REVIEW
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Concept Summary
think! Answers
32.2
When your rubber- or plastic-soled shoes
drag across the rug, they pick up electrons
from the rug in the same way you charge
a rubber or plastic rod by rubbing it with
a cloth. You have more electrons after you
scuff your shoes, so you are negatively
charged (and the rug is positively charged).
•
•
•
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Like charges repel and opposite charges
attract.
An object that has unequal numbers
of electrons and protons is electrically
charged.
Coulomb’s law states that for charged
particles or objects that are small com-
pared with the distance between them,
the force between the charges varies
directly as the product of the charges and
inversely as the square of the distance
between them.
Electrons move easily in good conductors
and poorly in good insulators.
Electric charge can be transferred by fric-
tion and by contact.
If a charged object is brought near a con-
ducting surface, electrons will move in
the conducting surface.
Charge polarization can occur in insula-
tors that are near a charged object.
••••••
32.3.1 The small value of G indicates that gravity
       is a weak force; the large value of k indi-
       cates that the electrical force is enormous
       in comparison.
32.3.2 a. In accord with the inverse-square law,
       at twice the distance the force will be one-
       fourth as much.
       b. Since there is a force of attraction, the
       charges must be opposite in sign, so the
       charged particle is positive.
32.6
In the charging process of Figure 32.8, no
contact was made between the negative rod
and either of the spheres. In the charging
process of Figure 32.9, however, the rod
touched the sphere when it was positively
charged. A transfer of charge by contact
reduced the negative charge on the rod.
Key Terms
electrostatics (p. 644)
electrical forces
   (p. 645)
charge (p. 645)
conservation of
   charge (p. 647)
Coulomb’s law
   (p. 648)
coulomb (p. 649)
658
conductor (p. 651)
insulator (p. 651)
semiconductor
   (p. 652)
induced (p. 653)
induction (p. 653)
grounding (p. 654)
electrically
   polarized (p. 655)
658

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Section 32.1
ASSESS
ASSESS
••••••
Check Concepts
Check Concepts
1. Which force—gravitational or electrical—
   repels as well as attracts?
2. Gravitational forces depend on the prop-
   erty called mass. What comparable property
   underlies electrical forces?
3. How do protons and electrons differ in their
   electric charge?
10. a. If electrons are rubbed from cat’s fur onto
       a rubber rod, does the rod become posi-
       tively or negatively charged?
    b. How about the cat’s fur?
Section 32.3
11. a. How is Coulomb’s law similar to Newton’s
       law of gravitation?
    b. How are the two laws different?
12. The SI unit of mass is the kilogram. What is
    the SI unit of charge?
13. The proportionality constant k in Cou-
    lomb’s law is huge in ordinary units,
    whereas the proportionality constant G in
    Newton’s law of gravity is tiny. What does
    this mean in terms of the relative strengths
    of these two forces?
Section 32.4
4. Is an electron in a hydrogen atom the same
   as an electron in a uranium atom?
5. Which has more mass—a proton or an
   electron?
6. In a normal atom, how many electrons are
   there compared with protons?
7. a. How do like charges behave toward each
      other?
   b. How do unlike charges behave toward
      each other?
Section 32.2
14. a. Why are metals good conductors?
    b. Why are materials such as rubber and
       glass good insulators?
15. What is a semiconductor?
Section 32.5
16. Which two methods of charging objects
    involve touching?
8. How does a negative ion differ from a
   positive ion?
9. What does it mean to say that charge is
   conserved?
CHAPTER 32
ELECTROSTATICS
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17.
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Section 32.6
Section 32.7
ASSESS
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17. Which method of charging objects involves
    no touching?
18. What is lightning?
19. What is the function of a lightning rod?
20. What does it mean to say an object is elec-
    trically polarized?
21. When a charged object polarizes another,
    why is there an attraction between the
    objects?
22. What is an electric dipole?
Think and Rank
24. Three separate pairs of uncharged metal
    spheres are in contact. A (positively or
    negatively) charged rod is brought up to the
    same distance from each set of spheres.
    Rank the resulting charge on each sphere
    from greatest positive to greatest negative.
A B
D
E
F
Think and Rank
••••••
Rank each of the following sets of scenarios in
order of the quantity or property involved. List
them from left to right. If scenarios have equal
rankings, then separate them with an equal sign.
(e.g., AB)
23. The three pairs of metal spheres below are
    all the same size and have different charges
    on their surfaces, as indicated. The pairs of
    spheres are brought into contact with each
    other. After several moments the spheres
    are separated. Rank from greatest to least
    the total amount of charge on the pairs of
    spheres after separation.
25. Indicated below are pairs of electric charges
    in three different arrangements. In each
    figure, a test charge is located at the point
    labeled P. The other, much larger, charges all
    have the same magnitude and lie on a line
    that passes through P. Note some charges
    are positive and some are negative. Rank the
    arrangements on the basis of the strength
    of the electric force on the test charge, from
    strongest to weakest.
P
P
P
A
B
C
A
660
B
C
660

26. C, B, A
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26. Shown below are three separate pairs of
    point charges, pairs A, B, and C. Assume the
    pairs interact only with each other. Rank the
    magnitudes of the force between the pairs,
    from largest to smallest.
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Think and Explain
–
30. If electrons were positive and protons nega-
    tive, would Coulomb’s law be written the
    same or differently?
31. If you scuff electrons from your hair onto
    a comb, are you positively or negatively
    charged? How about the comb?
32. The five thousand billion billion freely mov-
    ing electrons in a penny repel one another.
    Why don’t they fly out of the penny?
33. If a glass rod that is rubbed with a plastic
    dry cleaner’s bag acquires a certain charge,
    why does the plastic bag have exactly the
    same amount of opposite charge?
34. Why do clothes often cling together after
    tumbling in a clothes dryer?
35. Why will dust be attracted to a CD wiped
    with a dry cloth?
36. When one material is rubbed against an-
    other, electrons jump readily from one to
    the other, but protons do not. Why is this?
    (Think in atomic terms.)
37. Plastic wrap becomes electrically charged
    when pulled from its container. Does the
    charged wrap stick better to glass bowls or
    metal bowls?
38. Explain how an object that is electrically
    neutral can be attracted to an object that is
    charged.
A
B
C
-4q
+3q
+2q
x
x
+2q
+3q
-2q
x/2
Think and Explain
••••••
27. Electrical forces between charges are enor-
    mous relative to gravitational forces. Yet,
    we normally don’t sense electrical forces
    between us and our environment, while we
    do sense our gravitational interaction with
    Earth. Why is this so?
28. Two equally charged particles exert equal
    forces on each other. Suppose that the
    charge on one of the particles is doubled.
    The charge on the other remains the same.
    a. How much stronger is the force between
       them?
    b. How does the force change if the charges
       of both particles are doubled?
29. How will the forces between two charged
    particles compare when one particle has ten
    times as much charge as the other? Defend
    your answer.
CHAPTER 32
ELECTROSTATICS
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39. 
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ASSESS
(continued)
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39. An electroscope is a simple device. It con-
    sists of a metal ball that is attached by a
    conductor to two fine gold leaves that are
    protected from air disturbances in a jar,
    as shown in the sketch. When the ball is
    touched by a charged object, the leaves that
    normally hang straight down spring apart.
    Why? (Electroscopes are useful not only
    as charge detectors, but also for measur-
    ing the amount of charge: the more charge
    transferred to the ball, the more the leaves
    diverge.)
42. When a car is moved into a painting cham-
    ber, a mist of paint is sprayed around it.
    When the body of the car is given a sudden
    electric charge and the mist of paint is at-
    tracted to it, presto—the car is quickly and
    uniformly painted. What does the phenom-
    enon of polarization have to do with this?
40. Would it be necessary for a charged object
    to actually touch the leaves of an electro-
    scope (see Question 39) for the leaves to
    diverge? Defend your answer.
41. Figure 32.12 shows a negatively charged
    plastic comb attracting bits of paper with
    no net charge. If the comb were positively
    charged, would it attract the same bits of
    paper? Defend your answer.
43. Imagine a proton at rest a certain distance
    from a negatively charged plate. It is released
    and collides with the plate. Then imagine
    the similar case of an electron at rest the
    same distance away from a plate of equal
    and opposite charge. In which case would
    the moving particle have the greater speed
    when the collision occurs? Why?
44. Consider a pair of particles with equal
    charges. When released, they fly apart
    from each other. Your teacher asks how the
    speeds will compare when they are ten times
    farther apart than when first released. Jess
    says that since the force on the particles
    decreases with distance, their speeds will be
    less. Marie says no, the speed of the repelled
    particles increases as long as they interact
    with each other. With whom do you agree
    or disagree, and why?
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Think and Solve
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45. A pair of isolated protons will fly apart from
    each other. The same is true for a pair of
    isolated electrons. Your teacher asks which
    has the greater initial acceleration if the
    initial distance between the particles is the
    same. Sophia says the initial accelerations
    will be equal because the forces are equal.
    Sandra says no, that the electrons will
    accelerate more—but can’t explain why.
    Both look to you for your input. What is
    your thinking?
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Think and Solve
••••••
46. The charge on an electron is 1.6 10 19 C.
    How many electrons make a charge of 1 C?
47. By how much is the electrical force between
    a pair of ions reduced when their separation
    distance is doubled? Tripled?
48. Two pellets, each with a charge of 1 mC, are
    separated by a distance of 0.30 m. Show that
    the electric force between them is 0.1 N.
49. Two identical metal spheres are brought
    together into contact. Originally one had a
    charge of 40 mC and the other a charge of
      10 mC. What is the charge on each after
    contact?
50. Consider two small charged objects, one
    with a charge of 15 mC and the other of un-
    known charge. When they are separated by
    a distance of 1.2 m, each exerts a force of
    2.8 N on the other. What is the charge of
    the second object?
51. Proportional reasoning: Consider a pair of
    electrically charged coins suspended from
    insulating threads, a certain distance from
    each other. There is a specific amount of
    electrostatic force between them.
    a. If the charge on one coin were halved,
       what would happen to the force between
       them?
    b. If the charges on both coins were dou-
       bled, what would happen to the force
       between them?
    c. If the distance between the coins were
       tripled, what would happen to the force
       between them?
    d. If the distance between them were re-
       duced to one-fourth the original distance,
       what would happen to the force between
       them?
    e. If the charge on each object were doubled
       and the distance between them were
       doubled, what would happen to the force
       between them?
52. Two spherical inflated rubber balloons each
    have the same amount of charge spread
    uniformly on their surfaces. If the repelling
    force is 2.5 N and the distance between the
    balloon centers is 0.30 m, find how much
    charge is on each balloon.
Teaching Resources
• Computer Test Bank
• Chapter and Unit Tests
More Problem-Solving Practice
Appendix F
CHAPTER 32
ELECTROSTATICS
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