative potential to a point at a positive potential.e. as described in both (a) and (c).

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

a. loses potential difference and kinetic energy when the charged particlemoves 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.

85. A system consisting of a negatively-charged particle and an electric field

a. gains potential difference and kinetic energy when the charged particlemoves in the direction of the field.

b. loses electric potential energy when the charged particle moves in the

direction of the field.c. gains 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.

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68 CHAPTER 25

86. The Bohr model pictures a hydrogen atom in its ground state as a proton and an

electron separated by the distance . The electric potentialcreated by the proton at the position of the electron is

a0 = 0.529 × 10−10 m

a. .−13.6 Vb. .+13.6 V

c. .−27.2 Vd. .+27.2 V

e. .+5.12 × 109 V

87. The Bohr model pictures a hydrogen atom in its ground state as a proton and an

electron separated by the distance . The electric potentialcreated by the electron at the position of the proton is

a = 0.529 × 10−10 m0

+5.12 × 10 V

a. .−13.6 Vb. .+13.6 Vc. .−27.2 Vd. .+27.2 V

9e. .

88. The electric potential at the surface of a charged conductor

a. is always zero.b. is always independent of the magnitude of the charge on the surface.c. may be set equal to zero by adding an appropriate constant to the potential

at all points of space.d. is always such that the potential is zero at all points inside the conductor.e. is always such that the potential is always zero within a hollow space inside

the conductor.

89. An electron is released form rest in a region of space where a uniform electricfield is present. Joanna claims that its kinetic and potential energies both increaseas it moves from its initial position to its final position. Sonya claims that they both decrease. Which one, if either, is correct?

a. Joanna, because the electron moves opposite to the direction of the field.b. Sonya, because the electron moves opposite to the direction of the field.c. Joanna, because the electron moves in the direction of the field.d. Sonya, because the electron moves in the direction of the field.e. Neither, because the kinetic energy increases while the electron moves to a

point at a higher potential.

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90. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potentialenergy from greatest to least when traveling from A to B.

• B • B • B • A

• A • A • A • B

I II III IV

a. .I=II=III=IVb. .II=III>I>IVc. .III>I=IV>IId. .II>I=IV>III

I>II=III>IVe. .

91. Four electrons move from point A to point B in a uniform electric field as shown

below. Rank the electrons in diagrams I through IV by the changes in potentialfrom greatest to least when traveling from A to B.

• B • B • B • A

• A • A • A • B

I II III IV

a. .I=II=III=IVII=III>I>IV

III>I=IV>II

II>I=IV>IIII>II=III>IV

b. .c. .

d. .e. .

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70 CHAPTER 25

92. An infinite plane of charge with σ = +5.55C

m2

is tilted at a angle to the

vertical direction as shown below. The potential difference, V , in volts, between points A and B, a 4.50 m distance apart, is

45°

B − V

A

• B

• A

a. .−7.06b. .−9.98c. .−14.11d. .+7.06

+9.98

σ = +5.55

e. .

93. An infinite plane of charge withC

m2

is tilted at a angle to the

vertical direction as shown below. The potential difference, V , in volts, between points A and B a 4.50 m distance apart is

45°

A − V

B

• B

• A

a. .−7.06−9.98−14.11+7.06+9.98

b. .c. .d. .e. .

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Open-Ended Problems

94. How much electrical charge is needed to raise an isolated metal sphere of radius1.0 m to a potential of 1.0 × 106 V?

95. In the Bohr model of the hydrogen atom, the electron circles the proton at adistance of 0.51 × 10–10 m. Find the potential at the position of the electron.

96. The gap between electrodes in a spark plug is 0.06 cm. In order to produce anelectric spark in a gasoline-air mixture, the electric field must reach a value of3 × 106 V/m. What minimum voltage must be supplied by the ignition circuitwhen starting the car?

97. To recharge a 12-V battery, a battery charger must move 3.6 × 105 C of chargefrom the negative to the positive terminal. What amount of work is done by the battery charger? How many kilowatt hours is this?

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72 CHAPTER 25

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Chapter 25

Electric Potential

1. b

2. c

3. d

4. b

5. c

6. b

7. b

8. c

9. a10. b

11. c

12. b

13. a

14. a

15. b

16. d

17. b

18. d

19. b

20. c

21. d

22. c

23. d

24. b

25. d

26. c

27. d

28. b

29. c

30. d

31. b

32. c

33. a

34. a

35. b

36. c

37. b

38. c

39. b

40. d41. b

42. a

43. c

44. d

45. b

46. c

47. b

48. c

49. b

50. d

51. c

52. c

53. a

54. a

55. c

56. a

57. c

58. b

59. d

60. b

61. c

62. a

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74 CHAPTER 25

63. d

64. a

65. d

66. c

67. a68. c

69. c

70. b

71 e

72. e

73. d

74. c

75. c

76. c

77. c

78. e

79. a

80. d

81. b

82. d

83. c

84. b

85. d86. d

87. c

88. c

89. e

90. d

91. c

92. b

93. e

94. 1.1 × 10–4 C

95. 28.2 Volts

96. 1800 V

97. 4.32 MJ, 1.2 kWh

119004340-Chapter-25

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