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# A rubber rod rubbed with fur acquires a charge of (a) Is the charge on the fur (1) positive, (2) zero, or (3) negative Why (b) What is the charge on the fur..

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A rubber rod rubbed with fur acquires a charge of (a) Is the charge on the fur (1) positive, (2) zero, or (3) negative Why (b) What is the charge on the fur, and how

thWilson, College Physics, 6 Edition

Chapter 15

Exercises*

MC = Multiple Choice Question, CQ = Conceptual Question, and IE = Integrated Exercise. Throughout the text,

many exercise sections will include “paired” exercises. These exercise pairs, identified with red numbers, are

intended to assist you in problem solving and learning. In a pair, the first exercise (even numbered) is worked out in the Study Guide so that you can consult it should you need assistance in solving it. The second exercise (odd numbered) is similar in nature, and its answer is given at the back of the book.

15.1 Electric Charge

;1,1,1. MC A combination of two electrons and three protons would have a net charge of (a) (b) (c)

1919;！1.610C,；！1.610 C. (d) (c)

2. MC An electron is just above a fixed proton. The direction of the force on the electric proton is (a) up, (b)

down, (c) zero. (a)

3. MC In Exercise 2, which one feels the bigger size force: (a) The electron, (b) proton, or (c) both feel the

same size force? (c)

4. CQ (a) How do we know that there are two types of electric charge? (b) What would be the effect of

designating the charge on the electron as positive and the charge on the proton as negative? see ISM

5. CQ An electrically neutral object can be given a net charge by several means. Does this violate the

conservation of charge? Explain. no, see ISM

6. CQ If a solid neutral object becomes positively charged, does its mass increase or decrease? What if it

becomes negatively charged? decrease; increase

7. CQ How can you determine the type of charge on an object using an electroscope that has a net charge of a

known sign? Explain. see ISM

8. CQ If two objects electrically repel each other, are both necessarily charged? What if they attract each

other? yes; not necessarily (polarization)

13；！1.610C9. ; What is the net charge of an object that has 1.0 million excess electrons?

50C.10. ; In walking across a carpet, you acquire a net negative charge of How many excess electrons do

1

143.110 electrons you have?

11. ;; An alpha particle is the nucleus of a helium atom with no electrons. What would be the charge on two

19;！6.4010Calpha particles?

10;！8.010C.12. IE ;; A glass rod rubbed with silk acquires a charge of (a) Is the charge on the silk (1)

positive, (2) zero, or (3) negative? Why? (b) What is the charge on the silk, and how many electrons have

been transferred to the silk? (c) How much mass has the glass rod lost? see ISM

9；！4.810C.13. IE ;; A rubber rod rubbed with fur acquires a charge of (a) Is the charge on the fur (1)

positive, (2) zero, or (3) negative? Why? (b) What is the charge on the fur, and how much mass is transferred

；；920;！！4.810C,2.710kg,to the rod? (c) How much mass has the rubber rod gained? (a) (1) positive (b)

202.710kg(c)

15.2 Electrostatic Charging

14. MC A rubber rod is rubbed with fur. The fur is then quickly brought near the bulb of an uncharged

electroscope. The sign of the charge on the leaves of the electroscope is (a) positive, (b) negative, (c)

zero. (a)

15. MC A stream of water is deflected toward a nearby electrically charged object that is brought close to it. The

sign of the charge on the object (a) is positive, (b) is negative, (c) is zero, (d) can’t be determined by the data

given. (d)

16. MC A balloon is charged and then clings to a wall. The sign of the charge on the balloon (a) is positive, (b)

is negative, (c) is zero, (d) can’t be determined by the data given. (d)

17. CQ Fuel trucks often have metal chains reaching from their frames to the ground. Why is this important? to

remove excess charge due to friction of rubber on road

18. CQ Is there a gain or loss of electrons when an object is electrically polarized? Explain. no, charges simply

reorient themselves

19. CQ Explain carefully the steps you would use to create an electroscope that is positively charged by

induction. After you are done, how can you verify that the electroscope is positively (and thus not negatively)

charged? see ISM

2

20. CQ Two metal spheres mounted on insulated supports are in contact. Bringing a negatively charged object

close to the right-hand sphere would enable you to temporarily charge both spheres by induction. Explain

clearly how this would work and what the sign of the charge on each sphere would be. see ISM

15.3 Electric Force

21. MC How does the magnitude of the electric force between two point charges change as the distance between

them is increased? The force (a) decreases, (b) increases, (c) stays the same. (a)

22. MC Compared with the electric force, the gravitational force between two protons is (a) about the same, (b)

somewhat larger, (c) very much larger, (d) very much smaller. (d)

23. CQ The Earth attracts us by its gravitational force, but we have seen that the electric force is much greater

than the gravitational force. Why don’t we experience an electric force from the Earth? objects are

electrically neutral

24. CQ Two nearby electrons would fly apart if released. How could you prevent this by placing a single charge

in their neighborhood? Explain clearly what the sign of the charge and its location would have to be. see

ISM

25. CQ Coulomb’s law is an example of an inverse-square law. Use this inverse-square idea to determine the

ratio of electric force (final divided by initial) between two charges when the distance between them is cut to

one third of its initial value. 9

26. IE ; An electron that is a certain distance from a proton is acted on by an electrical force. (a) If the electron

1,were moved twice that distance away from the proton, would the electrical force be (1) 2, (2) (3) 4, or 2

1(4) times the original force? Why? (b) If the initial electric force is F, and the electron were moved to one 4

1third the original distance toward the proton, what would be the new electrical force? (a) (4) (b) 9F 4

27. ; Two identical point charges are a fixed distance apart. By what factor would the magnitude of the electric

force between them change if (a) one of their charges were doubled and the other were halved, (b) both their

11charges were halved, and (c) one charge were halved and the other were left unchanged? (a) 1 (b) (c) 42

28. ; In a certain organic molecule, the nuclei of two carbon atoms are separated by a distance of 0.25 nm. What

71.310Nis the magnitude of the electric force between them?

3

29. ; An electron and a proton are separated by 2.0 nm. (a) What is the magnitude of the force on the electron?

115.810N (b) zero (b) What is the net force on the system? (a)

4

30. IE ; Two charges originally separated by a certain distance are moved farther apart until the force between

them has decreased by a factor of 10. (a) Is the new distance (1) less than 10, (2) equal to 10, or (3) greater

than 10 times the original distance? Why? (b) If the original distance was 30 cm, how far apart are the

charges? (a) (1) less than 10 times (b) 95 cm

31. ; Two charges are brought together until they are 100 cm apart, causing the electric force between them to

increase by a factor of exactly 5. What was their initial separation distance? 2.24 m

32. ; The distance between neighboring singly charged sodium and chlorine ions in crystals of table salt (NaCl)

1092.8210m.2.9010N What is the attractive electric force between the ions? is

2.0C33. ;; Two point charges of are fixed at opposite ends of a meterstick. Where on the meterstick

could (a) a free electron and (b) a free proton be in electrostatic equilibrium? (a) 50 cm (b) 50 cm

1.0C;1.0C34. ;; Two point charges of and are fixed at opposite ends of a meterstick. Where could

(a) a free electron and (b) a free proton be in electrostatic equilibrium? (a) nowhere (b) nowhere

qq,35. ;; Two charges, and are located at the origin and at (0.50 m, 0), respectively. Where on the x-12

q,qqaxis must a third charge, of arbitrary sign be placed to be in electrostatic equilibrium if (a) and 312

qqare like charges of equal magnitude, (b) and are unlike charges of equal magnitude, and (c) 12

q？；7.0C?qq？;3.0Cx0.25mx？；0.94m and (a) (b) nowhere (c) for 231

36. ;; Compute the gravitational force and electrical force between the electron and proton in the hydrogen

115.310matom (;Fig. 15.24) assuming they are apart. Then calculate the ratio of the magnitudes of the

；；47839FF？！？！！3.610N,8.210N,2.310electric force to the gravitational force. ge

115.310m37. ;;; On average, the electron and proton in a hydrogen atom are separated by a distance of

(Fig. 15.24). Assuming the orbit of the electron to be circular, (a) what is the electric force on the electron?

(b) What is the electron’s orbital speed? (c) What is the magnitude of the electron’s centripetal acceleration

86218.210N2.210ms9.210gin units of g? (a) (b) (c)

38. ;;; Three charges are located at the corners of an equilateral triangle, as depicted in ;Fig. 15.25. What

q?are the magnitude and the direction of the force on 3.6 N in the positive x-direction 1

5

39. ;;; Four charges are located at the corners of a square, as illustrated in ;Fig. 15.26. What are the

qq? and (b) on charge (a) 96 N, 39? below magnitude and the direction of the force (a) on charge 24

positive x-axis (b) 61 N, 84? above negative x-axis

40. ;;; Two 0.10-g pith balls are suspended from the same point by threads 30 cm long. (Pith is a light

insulating material once used to make helmets worn in tropical climates.) When the balls are given equal

charges, they come to rest 18 cm apart, as shown in ;Fig. 15.27. What is the magnitude of the charge on

83.310Ceach ball? (Neglect the mass of the thread.)

15.4 Electric Field

41. MC How is the magnitude of the electric field due to a point charge reduced when the distance from that

charge is tripled: (a) It stays the same, (b) it is reduced to one third of its original value charge, (c) it is

reduced to one ninth of its original value charge, or (d) it is reduced to one twenty-seventh of its original

value charge? (c)

NC,42. MC The SI units of electric field are (a) C, (b) (c) N, (d) J. (b)

43. MC At a point in space, an electric force acts vertically upward on an electron. The direction of the electric

field at that point is (a) down, (b) up, (c) zero, (d) undetermined by the data. (a)

44. CQ How is the relative magnitude of the electric field in different regions determined from a field vector

diagram? from the relative lengths of the electric field vectors

45. CQ How can the relative magnitudes of the field in different regions be determined from an electric field line

diagram? by the relative density or spacing of the field lines

46. CQ Explain clearly why electric field lines can never cross. see ISM

47. CQ A positive charge is inside an isolated metal spherical shell, as shown in ;Fig. 15.28. Describe the

electric field in the three regions: between the charge and the inside surface of the shell, inside the shell

itself, and outside the outer shell surface. What is the sign of the charge on the two shell surfaces? How

48. CQ At a certain location, the electric field due to the excess charge on the Earth’s surface points downward.

What is the sign of the charge on the Earth’s surface at that location? Why? negative; see ISM

6

49. CQ (a) Could the electric field due to two identical negative charges ever be zero at some location(s) nearby?

Explain. If yes, describe and sketch the situation. (b) How would your answer change if the charges were

equal but oppositely charged? Explain. (a) yes, see ISM (b) no, see ISM

50. IE ; (a) If the distance from a charge is doubled, is the magnitude of the electric field (1) increased, (2)

decreased, or (3) the same compared to the initial value? (b) If the original electric field due to a charge is

41.010NC, what is the magnitude of the new electric field at twice the distance from the charge? (a)

52.510NC(2) decreased (b)

143.210N.51. ; An electron is acted on by an electric force of What is the magnitude of the electric field at

52.010NCthe electron’s location?

52. ; What is the magnitude and direction of the electric field at a point 0.75 cm away from a point charge of

23.210NC;2.0pC? away from the charge

571.010NC?1.210m53. ; At what distance from a proton is the magnitude of its electric field away

form the charge

4.0C5.0C,54. IE ;; Two fixed charges, and are separated by a certain distance. (a) Is the net

4.0Celectric field at a location halfway between the two charges (1) directed toward the charge, (2)

5.0Czero, or (3) directed toward the charge? Why? (b) If the charges are separated by 20 cm, calculate

5.0Cthe magnitude of the net electric field halfway between the charges? (a) (3) toward the charge (b)

59.010NC

55. ;; What would be the magnitude and the direction of an electric field that would just support the weight of

7111.010NC5.610NCa proton near the surface of the Earth? What about an electron? upward;

downward

(0.50m,0)3.0C4.0C,56. IE ;; Two charges, and are located at and (0.50 m, 0), respectively.

There is a point on the x-axis between the two charges where the electric field is zero. (a) Is that point (1) left

of the origin, (2) at the origin, or (3) right of the origin? (b) Find the location of the point where the electric

(0.036m,0)field is zero. (a) (1) left of the origin (b)

7

8

;；2.5C,4.8C,？？6.3C, and are located at 57. ;; Three charges,

(0.20m,0.15m),(0.50m,0.35m),；；(0.42m,0.32m),；； and respectively. What is the electric field at

55Exy？！;；！(2.210NC)(4.110NC)the origin?

;4.0C;9.0C58. ;; Two charges of and are 30 cm apart. Where on the line joining the charges is the

4.0Celectric field zero? 12 cm from the charge of (between the charges)

65.410NC59. ;;; What is the electric field at the center of the triangle in Fig. 15.25? toward the charge

4.0Cof

qq60. ;;; Compute the electric field at a point midway between charges and in Fig. 12

61.210NC4.0 C15.25. toward the charge of

73.810NC61. ;;; What is the electric field at the center of the square in Fig. 15.26? in the

;y-direction

52.010kg;2.0C62. ;;; A particle with a mass of and a charge of is released in a (parallel-plate)

12NC.uniform horizontal electric field of (a) How far horizontally does the particle travel in 0.50 s? (b) What is the horizontal component of its velocity at that point? (c) If the plates are 5.0 cm on each side, how

0.60ms0.27pCmuch charge is on each? (a) 0.15 m (b) (c)

63. ;;; Two very large parallel plates are oppositely and uniformly charged. If the field between the plates is

2261.710NC,Cm15Cm how dense is the charge on each plate (in )?

64. ;;; Two square, oppositely charged conducting plates measure 20 cm on each side. The plates are close

;4.0nC4.0nC,together and parallel to each other. Their charges are and respectively. (a) What is the

electric field between the plates? (b) What force is exerted on an electron between the plates? (a)

4151.110NC1.810N toward negative plate (b) toward positive plate

qq65. ;;; Compute the electric field at a point 4.0 cm from along a line running toward in Fig. 23

67Exy？；！;！(4.410NC)(7.310NC)15.26.

9

66. ;;; Two equal and opposite point charges form a dipole, as shown in ;Fig. 15.29. (a) Add the electric

fields due to each end at point P, thus graphically determining the direction of the field there. (b) Derive a

symbolic expression for the magnitude of the electric field at point P, in terms of k, q, d, and x. (c) If point P

3Ekqdx. (d) Why is it an inverse-cube fall-off instead is very far away, use the exact result to show that

of inverse-square? Explain. see ISM

15.5 Conductors and Electric Fields

67. MC In electrostatic equilibrium, is the electric field just below the surface of a charged conductor (a) the

same value as the field just above the surface (b) zero, (c) dependent on the amount of charge on the

2kqR?conductor, or (d) given by (b)

68. MC An uncharged thin metal slab is placed in an external electric field that points horizontally to the left.

What is the electric field inside the slab: (a) zero, (b) the same value as the original external field but

oppositely directed, (c) less than the original external field value but not zero, or (d) depends on the

magnitude of the external field? (a)

69. MC The direction of the electric field at the surface of a charged conductor under electrostatic conditions (a)

is parallel to the surface, (b) is perpendicular to the surface, (c) is at a 45? angle to the surface, or (d) depends

on the charge on the conductor. (b)

70. CQ Is it safe to stay in a car in a lightning storm (;Fig. 15.30)? Explain. yes, see ISM

71. CQ Under electrostatic conditions, the excess charge on a conductor is uniformly spread over its surface.

What is the shape of the surface? spherical

72. CQ Tall buildings have lightning rods to protect them from lightning strikes. Explain why the rods are

pointed in shape and taller than the buildings. charges accumulate at sharp points and lightning hits the tall

rods first

73. IE ; A solid conducting sphere is surrounded by a thick, spherical conducting shell. Assume that a total

;Qcharge is placed at the center of the sphere and released. (a) After equilibrium is reached, the inner

surface of the shell will have (1) negative, (2) zero, (3) positive charge. (b) In terms of Q, how much charge

is on the interior of the sphere? (c) The surface of the sphere? (d) The inner surface of the shell? (e) The

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