Physics Ch25

© 2000 by Harcourt College Publishers. All rights reserved.

Chapter 25

Electric Potential

Multiple Choice

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

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 an electric force.As the particle moves 25 cm from point A to point B, its kinetic energy increases by 1.5 mJ.Determine the electric potential difference, V B – VA.

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 electric field is uniform andgiven by E = (4i + 3j) N/C. What is the potential difference VA – VB?

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 act on it has akinetic energy of 5.0 J at point A. The particle subsequently passes through point B whichhas an electric potential of +1.5 kV relative to point A. Determine the kinetic energy ofthe particle as it moves through point B.

a . 3.0 Jb. 2.0 Jc. 5.0 Jd. 8.0 Je. 10.0 J

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5. A particle (mass 6.7 × 10–27 kg, charge 3.2 × 10–19 µC) moves along the positive x axis witha speed of 4.8 × 105 m/s. It enters a region of uniform electric field parallel to its motionand comes to rest after moving 2.0 m into the field. What is the magnitude of the electricfield?

a . 2.0 kN/Cb. 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 µC) moves from point A to point Bunder the influence of an electrostatic force only. At point A the proton moves with aspeed of 50 km/s. At point B the speed of the proton is 80 km/s. Determine the potentialdifference VB – VA.

a . +20 Vb. –20 Vc. –27 Vd. +27 Ve. –40 V

7. A proton (mass = 1.67 × 10–27 kg, charge = 1.60 × 10–19 µC) moves from point A to point Bunder the influence of an electrostatic force only. At point A the proton moves with aspeed of 60 km/s. At point B the speed of the proton is 80 km/s. Determine the potentialdifference VB – VA.

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 a potentialdifference 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 and has a speedof 5.0 × 106 m/s at point B. Only electric forces act on it during this motion. Determine theelectric potential difference VA – VB.

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

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10. A proton (m = 1.7 × 10–27 kg, q = +1.6 × 10–19 C) starts from rest at point A and has a speedof 40 km/s at point B. Only electric forces act on it during this motion. Determine theelectric potential difference VB – VA.

a . +8.5 Vb. –8.5 Vc. –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 onlyelectric forces acting on it) to point B where its speed is 80 m/s. Determine the electricpotential difference VA – VB.

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

12. A particle (m = 8.0 µg, q = +6.0 nC) has a speed of 80 m/s at point A and moves to point Bwhere the electric potential is 2.0 kV greater than at point A. What is the particle'skinetic energy at point B? Only electric forces act on the particle during this motion.

a . 14 µJb. 38 µJc. 10 µJd. 34 µJe. 40 µJ

13. An alpha particle (m = 6.7 × 10–27 kg, q = +3.2 × 10–19 C) has a speed of 20 km/s at point Aand moves to point B where it momentarily stops. Only electric forces act on the particleduring this motion. Determine the electric potential difference VA – VB.

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

14. Points A [at (3, 6) m] and B [at (8, –3) m] are in a region where the electric field is uniformand given by E = 12i N/C. What is the electric potential difference VA – VB?

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

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15. If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = –3.0 nC in the figure, what is the potentialdifference VA – VB?

a b a

BAq Q

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

16. Several charges in the neighborhood of point P produce an electric potential of 6.0 kV(relative to zero at infinity) and an electric field of 36i N/C at point P. Determine thework required of an external agent to move a 3.0-µC charge from infinity to point P(without any net change in the kinetic energy of the particle) along the x axis.

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

17. Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = –2.0 nC, a = 3.0 m, andb = 4.0 m, what is the electric potential difference, VA – VB?

b

a

a90°90°

B

A

Q

q90°90°

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

18. Three charged particles lie on the x axis. There are a 70-nC charge at x = –7, a –100-nCcharge at x = –3, and a 50-nC charge at x = 10. What is the electric potential (relative tozero at infinity) at the origin? (All distances are in meters.)

a . –0.17 kVb. +0.44 kVc. +0.83 kVd. –0.26 kVe. –0.48 kV

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

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

20. 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 the corner of this rectanglenearest the positive charge and point B is located at the intersection of the diagonals ofthe rectangle, determine the potential difference, VB – VA.

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

21. Identical 2.0-µC charges are located on the vertices of a square with sides that are 2.0 min length. Determine the electric potential (relative to zero at infinity) at the center ofthe square.

