THE B

IGID

EA

..........

644

ELECTROSTA

TICS

Electricity

in one

form

or another

underlies

just about everything

around you. It’s in

the lightning

from the sky; it’s in the

spark

beneath

your feet

when

you scuff

across a

rug;

and

it’s w

hat hold

s atom

s tog

ether to form m

olecules. This chapter is

about

electrostatics, or electricity at rest. Electro statics involves electric charg

es, the forces b

etween them

, and their b

ehavior in m

aterials. A

n understand

ing of electricity

requires a step

-by-step

app

roach, for one concep

t is the build

ing b

lock for the next. So p

lease study this m

aterial with extra care.

It is a good

idea at this tim

e to lean more

heavily on the laboratory p

art of your course, for d

oing p

hysics is better than only stud

ying p

hysics.

Electrostatics involves electric charges, the forces between them

, and their behavior in m

aterials.

3

How

Can an O

bject B

ecome Electrically

Charg

ed?

1.O

btain an electrophorus and rub the insulat-ing plate w

ith a piece of wool, fur, or cloth.

2.Low

er the pie pan onto the plate. 3.

Touch the pie pan with your finger. The pan

should now be charged.

4.B

ring the pan in contact with an electroscope

or hold it near a thin stream of w

ater or small

pieces of paper.

Analyze and

Conclud

e1.

Observing

What evidence do you have that

the pie pan was actually charged?

2.Predicting H

ow m

any times do you think you

can charge the pie pan without having to

once again rub the insulating plate?3.

Making G

eneralizations Based on your exper-

imentation w

ith the electrophorus, how w

ould you define electric charge?

disco

ver!

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4

ELECTR

OSTA

TICS

Ob

jectiv

es

• Describ

e the fu

nd

amen

tal rule

at the b

ase of all electrical

ph

eno

men

a. (32.1)

• Explain

ho

w an

ob

ject beco

mes

electrically charg

ed. (32.2)

• Describ

e Co

ulo

mb

’s law. (32.3)

• Distin

gu

ish b

etween

a g

oo

d co

nd

ucto

r and

a go

od

in

sulato

r. (32.4)

• Describ

e two

ways electric

charg

es can b

e transferred

. (32.5)

• Describ

e wh

at hap

pen

s wh

en a

charg

ed o

bject is p

laced n

ear a co

nd

uctin

g su

rface. (32.6)

• Describ

e wh

at hap

pen

s wh

en

an in

sulato

r is in th

e presen

ce o

f a charg

ed o

bject. (32.7)

disco

ver!M

ATE

RIA

LS electrop

ho

rus,

piece o

f wo

ol, fu

r, or clo

th,

electrosco

pe, fau

cet, pap

er

EX

PE

CTE

D OU

TCO

ME Stu

den

ts w

ill charg

e the m

etal pie

pan

of an

electrop

ho

rus b

y in

du

ction

.

AN

ALY

ZE A

ND C

ON

CLU

DE

There is an

electrical in

teraction

betw

een th

e p

an an

d th

e electrosco

pe,

water, o

r pap

er.

In th

eory, th

e charg

ing

o

f the p

ie pan

cou

ld b

e rep

eated in

defin

itely. H

ow

ever, the in

sulatin

g

plate slo

wly d

ischarg

es to

the su

rrou

nd

ing

s and

need

s to

be ch

arged

by co

ntact

perio

dically.

Electric charg

e is the so

urce

of th

e electrical force th

at cau

ses ob

jects to attract o

r rep

el each o

ther.

1.2.3.

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CH

APTER 32

ELECTRO

STATICS 645

32.1 Electrical Forces and Charges

You are familiar w

ith the force of gravity. It attracts you to Earth, and you call it your w

eight. Now

consider a force acting on you that is billions upon billions of tim

es stronger. Such a force could compress

you to a size about the thickness of a piece of paper. But suppose

that in addition to this enormous force there is a repelling force that

is also billions upon billions of times stronger than gravity. T

he two

forces acting on you would balance each other and have no notice-

able effect at all, as shown in Figure 32.1. It so happens that there is a

pair of such forces acting on you all the time—

electrical forces.

The Atom

Electrical forces arise from particles in atom

s. In the sim

ple model of the atom

proposed in the early 1900s by Ernest R

utherford and Niels B

ohr, a positively charged nucleus is sur-rounded by electrons, as illustrated in Figure 32.2. T

he protons in the nucleus attract the electrons and hold them

in orbit. Electrons are attracted to protons, but electrons repel other electrons. T

he funda-m

ental electrical property to which the m

utual attractions or repul-sions betw

een electrons or protons is attributed is called charge. 32.1

By convention (general agreem

ent), electrons are negatively charged and protons positively charged. N

eutrons have no charge, and are nei-ther attracted nor repelled by charged particles.

Here are som

e important facts about atom

s:

1. Every atom

has a positively charged nucleus surrounded by nega-tively charged electrons.

2. A

ll electrons are identical; that is, each has the same m

ass and the sam

e quantity of negative charge as every other electron.

3. T

he nucleus is composed of protons and neutrons. (T

he comm

on form

of hydrogen, which has no neutrons, is the only exception.)

All protons are identical; sim

ilarly, all neutrons are identical. A

proton has nearly 2000 times the m

ass of an electron, but its positive charge is equal in m

agnitude to the negative charge of an electron. A

neutron has slightly greater mass than a proton and

has no charge.

4. A

toms have as m

any electrons as protons, so a neutral atom has

zero net charge.

Attraction and Repulsion

Just why electrons repel electrons and

are attracted to protons is beyond the scope of this book. We sim

ply say that this electric behavior is fundam

ental, or basic. T

he fun-dam

ental rule at the base of all electrical phenomena is that like

charges repel and opposite charges attract.

FIGU

RE 32.1 !

The enormous attractive

and repulsive electri-cal forces betw

een the charges in Earth and the charges in your body balance out, leaving the relatively w

eaker force of gravity, w

hich only attracts. H

ence your w

eight is due only to gravity.

FIGU

RE 32.2 !

The helium nucleus is com

-posed of tw

o protons and tw

o neutrons. The positively charged protons attract tw

o negative electrons.

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645

32.1 Electrical Forces and ChargesK

ey

Term

selectro

statics, electrical force,

charg

e

" Teach

ing

Tip B

egin

by

com

parin

g th

e streng

th o

f the

electrical force to

gravitatio

nal

force—

the electrical fo

rce is b

illion

s of b

illion

s of tim

es stro

ng

er. Ackn

ow

ledg

e the

fun

dam

ental ru

le of electricity:

Like charg

es repel an

d u

nlike

charg

es attract. Wh

y? No

bo

dy

kno

ws. H

ence w

e say it is fu

nd

amen

tal.

Use fu

r, rub

ber, g

lass rod

s, an

d su

spen

ded

pith

balls (o

r th

eir alternatives) to

sho

w th

e effects o

f transferrin

g ch

arge,

i.e., attraction

and

repu

lsion

. D

escribe th

e transfer o

f electro

ns in

each case.

Dem

on

stratio

nD

em

on

stratio

n

The study of electricity begins with electrostatics, which is best introduced as a series of coordinated dem

onstrations. A

fter showing charging via fur, rubber rods, etc., and electrostatic attraction and repulsion (Coulom

b’s law), show (1) the electrophorus (a m

etal plate charged by induction with a sheet of acrylic glass), (2) the W

himshurst m

achine (electrostatic generator), and (3) the Van de Graaff generator. The dem

onstration sequence, 1, 2, and 3, with explanations should m

ake this a great lecture.

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646

The old saying that opposites attract, usually referring to people,

was first popularized by public lecturers w

ho traveled about by horse and w

agon to entertain people by demonstrating the scientific m

ar-vels of electricity. A

n important part of these dem

onstrations was the

charging and discharging of pith balls. Pith is a light, spongy plant tissue. B

alls of pith were coated w

ith aluminum

paint so their sur-faces w

ould conduct electricity. When suspended from

a silk thread, such a ball w

ould be attracted to a rubber rod just rubbed with cat’s

fur, but when the tw

o made contact, the force of attraction w

ould change to a force of repulsion. T

hereafter, the ball would be repelled

by the rubber rod but attracted to a glass rod that had just been rubbed w

ith silk. Figure 32.3 shows how

a pair of pith balls charged in different w

ays exhibits both attraction and repulsion forces. The

lecturer pointed out that nature provides two kinds of charge, just as

it provides two sexes.

CON

CEPT

CHECK

......What is the fund

amental rule at the b

ase of all electrical p

henomena?

32.2 Conservation of C

hargeElectrons and protons have electric charge. In a neutral atom

, there are as m

any electrons as protons, so there is no net charge. The total

positive charge balances the total negative charge exactly. If an elec-tron is rem

oved from an atom

, the atom is no longer neutral. T

he atom

has one more positive charge (proton) than negative charge

(electron) and is said to be positively charged.A

charged atom is called an ion. A

positive ion has a net positive charge; it has lost one or m

ore electrons. A negative ion has a net

negative charge; it has gained one or more extra electrons.

If you scuff electrons onto your shoes w

hile walk-

ing across a rug, are you negatively or positively charged? Answ

er: 32.2

thin

k!

Negative and positive

are just the names given

to opposite charges. The nam

es chosen could just as w

ell have been “east and w

est” or “top and dow

n” or “Mary and

Larry.”

FIGU

RE 32.3 !The fundam

ental rule of all electrical phenom

ena is that like charges repel and oppo-site charges attract.

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64

6

! Teach

ing

Tip Exp

lain w

hat

it mean

s to say an

ob

ject is electrically ch

arged

. Ch

argin

g

som

ethin

g can

be co

mp

ared to

rem

ovin

g b

ricks from

a road

an

d p

uttin

g th

em o

n a sid

ewalk:

There are exactly as m

any

“ho

les” in th

e road

as there are

bricks o

n th

e sidew

alk.

! Teach

ing

Tip Exp

lain th

at electrical effects are d

ue to

electric ch

arges, n

egative fo

r th

e electron

and

po

sitive for th

e p

roto

n. D

iscuss th

e near b

alance

that exists in

com

mo

n m

aterials, an

d th

e sligh

t imb

alance w

hen

electro

ns m

ove fro

m o

ne m

aterial to

ano

ther. Exp

lain th

at differen

t m

aterials have d

ifferent affin

ities fo

r electron

s. This exp

lains w

hy

charg

e mo

ves from

fur to

rub

ber

wh

en th

ey are rub

bed

tog

ether.

It also exp

lains w

hy it is p

ainfu

l fo

r peo

ple w

ith silver fillin

gs in

th

eir teeth to

chew

alum

inu

m

foil. Silver h

as mo

re affinity fo

r electro

ns th

an alu

min

um

. The

mild

ly acidic saliva in

the m

ou

th

facilitates a flow

of electro

ns

wh

ich, w

hen

transm

itted to

the

nerves o

f the teeth

, pro

du

ce that

familiar u

np

leasant sen

sation

.

Th

e fun

dam

ental

rule at th

e base o

f all electrical p

hen

om

ena is th

at like ch

arges rep

el and

op

po

site ch

arges attract.

Te

ac

hin

g R

es

ou

rc

es

• Reading and Study W

orkbook• Laboratory M

anual 89, 90• Presentation

EXPR

ESS

• Interactive Textbook• Conceptual Physics A

live! D

VD

s Electrostatics

CO

NCEP

TCH

ECK

......

CO

NCEP

TCH

ECK

......

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CH

APTER 32

ELECTRO

STATICS 647

Electrically Charged Objects M

atter is made of atom

s, and atom

s are made of electrons and protons (and neutrons as w

ell). A

n object that has equal numbers of electrons and protons has no

net electric charge. But if there is an im

balance in the numbers, the

object is then electrically charged. An im

balance comes about by add-

ing or removing electrons.

Although the innerm

ost electrons in an atom are bound very

tightly to the oppositely charged atomic nucleus, the outerm

ost electrons of m

any atoms are bound very loosely and can be easily

dislodged. How

much energy is required to tear an electron aw

ay from

an atom varies for different substances. T

he electrons are held m

ore firmly in rubber than in fur, for exam

ple. Hence, w

hen a rub-ber rod is rubbed by a piece of fur, as illustrated in Figure 32.4, elec-trons transfer from

the fur to the rubber rod. The rubber then has

an excess of electrons and is negatively charged. The fur, in turn, has

a deficiency of electrons and is positively charged. If you rub a glass or plastic rod w

ith silk, you’ll find that the rod becomes positively

charged. The silk has a greater affinity for electrons than the glass or

plastic rod. Electrons are rubbed off the rod and onto the silk. A

n object that has unequal numbers of electrons and pro-

tons is electrically charged. If it has more electrons than protons, the

object is negatively charged. If it has fewer electrons than protons, it

is positively charged.

Principle of Conservation of Charge T

he principle that elec-trons are neither created nor destroyed but are sim

ply transferred from

one material to another is know

n as conservation of charge. In every event, w

hether large-scale or at the atomic and nuclear level,

the principle of conservation of charge applies. No case of the cre-

ation or destruction of net electric charge has ever been found. The

conservation of charge is a cornerstone in physics, ranking with the

conservation of energy and mom

entum.

Any object that is electrically charged has an excess or deficiency

of some w

hole number of electrons—

electrons cannot be divided into fractions of electrons. T

his means that the charge of the object

is a whole-num

ber multiple of the charge of an electron. It can-

not have a charge equal to the charge of 1.5 or 1000.5 electrons, for exam

ple. 32.2 All charged objects to date have a charge that is a w

hole-num

ber multiple of the charge of a single electron.

CON

CEPT

CHECK

......What causes an ob

ject to becom

e electrically charg

ed?

Conservation of charge is another of the physics conservation principles. Recall, from

previous chapters, conservation of m

omentum

and con-servation of energy.

FIGU

RE 32.4 !W

hen electrons are trans-ferred from

the fur to the rod, the rod becom

es negatively charged.

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647

32.2 Conservation of Charge

Ke

y Te

rmco

nservatio

n o

f charg

e

" Teach

ing

Tip Po

int o

ut

that co

nservatio

n o

f charg

e is an

oth

er on

e of th

e con

servation

p

rincip

les. Briefly review

co

nservatio

n o

f mo

men

tum

and

co

nservatio

n o

f energ

y and

po

int

ou

t the sim

ilarities amo

ng

all th

ree.

A

n o

bject th

at has

un

equ

al nu

mb

ers of

electron

s and

pro

ton

s is electrically ch

arged

.

Te

ac

hin

g R

es

ou

rc

es

• Reading and Study W

orkbook• Presentation

EXPR

ESS

• Interactive Textbook

CON

CEPT

CHECK

......

CON

CEPT

CHECK

......

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648

32.3 Coulom

b’s LawR

ecall from N

ewton’s law

of gravitation that the gravitational force betw

een two objects of m

ass m1 and m

ass m2 is proportional to the

product of the masses and inversely proportional to the square of the

distance d between them

:

F�

Gm

1 m2

d2

where G

is the universal gravitational constant.

Force, Charges, and Distance T

he electrical force between

any two objects obeys a sim

ilar inverse-square relationship with

distance. The relationship am

ong electrical force, charges, and distance, now

known as C

oulomb’s law

, was discovered by the

French physicist Charles C

oulomb (1736–1806) in the eighteenth

century. C

oulomb’s law

states that for charged particles or objects that are sm

all compared w

ith the distance between them

, the force betw

een the charges varies directly as the product of the charges and inversely as the square of the distance betw

een them.

Coulom

b’s law can be expressed as

F�

kq

1 q2

d2

where d is the distance betw

een the charged particles; q1 represents

the quantity of charge of one particle and q2 the quantity of charge of

the other particle; and k is the proportionality constant.

Coulomb’s law

is like N

ewton’s law

of gravity. But unlike gravity, electric forces can be attractive or repulsive.

The Threat of Static Charge

Today electronics technicians in high-technology firm

s that build, test, and repair electronic circuit com

ponents follow procedures

to guard against static charge, to prevent dam

age to delicate circuits. Som

e circuit components

are so sensitive that they can be “fried” by static electric sparks. So electronics technicians w

ork in environm

ents free of high-resistance surfaces w

here static charge can accum

ulate and w

ear clothing of special fabric with ground w

ires betw

een their sleeves and their socks. Some w

ear

special wrist bands that are

clipped to a grounded surface, so that any charge that builds up, by m

ovement on a chair

for example, is discharged. As

electronic components becom

e sm

aller and circuit elements are

placed closer together, the threat of electric sparks producing short circuits becom

es greater and greater.

Critical Thinking What effects

on your daily life are caused by static charge? W

hat can you do to m

inimize these effects?

Scie

nce

, Tech

no

logy, a

nd

So

ciety

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8 Scie

nce

, Tech

no

logy

an

d S

ocie

ty

CR

ITICA

L THIN

KIN

G Students

should give examples of static

charge, e.g., clinging clothes, static charge experienced after w

alking across a floor and touching a doorknob, etc. Accept all reasonable responses.

32.3 Coulomb’s Law

Ke

y Te

rms

Co

ulo

mb

’s law, co

ulo

mb

Sho

w yo

ur stu

den

ts the

eno

rmo

us d

ifference in

stren

gth

betw

een th

e forces

of electricity an

d g

ravity. Use

a charg

ed co

mb

to p

ick up

co

nfetti-sized

pieces o

f pap

er. Th

en elab

orate o

n w

hat h

as h

app

ened

: The h

ug

e Earth

with

its gravitatio

nal fo

rce is p

ullin

g d

ow

n o

n th

e pieces

of p

aper. Th

e small electric

charg

e on

the co

mb

is pu

lling

u

p o

n th

e pap

er. In th

e battle

betw

een th

e hu

ge Earth

and

th

e small co

mb

, the electric

charg

e on

the co

mb

win

s! The

gravitatio

nal fo

rce is a billio

n

billio

n tim

es weaker th

an th

e electrical fo

rce. (The electrical

force also

has th

e add

ed

advan

tage o

f the sm

aller d

istance sin

ce bo

th fo

rces fo

llow

the in

verse-squ

are law.)

Dem

on

stratio

nD

em

on

stratio

n

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CH

APTER 32

ELECTRO

STATICS 649

The SI unit of charge is the coulom

b, abbreviated C. C

omm

on sense m

ight say that it is the charge of a single electron, but it isn’t. For historical reasons, it turns out that a charge of 1 C

is the charge of 6.24 billion billion (6.24 !

1018) electrons. T

his might seem

like a great num

ber of electrons, but it represents only the amount of

charge that passes through a comm

on 100-W lightbulb in about

one second.

The Electrical Proportionality Constant The proportionality

constant k in Coulom

b’s law is sim

ilar to G in N

ewton’s law

of gravi-tation. Instead of being a very sm

all number like G

, the electrical pro-portionality constant k is a very large num

ber. Rounded off, it equals

k�

9,000,000,000 N�m

2/C2

or, in scientific notation, k = 9.0 !

109 N

.m2/C

2. The units N

.m2/C

2

convert the right side of the equation to the unit of force, the new-

ton (N), w

hen the charges are in coulombs (C

) and the distance is in m

eters (m). N

ote that if a pair of charges of 1 C each w

ere 1 m

apart, the force of repulsion between the tw

o charges would be 9 bil-

lion newtons. 32.3.1 T

hat would be m

ore than 10 times the w

eight of a battleship! O

bviously, such amounts of net charge do not exist in our

everyday environment.

As can be seen in Figure 32.5, N

ewton’s law

of gravitation for m

asses is similar to C

oulomb’s law

for electric charges. 32.3.2 Whereas

the gravitational force of attraction between a pair of one-kilogram

m

asses is extremely sm

all, the electrical force between a pair of one-

coulomb charges is extrem

ely large. The greatest difference betw

een gravitation and electrical forces is that w

hile gravity only attracts, electrical forces m

ay either attract or repel.

Electrical Forces in Atom

sB

ecause most objects have alm

ost exactly equal num

bers of electrons and protons, electrical forces usually balance out. B

etween Earth and the m

oon, for example,

there is no measurable electrical force. In general, the w

eak gravita-tional force, w

hich only attracts, is the predominant force betw

een astronom

ical bodies.

For:Visit:W

eb Code: –

thin

k!

Links on Coulomb’s law

ww

w.SciLinks.org

csn

3203

What is the chief signifi-

cance of the fact that G in

New

ton’s law of gravita-

tion is a small num

ber and k in C

oulomb’s law

is a large num

ber when both

are expressed in SI units?Answ

er: 32.3.1

! FIG

URE 32.5

New

ton’s law of gravitation

is similar to C

oulomb’s law

.

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650

Although electrical forces balance out for astronom

ical and everyday objects, at the atom

ic level this is not always true. O

ften tw

o or more atom

s, when close together, share electrons. T

he nega-tive electrons of one atom

may at tim

es be closer to the neighboring atom

’s positive nucleus than they are to the average location of the neighbor’s electrons. T

hen the attractive force between these charges

is greater than the repulsive force. This is called bonding and leads to

the formation of m

olecules. It would be w

ise for anyone planning to study chem

istry or biology to know som

ething about electricity.

CON

CEPT

CHECK

......What d

oes Coulom

b’s law

state?

How

does the electrical force b

etween the p

roton and the

electron in a hydrog

en atom com

pare to the g

ravitational force b

etween these tw

o particles?

The hydrogen atom’s nucleus is a proton (m

ass 1.7 ! 10

"27 kg), out-

side of which there is a single electron (m

ass 9.1 ! 10

"31 kg) at an

average separation distance (d) of 5.3 !

10"

11 m.

To solve for the electrical force, use Coulom

b’s law, w

here both the electron charge q

e and the proton charge qp

have the same m

agni-tude

(1.6!

10"

19 C).

Fe

?9.0�

109 N

�m2/C

2�8.2

� 10

�8 N

?1.6�

10�

19C� 2

?5.3�

10�

11m� 2

qe q

p

d2

� k

��

The gravitational force Fg betw

een them is F

g

me m

p

d2

�G

?6.7�

10�

11 N�m

2/kg2�

?9.1�

10�

31kg�?1.7�

10�

27kg�?5.3

�10

�11m

� 2�

3.7�

10�

47 N�

A com

parison of the two forces is best show

n by their ratio:

2.2�

1039

8.2�

10�

8N3.7

�10

�47N

Fe

Fg

��

The electrical force between the particles is m

ore than 1039 tim

es greater than the gravitational force. In other w

ords, the electric forces that sub-atom

ic particles exert on one another are so much stronger than their

mutual gravitational forces that gravitation can be com

pletely neglected.

do

the

ma

th!

thin

k!

a. If an electron at a certain distance from

a charged particle is attracted w

ith a certain force, how

will the force

compare at tw

ice this distance?b. Is the charged particle in this case positive or negative?Answ

er: 32.3.2

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0

! Teach

ing

Tip Exp

lain th

at w

hen

a po

sitive and

a neg

ative ch

arge are u

sed in

Co

ulo

mb

’s law

, the an

swer w

ill be

neg

ative, wh

ich m

eans a fo

rce o

f attraction

. Wh

en th

e charg

es are eith

er bo

th n

egative o

r bo

th

po

sitive, the an

swer w

ill be

po

sitive, wh

ich m

eans a fo

rce of

repu

lsion

.

C

ou

lom

b’s law

states th

at for ch

arged

p

articles or o

bjects th

at are small

com

pared

with

the d

istance

betw

een th

em, th

e force

betw

een th

e charg

es varies d

irectly as the p

rod

uct o

f the

charg

es and

inversely as th

e sq

uare o

f the d

istance b

etween

th

em.

Te

ac

hin

g R

es

ou

rc

es

• Reading and Study W

orkbook• Concept-D

evelopment

Practice Book 32-1• Problem

-Solving Exercises in Physics 16-1

• PresentationEX

PRESS

• Interactive Textbook• N

ext-Time Q

uestion 32-1

CO

NCEP

TCH

ECK

......

CO

NCEP

TCH

ECK

......

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CH

APTER 32

ELECTRO

STATICS 651

32.4 Conductors and Insulators

Electrons are more easily m

oved in some m

aterials than in others. O

uter electrons of the atoms in a m

etal are not anchored to the nuclei of particular atom

s, but are free to roam in the

material. M

aterials through which electric charge can flow

are called

conductors. Metals are good conductors for the m

otion of electric charges for the sam

e reason they are good conductors of heat: T

heir electrons are “loose.”Electrons in other m

aterials—rubber and glass, for exam

ple—are

tightly bound and remain w

ith particular atoms. T

hey are not free to w

ander about to other atoms in the m

aterial. These m

aterials, known

as insulators, are poor conductors of electricity, for the sam

e reason they are generally poor conductors of heat.

Whether a substance is classified as a conductor or an insulator

depends on how tightly the atom

s of the substance hold their elec-trons.

Electrons move easily in good conductors and poorly in

good insulators. All substances can be arranged in order of their abil-

ity to conduct electric charges. Those at the top of the list are the con-

ductors, and those at the bottom are the insulators. T

he ends of the list are very far apart. T

he conductivity of a metal, for exam

ple, can be m

ore than a million trillion tim

es greater than the conductivity of an insulator such as glass. In pow

er lines, such as those shown in Figure

32.6, charge flows m

uch more easily through hundreds of kilom

eters of m

etal wire than through the few

centimeters of insulating m

ate-rial that separates the w

ire from the supporting tow

er. In a comm

on appliance cord, charges w

ill flow through several m

eters of wire to

the appliance, and then through its electrical network, and then back

through the return wire rather than flow

directly across from one w

ire to the other through the tiny thickness of rubber insulation.

For:

–Visit:W

eb Code:

Links on conductorsand insulators w

ww.SciLinks.org

csn 3204

! FIG

URE 32.6

It is easier for electric charge to flow

through hundreds of kilom

eters of m

etal wire than through

a few centim

eters of insulating m

aterial.

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651

32.4 Conductors and Insulators

Ke

y Te

rms

con

du

ctor, in

sulato

r, sem

icon

du

ctor

Co

mm

on

Misco

ncep

tion

Lightning never strikes the same

place twice.

FAC

T Ligh

tnin

g d

oes favo

r certain

spo

ts, main

ly hig

h lo

cation

s. The

Emp

ire State Bu

ildin

g is stru

ck by

ligh

tnin

g ab

ou

t 25 times every

year.

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652

Some m

aterials, such as germanium

and silicon, are good insu-lators in their pure crystalline form

but increase tremendously in

conductivity when even one atom

in ten million is replaced w

ith an im

purity that adds or removes an electron from

the crystal structure. Sem

iconductors are materials that can be m

ade to behave som

etimes as insulators and som

etimes as conductors. A

toms in a

semiconductor hold their electrons until given sm

all energy boosts. T

his occurs in photovoltaic cells that convert solar energy into elec-trical energy. T

hin layers of semiconducting m

aterials sandwiched

together make up transistors, w

hich are used in digital media players,

computers, and a variety of electrical applications. Transitors am

plify electric signals and act as electric sw

itches to control current in cir-cuits—

with very little pow

er.

CON

CEPT

CHECK

......What is the d

ifference betw

een a good

conductor

and a g

ood insulator?

32.5 Charging by Friction and C

ontactTw

o ways electric charge can be transferred are by friction and

by contact. We are all fam

iliar with the electrical effects produced by

friction. We can stroke a cat’s fur and hear the crackle of sparks that

are produced, or comb our hair in front of a m

irror in a dark room

and see as well as hear the sparks of electricity. W

e can scuff our shoes across a rug and feel the tingle as w

e reach for the doorknob, or do the sam

e when sliding across seats w

hile parked in an automo-

bile, as illustrated in Figure 32.7. In all these cases electrons are being transferred by friction w

hen one material rubs against another.

Electrons can also be transferred from one m

aterial to another by sim

ply touching. When a charged rod is placed in contact w

ith a neutral object, som

e charge will transfer to the neutral object. T

his m

ethod of charging is simply called charging by contact. If the object

is a good conductor, the charge will spread to all parts of its surface

because the like charges repel each other. If it is a poor conductor, the extra charge w

ill stay close to where the object w

as touched.

CON

CEPT

CHECK

......What are tw

o ways electric charg

e can be

transferred?

Materials that don’t hold

electrons tightly lose them

to materials that hold

electrons more tightly.

FIGU

RE 32.7 !

If you slide across a seat in an autom

obile you are in danger of being charged by friction.

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2

Electro

ns m

ove easily

in g

oo

d co

nd

ucto

rs an

d p

oo

rly in g

oo

d in

sulato

rs.

Te

ac

hin

g R

es

ou

rc

es

• Next-Tim

e Question 32-2

32.5 Charging by Friction and Contact

Co

mm

on

Misco

ncep

tion

Friction is a necessary factor in charging an object.

FAC

T Electron

s can b

e transferred

fro

m o

ne m

aterial to an

oth

er sim

ply b

y tou

chin

g.

" Teach

ing

Tip C

harg

e sep

aration

can also

occu

r with

ou

t frictio

n b

y the sim

ple co

ntact

betw

een d

issimilar in

sulatin

g

materials. In

this case ch

arge

simp

ly peels fro

m o

ne m

aterial to

ano

ther, like d

ust is p

eeled fro

m

a surface w

hen

a piece o

f sticky tap

e is pu

lled fro

m it.

In a co

mp

letely darken

ed

roo

m, q

uickly p

ull th

e tape

off a ro

ll of electrician

’s tape.

Yo

ur stu

den

ts sho

uld

see sp

arks!

Tw

o w

ays electric ch

arge can

be

transferred

are by frictio

n an

d b

y co

ntact.

Te

ac

hin

g R

es

ou

rc

es

• Reading and Study W

orkbook• Presentation

EXPR

ESS

• