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Chapter 18: Electrostatics

Assignment

Electric Charge (a)

1

How could you find out which strip of tape, the one pulled off the desk or the one pulled off the back of the other tape, is positively charged ?

6

The combined charge of all electrons in a nickel coin is hundreds of thousands of coulombs, a unit of electrical charge. Does that imply anything about the net charge on the coin? Explain.

Answer Answer Rub a piece of hard plastic with wool. The plastic is charged negatively. It will repel the negatively charged strip of tape and attract the positively charged one. 2

Suppose you attach a long metal rod to a plastic handle so the rod is isolated. You touch a charged glass rod to one end of the metal rod. Describe the charges on the metal rod.

No. Net charge is the difference between positive and negative charges. It can still be zero.

7

List some insulators and conductors. Answer

Answer

Student answers will vary, but may include dry air, wood, plastic, glass, cloth, and deionized water as insulators; and metals, tap water, and your body as conductors.

The glass rod was positively charged. This charge spreads over the entire metal rod, charging it positively.

3

In the 1730s, Stephan Gray tried to see how far electrical charge could be conducted by metal rods. He hung metal rods by thin silk cords from the ceiling. When the rods were longer than 293 feet, the silk broke. Gray replaced the silk with stronger wires made of brass, but now the experiments failed. The metal rod would no longer transmit charge from one end to the other. Why?

8

What property makes a metal a good conductor and rubber a good insulator? Answer Metals contain free electrons; rubber has bound electrons.

Answer 9 Brass is a conductor. The electric charge flowed into the ceiling instead of along the metal rod.

Why does a woolen sock taken from a clothes dryer sometimes cling to other clothes? Answer

4

Suppose there was a third type of charge. What experiments could you suggest to explore its properties?

It has been charged by the tumbling of the clothes and is attracted to the other clothing.

Answer 10 If the new type is different from the other two types, then it should repel (or attract) both positively and negatively charged objects.

5

If you wipe a stereo record with a clean cloth, why does the record now attract dust? Answer Rubbing the record charges it. Neutral particles such as dust are attracted to a charged object.

If you comb your hair on a dry day, the comb can become positively charged. Can your hair remain neutral? Explain. Answer

How does the charge of an electron differ from the charge of a proton?

No. By conservation of charge, your hair must become negatively charged.

Answer

11

The charge of the proton is exactly the same size as the electron, but has the opposite sign.

Chapter 18: Electrostatics

Assignment

Electric Charge (a)

12

13

14

If you scuff electrons from your feet while walking across a rug, are you now negatively charged or positively charged?

17

Explain why a balloon that has been rubbed on a wool shirt sticks to the wall .

Answer

Answer

When you lose electrons, you become positively charged.

The balloon becomes charged by rubbing. It is attracted to the neutral wall because it separates the charges in the wall.

Using a charged rod and an electroscope, how can you find if an object is a conductor?

18

Name three methods to charge an object.

Answer

Answer

Use a known insulator to hold one end of the object against the electroscope. Touch the other end with the charged rod. If the electroscope indicates a charge, the object is a conductor.

conduction, friction, induction

Explain why an insulator that is charged can be discharged by passing it above a flame.

19

Explain how to charge a conductor negatively if you have only a positively-charged rod. Answer

Answer Without touching the conductor, bring it close to, but not touching, the rod. Momentarily touch the side of the conductor farthest from the rod. The conductor will be charged by induction.

The hot gases above the flame are a plasma, which acts as a conductor and pulls excess charges away from the insulator.

15

A charged rod is brought near a pile of tiny plastic spheres. Some of the spheres are attracted to the rod, but as soon as they touch the rod, they fly away in different directions. Explain .

20

The text describes Coulomb's method for obtaining two charged spheres, A and B, so that the charge on B was exactly half the charge on A. Suggest a way Coulomb could have placed a charge on sphere B that was exactly one third the charge on sphere A.

Answer Answer The neutral spheres are initially attracted to the charged rod and all acquire the same charge as the rod when they touch it. subsequently, they are repelled from each other and from the rod.

16

A rod-shaped insulator is suspended so it can rotate. A negatively-charged comb held nearby attracts the rod. (a) Does this mean the rod is positively charged? Explain. (b) If the comb repelled the rod, what could you conclude, if anything, about the charge on the rod? Answer (a) No. Neutral objects are attracted by either charge. (b) It must be negative. Neutrals are never repelled .

After charging spheres A and B equally, sphere B is touched to two other equally sized balls that are touching each other. The charge on B will be divided equally among all three balls, leaving 1/3 the total charge on it.

Chapter 18: Electrostatics

Assignment

Separation of Charged Bodies (b)

21

Salt water drips slowly from a narrow dropper inside a negatively-charged metal ring, as seen in the figure. (a) Will the drops be charged? (b) If they are charged, are they positive or negative?

24

Explain what happens to the leaves of a positively-charged electroscope when rods with the following charges are nearby but not touching the electroscope. (a) positive (b) negative Answer (a) The leaves will move farther apart. (b) The leaves will droop slightly.

25

!

If two identical charges, 1.000 C each, are separated by a distance of 1.00 km, what is the force between them? Answer

Answer

+9.0 x 103 N

(a) yes (b) The drops will be positive by induction. 26 22

Benjamin Franklin once wrote that he had "erected an iron rod to draw the lightning down into my house, in order to make some experiment on it, with two bells to give notice when the rod should be electrify'd...." The chime had two small bells mounted side by side. One bell was connected to the iron rod for a charge; the other bell was attached to Earth. Between the two bells, a small metal ball was suspended on a silk thread so it could swing back and forth, striking the two bells. Explain why, when the one bell was charged, the ball would keep swinging, hitting first one bell then the other.

Answer -1.1 x 108 N; the force is attractive.

27

Answer (The metal ball is neutral initially. It is attracted toward the charged bell. When it hits, it becomes charged. The ball is now repelled. It is now attracted to the uncharged bell. It hits this bell, becomes discharged, and starts up the process again.

23

Two point charges are separated by 10.0 cm. If one charge is +20.00 mC and the other is -6.00 mC, what is the force between them?

Two identical point charges are 3.00 cm apart. Find the charge on each of them if the force of repulsion is 4.00 x 10 -7 N Answer +2.0 + 10-10C

28

Lightning usually occurs when a negative charge in a cloud is transported to Earth. If Earth is neutral, what provides the attractive force that pulls the electrons toward Earth?

A charge of 4.0 x 10-5 C is attracted by a second charge with a force of 350 N when the separation is 10.0 cm. Calculate the size of the second charge. Answer -9.7 x 10-6C

Answer (The charge in the cloud repels electrons on Earth, causing a charge separation by induction. The side of Earth closest to the cloud is positive, resulting in an attractive force.

29

Two positive charges of 6.0 x 10-6 C are separated by 0.50 m. What force exists between the charges? Answer 1.296 N

Chapter 19: Electrostatic Forces

Assignment

Coulomb's Law (c)

30

31

A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.30 m. What is the force between the two charges?

36

Two identical positive charges exert a repulsive force of 6.4 x 10-9 N when separated by a distance of 3.8 x 10-10 m. Calculate the charge of each.

Answer

Answer

-1.6 x 104N

3.2 x 10-19C

A negative charge of -6.0 x 10-6 C exerts an attractive force of 65 N on a second charge 0.050 m away. What is the magnitude of the second charge?

37

Find the force between a positive charge of 1.0 microcoulombs and a positive charge of 2.0 microcoulombs when they are 0.030 m apart? (1 microcoulomb = 1 x 10-6 coulombs)

Answer Answer 3.0 x 10-6C

32

Object A has a charge + 1.8 x 10-6 C. Object B has a charge -1.0 x 10-6 C. They are 0.014 m apart. (a) What is the force on A? (b) What is the force on B?

20 N 38

A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.30 m. What is the force between the two charges? Answer

Answer 83 N toward A; 83 N toward B

33

-15,964 N 39

A positive and a negative charge, each of magnitude 1.5 x 10-5 C, are separated by a distance of 15 cm. Find the force on each of the particles.

Suppose you are testing Coulomb's law using a small, charged plastic sphere and a large, charged metal sphere. Both are charged positively. According to Coulomb's law, the force depends on 1/d2, where d is the distance between the centers of the spheres. As the two spheres get close together, the force is smaller than expected from Coulomb's law. Explain.

Answer Answer

90 N, toward the other charge

34

The charges on the large metal sphere are repelled and move away from the small sphere, reducing the force.

Two negatively-charged bodies with -5.0 x 10-5 C are 0.20 m from each other. What force acts on each particle? Answer

40

5.6 x 102 N

35

Answer

A force of -4.4 x 103 N exists between a positive charge of 8.0 x 10 -4 C and a negative charge of -3.0 x 10-4 C. What distance separates the charges? Answer 0.70 m

Two identical point charges are separated by a distance of 3.0 cm and they repel each other with a force of 4.0 x 10-5 N. What is the new force if the distance between the point charges is doubled?

1.0 x10-5 N

41

An electric force of 2.5 x 10-4 N acts between two small equally-charged spheres which are 2.0 cm apart. Calculate the force acting between the spheres if the charge on one of the spheres is doubled and the spheres move to a 5.0-cm separation. Answer 7.9 x 10-5 N

Chapter 19: Electrostatic Forces

Assignment

Variations in Coulomb's Law (d)

42

Two charged bodies exert a force on each other of 16 millinewtons. What will be the force between the same two bodies if the distance between them is halved?

47

Answer

Three particles are placed in a line. The left particle has a charge of -67 x 10-6 C, the middle, +45 x 10-6C,and the right, -83 x 10-6 C. The middle particle is 72 cm from each of the others. (a) Find the net force on the middle particle. (b) Find the net force on the right particle.

64 millinewtons or .064 newtons Answer 43

Coulomb's law and Newton's Law of Universal Gravitation appear similar. In what ways are the electrical and gravitational forces similar? How are they different? Answer

(a) 12.5 N, right (b) 40.7 N, left

48

Similar: inverse-square dependence on distance, force proportional to product of two masses or two charges. Different: only one sign of mass, so gravitational force is always attractive, while there are two signs of charge, so electrical force is either attractive or repulsive.

44

Coulombs Law and the Universal gravitational Law are very similar. (a) Calculate the repulsive Coulomb force between two protons 4 x 10-15 m apart inside a nucleus. (b) Calculate the gravitational force of attraction between the two protons. (c) Why doesn't a force of such magnitude, acting on a proton of mass about 1.67 x 10-24 g, cause the nucleus to fly apart? Answer

Answer (a) 3.7 x 102 N,away (b) 92 N, toward (c) Refer to Problems and Solutions Manual for diagram.

49

(a) 14.4 N (b) 1.17 x 10-35 N (c)

45

Three particles are placed on a straight line. The left particle has a charge of +4.6 x l0-6 C, the middle particle has a charge of -2.3 x l0-6 C, and the right particle has a charge of -2.3 x l0-6 C. The left particle is 12 cm from the middle particle and the right particle is 24 cm from the middle particle. The left particle is now moved directly above the middle particle, still 12 cm away. Find the force on the middle particle. Answer Hard 7.2° to the left or vertical 6.6 N

46

A positive charge of 3.0 x 10-6 C is pulled on by two negative charges. One, -2.0 x 10-5 C, is 0.050 m to the north and the other, -4.0 x 10-6 C, is 0.030 m to the south. What total force is exerted on the positive charge? Answer -9 N, North

Two charges, q1, and q2, are at rest near a positive test charge, q, of 7.2 x 10-6 C. The first charge, q1, is a positive charge of 3.6 x 10-6 C, located 0.025 m away from q at 350; q2 is a negative charge of -6.6 x 10-6 C, located 0.068 m away at 1250. (a) Determine the magnitude of each of the forces acting on q. (b) Sketch a force diagram. (c) Graphically determine the resultant force acting on q.

A small plastic sphere coated with a thin metalized surface has mass 0.05 g and carries a charge of +8 x 10-9 C. It is suspended by a light insulating thread at a point 3 cm below the center of a small fixed conducting sphere carrying -5 x 10-9 C. The thread is cut. (a) What is the electrostatic acceleration upward? (b) What is the net or observed acceleration? Answer (a) 8.0 m/s (b) 1.8 m/s2 downward

50

A charge Q1 = +10 x 10-9 C on the x axis at x = 0, and a second charge Q2 = +3 x 10-9 C is on the x axis at x = 5 m. A third charge Q3 = -10 x 10-9 C is placed on the x axis at x = 15 m. Calculate the magnitude and direction of the force on Q2. Answer 13.5 x 10-9 N toward the right

Chapter 19: Electrostatic Forces

Assignment

The Superpositon Principal (Planar) (g)

51

A triangle ABC, marked out on a flat surface, has sides of the following lengths: AB = 4 m, BC = 5 m, and AC = 3 m. At the corners are the following charges: -40 x 10-6 C at A, -160 x 10-6 C at B, and +90 x 10-6 C at (C) What are the magnitude and direction of the net force on the charge at A?