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

22. A +4.0-µC charge is placed on the x axis at x = +3.0 m, and a –2.0-µC charge is located onthe y axis at y = –1.0 m. Point A is on the y axis at y = +4.0 m. Determine the electricpotential 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

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

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

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

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

25. 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 the triangle?

a . 16 Vb. 10 Vc. 70 Vd. 46 Ve. 44 V

26. A particle (charge = Q) is kept in a fixed position at a position at a point P, and a secondparticle (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 particle after it hasmoved a distance of 10cm?

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

27. A particle (charge = q) is released from rest when it is a distance of 3.0 m from a pointcharge Q, which is held at a fixed position. If Q = 50 µC and q = –36 µC, what is thekinetic energy of the particle after it has traveled 1.0 m?

a . 3.3 Jb. 3.0 Jc. 2.7 Jd. 3.6 Je. 14 J

28. Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from restwith the distance between them equal to 1.0 m. If Q = 12 µC, what is the kinetic energy ofparticle 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

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

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

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

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

31. A particle (charge = 5.0 µC) is released from rest at a point x = 10 cm. If a 5.0-µC charge isheld fixed at the origin, what is the kinetic energy of the particle after it has moved90 cm?

a . 1.6 Jb. 2.0 Jc. 2.4 Jd. 1.2 Je. 1.8 J

32. A 60-µC charge is held fixed at the origin and a –20-µC charge is held fixed on the x axisat a point x = 1.0 m. If a 10-µC charge is released from rest at a point x = 40 cm, what is itskinetic 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

33. Two identical particles, each with a mass of 2.0 mg and a charge of 25 nC, are releasedsimultaneously from rest when the two are 4.0 cm apart. What is the speed of eitherparticle 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

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34. Two particles, each having a mass of 3.0 mg and having equal but opposite charges ofmagnitude 5.0 nC, are released simultaneously from rest when the two are 5.0 cm apart.What is the speed of either particle at the instant when the two 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

35. Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, are movingdirectly toward each other with equal speeds of 4.0 m/s at an instant when the distanceseparating the two is equal to 25 cm. What minimum separation distance will the twoachieve?

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

36. Two particles, each having a mass of 3.0 mg and having equal but opposite charges ofmagnitude of 6.0 nC, are released simultaneously from rest when they are a very largedistance apart. What distance separates the two at the instant when each has a speed of5.0 m/s?

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

37. A particle (q = +5.0 µC) is released from rest when it is 2.0 m from a charged particlewhich is held at rest. After the positively charged particle has moved 1.0 m toward thefixed particle, it has a kinetic energy of 50 mJ. What is the charge on the fixed particle?

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

38. Four identical point charges (+4.0 µC) are placed at the corners of a square which has20-cm sides. How much work is required to assemble this charge arrangement startingwith each of the charges a very large distance from either of the other charges?

a . +2.9 Jb. +3.9 Jc. +2.2 Jd. +4.3 Je. +1.9 J

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39. Identical 8.0-µC point charges are positioned on the x axis at x = ±1.0 m and released fromrest simultaneously. What is the kinetic energy of either of the charges after it hasmoved 2.0 m?

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

40. Two particles with equal masses and oppositely signed charges are placed on the x axis atx = ±4.0 m and released from rest at t = 0. If the magnitude of each of the charges is4.0 µC, what is the kinetic energy of either particle after it has moved 2.0 m?

a . 3.5 mJb. 5.1 mJc. 6.9 mJd. 9.0 mJe. 3.0 mJ

41. Through what potential difference must an electron (starting from rest) be accelerated ifit is to achieve a speed of 3.0 × 107 m/s?

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

42. Identical point charges (+50 µC) are placed at the corners of a square with sides of 2.0-mlength. How much external energy is required to bring a fifth identical charge frominfinity to the geometric center of the square?

a . 41 Jb. 16 Jc. 64 Jd. 10 Je. 80 J

43. A charge of +3.0 µC is distributed uniformly along the circumference of a circle with aradius of 20 cm. How much external energy is required to bring a charge of 25µC frominfinity to the center of the circle?

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

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

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

45. 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 µC from infinity to themidpoint of one of the 6.0-m lengths of the rectangle?

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

46. A charge per unit length given by λ(x) = bx, where b = 12 nC/m2, is distributed along thex axis from x = +9.0 cm to x = +16 cm. If the electric potential at infinity is taken to bezero, what is the electric potential at a 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

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

a . 71 Vb. 60 Vc. 49 Vd. 82 Ve. 150 V

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

60°60°

R

R

P++++++

+++

++

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

49. A charge of uniform density (0.80 nC/m) is distributed along the x axis from the origin tothe point x = 10 cm. What is the electric potential (relative to zero at infinity) at apoint, x = 18 cm, on the x axis?

a . 7.1 Vb. 5.8 Vc. 9.0 Vd. 13 Ve. 16 V

50. A charge of 20 nC is distributed uniformly along the x axis from x = –2 m to x = +2.0 m.What is the electric potential (relative to zero at infinity) at the point x = 5.0 m on thex axis?

