Electrostatic Q&A

AssignmentChapter 18: Electrostatics

Electric Charge (a)

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

1

Answer

Rub a piece of hard plastic with wool. The plastic ischarged negatively. It will repel the negativelycharged strip of tape and attract the positively chargedone.

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

2

Answer

The glass rod was positively charged. This chargespreads over the entire metal rod, charging itpositively.

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

3

Answer

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

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

4

Answer

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

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

5

Answer

No. By conservation of charge, your hair mustbecome negatively charged.

The combined charge of all electrons in a nickel coin ishundreds of thousands of coulombs, a unit of electricalcharge. Does that imply anything about the net charge onthe coin? Explain.

6

Answer

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

List some insulators and conductors.7

Answer

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

What property makes a metal a good conductor and rubbera good insulator?

8

Answer

Metals contain free electrons; rubber has boundelectrons.

Why does a woolen sock taken from a clothes dryersometimes cling to other clothes?

9

Answer

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

If you wipe a stereo record with a clean cloth, why does therecord now attract dust?

10

Answer

Rubbing the record charges it. Neutral particles suchas dust are attracted to a charged object.

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

11

Answer

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


Electric Charge (a)

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

12

Answer

When you lose electrons, you become positivelycharged.

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

13

Answer

Use a known insulator to hold one end of the objectagainst the electroscope. Touch the other end with thecharged rod. If the electroscope indicates a charge, theobject is a conductor.

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

14

Answer

The hot gases above the flame are a plasma, whichacts as a conductor and pulls excess charges awayfrom the insulator.

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

15

Answer

The neutral spheres are initially attracted to thecharged rod and all acquire the same charge as the rodwhen they touch it. subsequently, they are repelledfrom each other and from the rod.

A rod-shaped insulator is suspended so it can rotate. Anegatively-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?

16

Answer

(a) No. Neutral objects are attracted by either charge.(b) It must be negative. Neutrals are never repelled .

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

17

Answer

The balloon becomes charged by rubbing. It isattracted to the neutral wall because it separates thecharges in the wall.

Name three methods to charge an object.18

Answer

conduction,friction,induction

Explain how to charge a conductor negatively if you haveonly a positively-charged rod.

19

Answer

Without touching the conductor, bring it close to, butnot touching, the rod. Momentarily touch the side ofthe conductor farthest from the rod. The conductorwill be charged by induction.

The text describes Coulomb's method for obtaining twocharged spheres, A and B, so that the charge on B wasexactly half the charge on A. Suggest a way Coulombcould have placed a charge on sphere B that was exactlyone third the charge on sphere A.

20

Answer

After charging spheres A and B equally, sphere B istouched to two other equally sized balls that aretouching each other. The charge on B will be dividedequally among all three balls, leaving 1/3 the totalcharge on it.


Separation of Charged Bodies (b)

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

!

21

Answer

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

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

22

Answer

(The metal ball is neutral initially. It is attractedtoward the charged bell. When it hits, it becomescharged. The ball is now repelled. It is now attractedto the uncharged bell. It hits this bell, becomesdischarged, and starts up the process again.

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

23

Answer

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

Explain what happens to the leaves of a positively-chargedelectroscope when rods with the following charges arenearby but not touching the electroscope.(a) positive(b) negative

24

Answer

(a) The leaves will move fartherapart.(b) The leaves will droop slightly.

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

25

Answer

+9.0 x 103 N

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

26

Answer

-1.1 x 108 N; the force is attractive.

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

27

Answer

+2.0 + 10-10C

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

28

Answer

-9.7 x 10-6C

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

29

Answer

1.296 N

AssignmentChapter 19: Electrostatic Forces

Coulomb's Law (c)

A negative charge of -2.0 x 10-4 C and a positive charge of8.0 x 10-4 C are separated by 0.30 m. What is the forcebetween the two charges?

30

Answer

-1.6 x 104N

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

31

Answer

3.0 x 10-6C

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?

32

Answer

83 N toward A;83 N toward B

A positive and a negative charge, each of magnitude 1.5 x10-5 C, are separated by a distance of 15 cm. Find the forceon each of the particles.

33

Answer

90 N, toward the other charge

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

34

Answer

5.6 x 102 N

A force of -4.4 x 103 N exists between a positive charge of8.0 x 10 -4 C and a negative charge of -3.0 x 10-4 C. Whatdistance separates the charges?