57

Answer

Answer

5.09 N, 45 degrees from AC, 135 degrees from AB

52

Three charges, each of +80 x 10-6 C, are equally spaced along a straight line, successive charges being 6 m apart. (a) Calculate the force on one of the end charges. (b) Calculate the force on the central charge.

Two Ping-Pong balls painted with aluminum paint are suspended from the same point by threads 50 cm long. The mass of each ball is 20 g. When equal charges are given to the two balls, they come to rest in an equilibrium position in which their centers are 60 cm apart. Calculate the charge on each ball.

2.42 x 10-6 C

58

Two small spheres each having a mass of 0.050 g are suspended by silk threads from the same point. When given equal charges, they separate, the threads make an angle of 10 degrees with each other. What is the force of repulsion acting on each sphere?

Answer Answer

(a) 2.00 N away from the center (b) 0 newtons on the center charge.

53

Three masses, each of +80 x 106 kg, are equally spaced along a straight line, successive masses are 6.00 m apart. (a) Calculate the force on one of the end masses. (b) Calculate the force on the central mass.

4.3 x 10-5 N

59

Answer

Answer

(a) 1.48 x 104 N (b) 0 54

55

56

Equal charges of +15 x 10-6 C are placed at the four corners of a square 0.3 m on a side. Calculate the magnitude and direction of the force on one of the charges.

Two small spheres each having a mass of 0.10 g are suspended from the same point on silk threads 20 cm long. When given equal charges, they repel each other, coming to rest 24 cm apart. Find the charge on each sphere?

6.86 x 10-8 C

60

How many excess electrons are on a ball with a charge of -4.00 x 10-17 C?

Answer

Answer

43.1 N outward along the diagonal

250 electrons

Equal masses of 15 x 106 kg are placed at the four corners of a square 3 m on a side. Calculate the magnitude and direction of the force on one of the masses.

61

A strong lightning bolt transfers about 25 C to Earth. How many electrons are transferred?

Answer

Answer

3206 N

1.6 x 1020 electrons

Equal charges of +8 x 10-6 C are placed at the three corners of an equilateral triangle 2 m on a side. Calculate the magnitude and direction of the force on one of the charges. Answer .249 N away from the triangle, perpendicular to the opposite base.

62

How many electrons would be required to have a total charge of 1.00 C on a sphere? Answer 6.25 x 1018 electrons

Chapter 19: Electrostatic Forces

Assignment

Descriptive Electrostatics (a)

63

When a rubber rod is rubbed with wool, the rod becomes negatively charged. What can you conclude about the magnitude of the wool's charge after the rubbing process? Why?

69

Answer magnitude of wool's charge equals magnitude of rod's charge; charge is conserved

A small cork with an excess charge of +6 µC (1µ C = 10-6 C) is placed 0.12 m from another cork, which carries a charge of -4.3 µC. (a) What is the magnitude of the electric force between the corks? (b) Is theis force atractive or repulsive (c) How man excessive electrons are on te negative cork? (d) How many electrons has the postive cork lost? Answer

64

A typical lightning bolt has about 10.0 C of charge. How many excess electrons are in a typical lightning bolt?

(a) 16 N (b) attractive (c) 2.7 x 1013 electrons (d) 3.8 x 1013 electrons

Answer 6.25 x 1019 electrons 65

If you stick a piece of transparent tape on your desk and then quickly pull it off, you will find that the tape is attracted to other areas of your desk that are not charged. Why does this happen?

70

Answer

Answer

39.3 cm

The tape induces a surface charge on the desk, so the two are attracted to one another. 71 66

Two electrostatic point charges of +60 µC and +50.0 µC exert a repulsive force on each other of 175 N. What is the distance between the two charges?

Metals such as copper and silver can become charged by induction while plastic materials cannot. Explain why.

Consider three point charges at the corners of a triangle, as shown in the figure, where q1 = 6.00 x 109 C, q2 = -2.00 x 109 C, and q3 = 5.00 x 10-9 C. Find the magnitude and direction of the resultant force on q3.