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

51. Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m tox = 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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52. A linear charge of nonuniform density λ = bx, where b = 2.1 nC/m2, is distributed along thex axis from x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero atinfinity) of the point y = 4.0 m on the y axis.

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

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

a . 19 Vb. 17 Vc. 21 Vd. 23 Ve. 14 V

54. 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 atinfinity) at the point x = +5 m on the x axis?

a . ⌡⎮⌠

–2

3

90 dxx

b. ⌡⎮⌠

–2

3

90 dx5 – x

c. ⌡⎮⌠

–2

3

18 dxx

d. ⌡⎮⌠

–2

3

18 dx5 – x

e. ⌡⎮⌠

–2

3

90 dx5 + x

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

a . ⌡⎮⌠

0

3

27 dxx

b. ⌡⎮⌠

0

3

9 dx4 – x

c. ⌡⎮⌠

0

3

27 dx4 – x

d. ⌡⎮⌠

0

3

27 dxx

e. ⌡⎮⌠

0

3

27 dx4 + x

56. 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 atinfinity) at the origin?

a . ⌡⎮⌠

4

6

18 dx4 – x

b. ⌡⎮⌠

4

6

36 dxx

c. ⌡⎮⌠

4

6

18 dxx

d. ⌡⎮⌠

4

6

36 dx6 – x

e. ⌡⎮⌠

4

6

36 dx4 + x

57. A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m. Which ofthe following integrals is correct for the electric potential (relative to zero at infinity) atthe point x = +3 m on the x axis?

a . ⌡⎮⌠

0

4

45 dy(y2 + 9)1/2

b. ⌡⎮⌠

0

4

180 dy(y2 + 9)1/2

c. ⌡⎮⌠

0

4

45 dyy2 + 9

d. ⌡⎮⌠

0

4

180 dyy2 + 9

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e. ⌡⎮⌠

0

4

45 dy(y2 + 9)3/2

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58. Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 tox = +3 m. Which of the following integrals is correct for the electric potential (relative tozero at infinity) at the point y = +4 m on the y axis?

a . ⌡⎮⌠

0

3

54 dx(x2 + 16)1/2

b. ⌡⎮⌠

0

3

18 dx(x2 + 16)1/2

c. ⌡⎮⌠

0

3

54 dxx2 + 16

d. ⌡⎮⌠

0

3

18 dxx2 + 16

e. ⌡⎮⌠

0

3

18 dx(x2 + 16)1/2

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

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

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

a . ⌡⎮⌠

3

5

81 dy(y2 + 4)1/2

b. ⌡⎮⌠

3

5

162 dy(y2 + 4)1/2

c. ⌡⎮⌠

3

5

81 dyy2 + 4

d. ⌡⎮⌠

3

5

162 dyy2 + 4

e. ⌡⎮⌠

3

5

81 dyy

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61. Two large parallel conducting plates are 8.0 cm apart and carry equal but oppositecharges on their facing surfaces. The magnitude of the surface charge density on either ofthe facing surfaces is 2.0 nC/m2. Determine the magnitude of the electric potentialdifference between the plates.

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

62. Charge of density 3.0 µC/m fills a long cylindrical region having a 2.0-cm radius. If pointA is 1.0 cm from the symmetry-axis and point B is 2.0 cm from the symmetry-axis, what isthe potential difference VA – VB?

a . –25 mVb. +42 mVc. –42 mVd. +25 mVe. +20 mV

63. An infinite charged sheet has a surface charge density of 10 nC/m2. Determine thepotential difference between equipotential surfaces (on the same side of the sheet charge)that are separated by a distance of 7.0 mm.

a . 5.9 Vb. 4.0 Vc. 7.9 Vd. 9.9 Ve. 13 V

64. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformlyon its surface. If point A is located at the center of the sphere and point B is 15 cm from thecenter, what is the magnitude of the electric potential difference between these twopoints?

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

65. Charge of uniform density 50 nC/m3 is distributed throughout the inside of a longnonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potentialdifference 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

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66. Charge of uniform density 90 nC/m3 is distributed throughout the inside of a longnonconducting cylindrical rod (radius = 2.0 cm). Determine the magnitude of the potentialdifference 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

67. 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 cmaway?