35

Answer

0.70 m

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

36

Answer

3.2 x 10-19C

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

coulombs)

37

Answer

20 N

A negative charge of -2.0 x 10-4 C and a positive charge of8.0 x 10-4 C are separated by 0.30 m. What is the forcebetween the two charges?

38

Answer

-15,964 N

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 betweenthe centers of the spheres. As the two spheres get closetogether, the force is smaller than expected from Coulomb'slaw. Explain.

39

Answer

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

Two identical point charges are separated by a distance of3.0 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 pointcharges is doubled?

40

Answer

1.0 x10-5 N

An electric force of 2.5 x 10-4 N acts between two smallequally-charged spheres which are 2.0 cm apart. Calculatethe force acting between the spheres if the charge on one ofthe spheres is doubled and the spheres move to a 5.0-cmseparation.

41

Answer

7.9 x 10-5 N


Variations in Coulomb's Law (d)

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

42

Answer

64 millinewtons or .064 newtons

Coulomb's law and Newton's Law of Universal Gravitationappear similar. In what ways are the electrical andgravitational forces similar? How are they different?

43

Answer

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

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

44

Answer

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

Three particles are placed on a straight line. The leftparticle has a charge of +4.6 x l0-6 C, the middle particle hasa charge of -2.3 x l0-6 C, and the right particle has a chargeof -2.3 x l0-6 C. The left particle is 12 cm from the middleparticle and the right particle is 24 cm from the middleparticle. The left particle is now moved directly above themiddle particle, still 12 cm away. Find the force on themiddle particle.

45

AnswerHard

7.2° to the left or vertical6.6 N

A positive charge of 3.0 x 10-6 C is pulled on by twonegative charges. One, -2.0 x 10-5 C, is 0.050 m to the northand the other, -4.0 x 10-6 C, is 0.030 m to the south. Whattotal force is exerted on the positive charge?

46

Answer

-9 N, North

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

47

Answer

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

Two charges, q1, and q2, are at rest near a positive testcharge, q, of 7.2 x 10-6 C. The first charge, q1, is a positivecharge 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 maway at 1250.(a) Determine the magnitude of each of the forces actingon q.(b) Sketch a force diagram.(c) Graphically determine the resultant force acting on q.

48

Answer

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

A small plastic sphere coated with a thin metalized surfacehas mass 0.05 g and carries a charge of +8 x 10-9 C. It issuspended by a light insulating thread at a point 3 cm belowthe center of a small fixed conducting sphere carrying -5 x10-9 C. The thread is cut.(a) What is the electrostatic acceleration upward?(b) What is the net or observed acceleration?

49

Answer

(a) 8.0 m/s(b) 1.8 m/s2 downward

A charge Q1 = +10 x 10-9 C on the x axis at x = 0, and asecond 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 forceon Q2.

50

Answer

13.5 x 10-9 N toward the right


The Superpositon Principal (Planar) (g)

A triangle ABC, marked out on a flat surface, has sides ofthe 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 themagnitude and direction of the net force on the charge at A?

51

Answer

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

Three charges, each of +80 x 10-6 C, are equally spacedalong 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.

52

Answer

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

Three masses, each of +80 x 106 kg, are equally spacedalong 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.

53

Answer

(a) 1.48 x 104 N(b) 0

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

54

Answer

43.1 N outward along the diagonal

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

55

Answer

3206 N

Equal charges of +8 x 10-6 C are placed at the three cornersof an equilateral triangle 2 m on a side. Calculate themagnitude and direction of the force on one of the charges.

56

Answer

.249 N away from the triangle, perpendicular to theopposite base.

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

57

Answer

2.42 x 10-6 C

Two small spheres each having a mass of 0.050 g aresuspended by silk threads from the same point. Whengiven equal charges, they separate, the threads make anangle of 10 degrees with each other. What is the force ofrepulsion acting on each sphere?

58

Answer

4.3 x 10-5 N

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

59

Answer

6.86 x 10-8 C

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

60

Answer

250 electrons

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

61

Answer

1.6 x 1020 electrons

How many electrons would be required to have a totalcharge of 1.00 C on a sphere?

62

Answer



Descriptive Electrostatics (a)

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

63

Answer

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

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

64

Answer


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

65

Answer

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

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

66

Answer

Because plastic, an insulator, does not easily conductcharge

Why is an electrostatic spray gun more efficient than anordinary spray gun?

67

Answer

More paint hits the object being painted due to anelectrical attraction between the charged droplets andthe oppositely charged object.

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

68

Answer

Felectric = -8.2 x 10-8 NFg = 3.6 x 10-49 N

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 acharge of -4.3 µC.(a) What is the magnitude of the electric force between thecorks?(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?

69

Answer

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

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

70

Answer

39.3 cm

Consider three point charges at the corners of a triangle, asshown in the figure, where q1 = 6.00 x 109 C, q2 = -2.00 x109 C, and q3 = 5.00 x 10-9 C. Find the magnitude anddirection of the resultant force on q3.

71

Answer

7.16 x 10-9 Nq = 65.20

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

72

Answer

21 N, along the negative x-axis


The Superpositon Principal (Planar) (g)

Four charged particles are placed so that each particle is atthe 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 atthe upper right corner is -6.0 µC, the charge at the lowerleft corner is -2.4 µC, and the charge at the lower rightcorner 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?

73

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

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

74

Answer

p = 0.80 m from q2.

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

75

Answer

5.07 m

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 athird charge be placed so that the net electric force on it iszero?

76

Answer

35.2 cm from q1

(24.8 cm from q2)

How are conductors different from insulators?77

Answer

Conductors transfer charge easily; insulators do not.

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

78

Answer

opposite

A negatively charged balloon has 3.5 µC of charge. Howmany excess electrons are on this balloon?

79

Answer


Which activity does not produce the same results as theother 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

80

Answer

c

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

81

Answer

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

Explain from an atomic viewpoint why charge is usuallytransferred by electrons.

82

Answer

Protons are relatively fixed in the nucleus, whereaselectrons can be transferred from one atom to another.


Descriptive Electrostatics (a)

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

83

Answer

winter, because more charge can accumulate beforeelectric discharge occurs

A balloon is negatively charged by rubbing and then clingsto a wall. Does this mean that the wall is positivelycharged?

84

Answer

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

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

85

Answer

repulsion, because attraction can be the result of aninduced surface charge, but repulsion only occurswhen two objects each have a net charge

What determines the direction of the electric force betweentwo charges?

86

Answer

the signs of the charges

In which direction will the electric force from the two equalpositive charges pull the negative charge shown in thefigure below?

87

Answer

to the left

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

88

Answer

9.73 x 10-8 N11.50 below the positive x-axis

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?

89

Answer

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

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

90

Answer

4.8 x 10-6 C

The moon (m = 7.36 x 1022 kg) is bound to Earth (m = 5.98x 1024 kg) by gravity. The moon is 3.82 x 108 m from theearth. If, instead, the force of attraction were the result ofeach having a charge of the same magnitude but opposite insign, find the quantity of charge that would have to beplaced on each to produce the required force.

91

Answer

5.72 x 1013 C


Common Vectors & Coulomb's Law (i)

Two small metallic spheres, each with a mass of 0.20 g, aresuspended as pendulums by light strings from a commonpoint. They are given the same electric charge, and the twocome 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 themagnitude of the charge on each sphere?

92

Answer

7.17 x 10-9 C

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?

93

Answer

2.0 x 10-6 C

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

94

Answer

2.25 x 10-9 N/m

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 endsof the kite.(a) Calculate the magnitude of the electric force betweenthem. (b) If the separation of charges is doubled, what absolutevalue of equal and opposite charges would exert the sameelectric force?

95

Answer

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

In 1993, a chocolate chip cookie was baked in Arcadia,California. It contained about three million chips and was10.7 m long and 8.7 m wide. Suppose four charges areplaced in the corners of that cookie as follows: q1 = -12.0nC at the lower left corner, q2 = 5.6 nC at the upper leftcorner, q3 = 2.8 nC at the upper right corner, and q4 = 8.4nC at the lower right corner.(a) Draw a picture of the rectangular cooke(b) Find the magnitude and direction of the resultantelectric force acting on q1.

96

Answer

(a) Picture(b) 1.28 x 10-8 N450 above the positive x-axis

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

97

Answer

366 mC

In more than 30 years, Albert Klein, of California, drove2.5 x 106 km in one automobile. Consider two charges, q1 =2.0 C and q2 = 6.0 C, separated by Klein's total drivingdistance. A third charge, q3 = 4.0 C, is placed on the lineconnecting q1 and q2. How far from q1 should q3 be placedfor q3 to be in equilibrium?

98

Answer

9.3 x 108 m

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

99

Answer

6.8 x 103 electrons



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

100

Answer

542

Earth's mass is about 6.0 x 1024 kg, while the moon's massis 7.3 x 1022 kg. What equal charges must be placed onEarth and the moon to make the net force between themzero?

101

Answer

5.7 x 1013 C

In 1995, a single diamond was sold for more than16 million. It was not the largest diamond in the world, butits mass was an impressive 20.0 g. Consider such adiamond resting on a horizontal surface. It is known that ifthe diamond is given a charge of 2.0 µC and a charge of atleast -8.0 µC is placed on that surface at a distance of 1.7 mfrom it, then the diamond will barely keep from sliding.Calculate the coefficient of static friction between thediamond and the surface.

102

Answer

0.25

Mycoplasma is the smallest living organism known. Itsmass has an estimated value of 1.0 x 10-16 g.(a) If two specimens of this organism are placed 1.0 mapart and one electron is placed on each, what is their initialacceleration due to the electric force?(b) If the medium through which the Allycoplasma moveexerts a resistive force on the organisms, how large mustthat force be to balance the force of electrostatic repulsion?

103

Answer

(a) 2.3 x 10-9 m/s2

(b) 2.3 x 10-28 N

The parasitic wasp Carapractus cinctus has a mass of 5.0 x10-6 kg, which makes it one of the smallest insects in theworld. If two such wasps are given equal and oppositecharges with an absolute value of 2.0 x 10-15 C and areplaced 1.00 m from each other on a horizontal smoothsurface, what extra horizontal force must be applied to eachwasp to keep it from sliding? Take into account bothgravitational and electric forces between the wasps.

104

Answer

3.77 x 10-20 N

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

105

Answer

x = 0.64 m

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

106

Answer

1.39 m

The figure shows four identical conducting spheres that areactually well separated from one another. Sphere W (withan initial charge of zero) is touched to sphere A and thenthey 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 initialcharge of +48e), and then they are separated. The finalcharge on sphere W is +18e. What was the initial charge onsphere A?

107

Answer

(a) (0.829 N)ˆi ;(b) (-0.621 N)ˆj



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

108

Answer

-5.1 m

How far apart must two protons be if the magnitude of theelectrostatic force acting on either one due to the other isequal to the magnitude of the gravitational force on a protonat Earth's surface?

109

Answer

11.9 cm

The figure shows four situations in which five chargedparticles are evenly spaced along an axis. The charge valuesare indicated except for the central particle, which has thesame charge in all four situations. Rank the situationsaccording to the magnitude of the net electrostatic force onthe central particle, greatest first.

110

Answer

3, 1, 2, 4 (zero)

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

111

Answer

2kq2/r2 , up the page

In the figure, a central particle of charge -2q is surroundedby a square array of charged particles, separated by eitherdistance d or d/2 along the perimeter of the square. Whatare the magnitude and direction of the net electrostatic forceon the central particle due to the other particles? (Hint:Consideration of symmetry can greatly reduce the amountof work required here.)

112

Answer

6kq2/d2 , leftward

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

113

Answer

a and d tie, then b and c tie

A positively charged ball is brought close to an electricallyneutral isolated conductor. The conductor is then groundedwhile the ball is kept close. Is the conductor chargedpositively, 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 groundconnection is removed?(b) Is the conductor charged positively, charged negatively,or neutral if the ground connection is first removed and thenthe ball is taken away?

114

Answer

(a) neutral;(b) negatively


Coulomb's Law and Universal Gravity (e)

The nucleus in an iron atom has a radius of about 4.0 x 10-15

m and contains 26 protons.(a) What is the magnitude of the repulsive electrostaticforce between two of the protons that are separated by 4.0 x10-15 m?(b) What is the magnitude of the gravitational forcebetween those same two protons?

115

Answer

Electrostatic Q&A

Documents

Transcript of Electrostatic Q&A