Answer Because plastic, an insulator, does not easily conduct charge

67

Why is an electrostatic spray gun more efficient than an ordinary spray gun? Answer More paint hits the object being painted due to an electrical attraction between the charged droplets and the oppositely charged object.

68

The electron and proton of a hydrogen atom are separated on average by a distance of about 5.3 x 10-11 m. Find the magnitudes of the electric force and the gravitational force that each particle exerts on the other.

Answer 7.16 x 10-9 N q = 65.20

Answer Felectric = -8.2 x 10-8 N Fg = 3.6 x 10-49 N

72

Three charges are located on the x-axis. A 5.0 µC charge is located at x = 0. 0 cm, a 1. 5 µC charge is located at x = 3.0 cm, and a -3.0 µC charge is located at x = 5.0 cm. Find the resultant force on the 5.0 µC charge.

Answer 21 N, along the negative x-axis

Chapter 19: Electrostatic Forces

Assignment

The Superpositon Principal (Planar) (g)

73

Four charged particles are placed so that each particle is at the corner of a square. The sides of the square are 15 cm. The charge at the upper left corner is +3.0 µC, the charge at the upper right corner is -6.0 µC, the charge at the lower left corner is -2.4 µC, and the charge at the lower right corner is -9.0 µC. (a) What is the net electric force on the +3.0 µC charge? (b) What is the net electric force on the -6.0 µC charge? (c) What is the net electric force on the -9.0 µC charge?

77

How are conductors different from insulators? Answer Conductors transfer charge easily; insulators do not.

78

When a conductor is charged by induction, is the induced surface charge on the conductor the same or opposite the charge of the object inducing the surface charge? Answer

Answer (a) 13.0 N, 3 V below the positive x-axis (b) 25 N, 780 above the negative x-axis (c) 18 N, 750 below the positive x-axis

74

opposite

79

Three charges lie along the x-axis. One positive charge, q1 = 15 µC, is at x= 2.0 m, and another positive charge, q2 = 6.0 µC, is at the origin. At what point on the x-axis must a negative charge, q3, be placed so that the resultant force on it is zero?

A negatively charged balloon has 3.5 µC of charge. How many excess electrons are on this balloon? Answer 2.2 x 1013 electrons

80

Which activity does not produce the same results as the other three? (a) sliding over a plastic-covered automobile seat (b) walking across a woolen carpet (c) scraping food from a metal bowl with a metal spoon (d) brushing dry hair with a plastic comb

Answer Answer

c

p = 0.80 m from q2. 81 75

An electron is released above the Earth's surface. A second electron directly below it exerts just enough of an electric force on the first electron to cancel the gravitational force on it. Find the distance between the two electrons.

Answer No; if a charged object induces a surface charge on the suspended object, the two are attracted, but the suspended object has no net charge.

Answer 5.07 m

76

A charge q1 of -6.00 x 10-9 C and a charge q2 of -3.00 x 10-9 C are separated by a distance of 60.0 cm. Where could a third charge be placed so that the net electric force on it is zero?

Answer 35.2 cm from q1 (24.8 cm from q2)

If a suspended object is attracted to another object that is charged, can you conclude that the suspended object is charged?

82

Explain from an atomic viewpoint why charge is usually transferred by electrons. Answer Protons are relatively fixed in the nucleus, whereas electrons can be transferred from one atom to another.

Chapter 19: Electrostatic Forces

Assignment

Descriptive Electrostatics (a)

83

Because of a higher moisture content, air is a better conductor of charge in the summer than in the winter. Would you expect the shocks from static electricity to be more severe in summer or winter? Explain your answer.

88

Three positive point charges of 3.0 nC, 6.0 nC, and 2.0 nC, respectively, are arranged in a triangle, as shown in the figure below. Find the magnitude and direction of the electric force on the 6.0 nC charge.

Answer winter, because more charge can accumulate before electric discharge occurs

84

A balloon is negatively charged by rubbing and then clings to a wall. Does this mean that the wall is positively charged? Answer

Answer

No; the balloon clings because its charge induces a surface charge or the wall.

85

Which effect proves more conclusively that an object is charged, attraction to or repulsion from another object? Explain.

9.73 x 10-8 N 11.50 below the positive x-axis

89

Three point charges lie along the y-axis. A charge of q1 = -9.0 µC is at y = 6.0 m, and a charge of q2 = -8.0 µC is at y= -4.0 m. The net electric force on the third charge is zero. Where is this charge located?

Answer repulsion, because attraction can be the result of an induced surface charge, but repulsion only occurs when two objects each have a net charge

86

87

What determines the direction of the electric force between two charges?

Answer y = 0.8 m from the zero point or 5.1 from one end

90

Calculate the net charge on a substance consisting of a combination of 7.0 x 1013 protons and 4.0 x 1013 electrons.

Answer

Answer

the signs of the charges

4.8 x 10-6 C

In which direction will the electric force from the two equal positive charges pull the negative charge shown in the figure below?

91

The moon (m = 7.36 x 1022 kg) is bound to Earth (m = 5.98 x 1024 kg) by gravity. The moon is 3.82 x 108 m from the earth. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sign, find the quantity of charge that would have to be placed on each to produce the required force. Answer 5.72 x 1013 C

Answer to the left

Chapter 19: Electrostatic Forces

Assignment

Common Vectors & Coulomb's Law (i)

92

Two small metallic spheres, each with a mass of 0.20 g, are suspended as pendulums by light strings from a common point. They are given the same electric charge, and the two come to equilibrium when each string is at an angle of 5.00 with the vertical. If the string is 30.0 cm long, what is the magnitude of the charge on each sphere?

96

Answer 7.17 x 10-9 C

93

Three identical point charges, each of mass m = 0.10 kg, hang from three strings, as shown in the figure below. If L = 30.0 cm. and θ = 450, what is the value of θ?

Answer (a) Picture (b) 1.28 x 10-8 N 450 above the positive x-axis

97

94

In 1955, a water bore that was 2,231 m deep was drilled in Montana. Consider two charges, q2 = 1.60 mC and q1, separated by a distance equal to the depth of the well. If a third charge, q3 1.998 mC is placed 888 m from q2 and is between q2 and q1, this third charge will be in equilibrium. What is the value of q1?

Answer

Answer

2.0 x 10-6 C

366 mC

A DNA molecule (deoxyribonucleic acid) is 2.17 mm long. The ends of the molecule become singly ionized so that there is an increase of 1.00 percent upon becoming charged. Find the effective spring constant of the molecule.

98

Answer 2.25 x 10-9 N/m

95

In 1993, a chocolate chip cookie was baked in Arcadia, California. It contained about three million chips and was 10.7 m long and 8.7 m wide. Suppose four charges are placed in the corners of that cookie as follows: q1 = -12.0 nC at the lower left corner, q2 = 5.6 nC at the upper left corner, q3 = 2.8 nC at the upper right corner, and q4 = 8.4 nC at the lower right corner. (a) Draw a picture of the rectangular cooke (b) Find the magnitude and direction of the resultant electric force acting on q1.

In 1990, a French team flew a kite that was 1,034 m long. Imagine two charges, +2.0 nC and -2.8 nC, at opposite ends of the kite. (a) Calculate the magnitude of the electric force between them. ( b) If the separation of charges is doubled, what absolute value of equal and opposite charges would exert the same electric force?

In more than 30 years, Albert Klein, of California, drove 2.5 x 106 km in one automobile. Consider two charges, q1 = 2.0 C and q2 = 6.0 C, separated by Klein's total driving distance. A third charge, q3 = 4.0 C, is placed on the line connecting q1 and q2. How far from q1 should q3 be placed for q3 to be in equilibrium? Answer 9.3 x 108 m

99

The most accurate balance can measure objects with masses as small as 1.0 x 10-11 kg, which is less than the mass of the ink in the period at the end of this sentence. Suppose a mass this small is suspended by electric repulsion over a charge of -4.0 nC. How many extra electrons must be placed on the mass so that it will float 2.0 cm directly over the -4.0 nC charge?

Answer (a) 4.7 x 10-14 N (b) 4.7 x 10-9 C

Answer 6.8 x 103 electrons

Chapter 19: Electrostatic Forces

Assignment

Common Vectors & Coulomb's Law (i)

100 The CN Tower, in Toronto, Canada, is 553 m tall. Suppose two balls, each with a mass of 5.00 kg and a charge of 40.0 mC, are placed at the top and bottom of the tower, respectively. The ball at the top is then dropped. At what height is the acceleration on the ball zero? Answer

parasitic wasp Carapractus cinctus has a mass of 5.0 x 104 The 10-6 kg, which makes it one of the smallest insects in the world. If two such wasps are given equal and opposite charges with an absolute value of 2.0 x 10-15 C and are placed 1.00 m from each other on a horizontal smooth surface, what extra horizontal force must be applied to each wasp to keep it from sliding? Take into account both gravitational and electric forces between the wasps.