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

68. A charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cmradius. Point A is 1.0 cm from the center of the conductor and point B is 5.0 cm from thecenter of the conductor. Determine the electric potential difference VA – VB.

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

69. A 2.0-nC charge is uniformly distributed over the surface of a solid spherical(radius = 2.0 cm) conductor which is concentric with a hollow spherical conductor(radii = 3.0 cm and 5.0 cm) which has a net charge of –3.0 nC. Determine the electricpotential of the outer conductor relative to the inner conductor.

a . +0.30 kVb. –0.30 kVc. –0.45 kVd. +0.45 kVe. –0.15 kV

70. Two flat conductors are placed with their inner faces separated by 6.0 mm. If the surfacecharge density on one of the inner faces is 40 pC/m2, what is the magnitude of the electricpotential differences between the two conductors?

a . 36 mVb. 18 mVc. 32 mVd. 27 mVe. 14 mV

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

a . –24 Vb. +24 Vc. –18 Vd. +30 Ve. –6.0 V

Conceptual Problems

72. How much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m toa potential of 1.0 × 106 V?

73. In the Bohr model of the hydrogen atom, the electron circles the proton at a distance of0.51 × 10–10 m. Find the potential at the position of the electron.

74. The gap between electrodes in a spark plug is 0.06 cm. In order to produce an electric sparkin a gasoline-air mixture, an electric field of 3 × 106 V/m must be achieved. On starting acar, what minimum voltage must be supplied by the ignition circuit?

75. To recharge a 12-V battery, a battery charger must move 3.6 × 105 C of charge from thenegative to the positive terminal. What amount of work is done by the battery charger?How many kilowatthours is this?

76. 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. a charge moving at constant speed requires that the maximum amount of work be done

against electrical forces.d. a charge may be moved at constant speed without work against electrical forces.e. charges move by themselves.

77. 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.

Chapter 25 19


78. When a positive chanrge is released and moves along an electric field line, it moves to aposition 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.

79. When a negative charge is released and moves along an electric field line, it moves to aposition 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.

80. A charge is placed on a spherical conductor of radius r1. This sphere is then connected to adistant sphere of radius r2 (not equal to r1) by a conducting wire. After the charges on thespheres 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 V2V1

= q2q1

.

e. the potentials are in the ratio V2V1

= r2r1

.

81. 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 by the

resistance.

82. Which statement is always correct when applied to a charge distribution located in afinite 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.

20 Chapter 25


83. Which of the following represents the equipotential lines of a dipole?

A B C D E

84. 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.

Chapter 25 21


Chapter 25 1


Chapter 25

Electric Potential

1. Answer: b

2. Answer: c

3. Answer: d

4. Answer: b

5. Answer: c

6. Answer: b

7. Answer: b

8. Answer: c

9. Answer: a

10. Answer: b

11. Answer: c

12. Answer: a

13. Answer: b

14. Answer: a

15. Answer: a

16. Answer: b

17. Answer: d

18. Answer: a

19. Answer: b

20. Answer: d

21. Answer: b

22. Answer: c

23. Answer: d

2 Chapter 25


24. Answer: c

25. Answer: d

26. Answer: b

27. Answer: c

28. Answer: d

29. Answer: c

30. Answer: d

31. Answer: b

32. Answer: c

33. Answer: d

34. Answer: b

35. Answer: c

36. Answer: a

37. Answer: a

38. Answer: b

39. Answer: c

40. Answer: d

41. Answer: b

42. Answer: c

43. Answer: b

44. Answer: d

45. Answer: b

46. Answer: a

47. Answer: c

48. Answer: d

49. Answer: b

50. Answer: c

Chapter 25 3


51. Answer: b

52. Answer: c

53. Answer: b

54. Answer: d

55. Answer: c

56. Answer: c

57. Answer: a

58. Answer: a

59. Answer: c

60. Answer: a

61. Answer: c

62. Answer: e

63. Answer: b

64. Answer: b

65. Answer: d

66. Answer: b

67. Answer: c

68. Answer: a

69. Answer: b

70. Answer: d

71. Answer: a

72. Answer: 1.1 × 10–4 C

73. Answer: 28.2 Volts

74. Answer: 1800 V

75. Answer: 4.32 MJ, 1.2 kW/h

76. Answer: d

77. Answer: c

4 Chapter 25


78. Answer: a

79. Answer: c

80. Answer: c

81. Answer: b

82. Answer: e

83. Answer: e

84. Answer: d

Physics Ch25

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