542 Answer 24

is about 6.0 x 10 kg, while the moon's mass 101 Earth's mass is 7.3 x 1022 kg. What equal charges must be placed on Earth and the moon to make the net force between them zero? Answer 5.7 x 1013 C

102 In 1995, a single diamond was sold for more than 16 million. It was not the largest diamond in the world, but its mass was an impressive 20.0 g. Consider such a diamond resting on a horizontal surface. It is known that if the diamond is given a charge of 2.0 µC and a charge of at least -8.0 µC is placed on that surface at a distance of 1.7 m from it, then the diamond will barely keep from sliding. Calculate the coefficient of static friction between the diamond and the surface.

3.77 x 10-20 N

-9 105 A charge of +2.00 x 10 C-9is placed at theorigin, and another charge of +4 x 10 C is placed at x = 1.5 m. find the point between these two charges where a charge of +3.00 x 10-9C should be paced so that the net electric force on it is zero.

Answer x = 0.64 m

Answer 0.25

106 What must be the distance between point charge q1 = 26.0 µC and point charge q2 = -47 µC for the electrostatic force between them to have a magnitude of 5.70 N? Answer

known. Its 103 Mycoplasma is the smallest living organism mass has an estimated value of 1.0 x 10-16 g. (a) If two specimens of this organism are placed 1.0 m apart and one electron is placed on each, what is their initial acceleration due to the electric force? (b) If the medium through which the Allycoplasma move exerts a resistive force on the organisms, how large must that force be to balance the force of electrostatic repulsion?

Answer (a) 2.3 x 10-9 m/s2 (b) 2.3 x 10-28 N

1.39 m

107 The figure shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -32e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +48e), and then they are separated. The final charge on sphere W is +18e. What was the initial charge on sphere A?

Answer (a) (0.829 N)ˆi ; (b) (-0.621 N)ˆj

Chapter 19: Electrostatic Forces

Assignment

Common Vectors & Coulomb's Law (i)

108 An electron is in a vacuum near Earth's surface and located at y = 0 on a vertical y axis. At what value of y should a second electron be placed such that its electrostatic force on the first electron balances the gravitational force on the first electron? Answer

112 In the figure, a central particle of charge -2q is surrounded by a square array of charged particles, separated by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.)

-5.1 m

109 How far apart must two protons be if the magnitude of the electrostatic force acting on either one due to the other is equal to the magnitude of the gravitational force on a proton at Earth's surface? Answer 11.9 cm

110 The figure shows four situations in which five charged particles are evenly spaced along an axis. The charge values are indicated except for the central particle, which has the same charge in all four situations. Rank the situations according to the magnitude of the net electrostatic force on the central particle, greatest first.

Answer 6kq2/d2 , leftward

113 The figure shows four arrangements of charged particles. Rank the arrangements according to the magnitude of the net electrostatic force on the particle with charge +Q, greatest first.

Answer 3, 1, 2, 4 (zero)

111 In the figure, a central particle of charge -q is surrounded by two circular rings of charged particles. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.)

Answer a and d tie, then b and c tie

114 A positively charged ball is brought close to an electrically neutral isolated conductor. The conductor is then grounded while the ball is kept close. Is the conductor charged positively, charged negatively, or neutral if (a) Is the conductor charged positively, charged negatively, or neutral if the ball is first taken away and then the ground connection is removed? (b) Is the conductor charged positively, charged negatively, or neutral if the ground connection is first removed and then the ball is taken away? Answer

Answer 2kq2/r2 , up the page

(a) neutral; (b) negatively

Chapter 19: Electrostatic Forces

Assignment

Coulomb's Law and Universal Gravity (e)

-15 115 The nucleus in an iron atom has a radius of about 4.0 x 10 m and contains 26 protons. (a) What is the magnitude of the repulsive electrostatic force between two of the protons that are separated by 4.0 x 10-15 m? (b) What is the magnitude of the gravitational force between those same two protons?

Answer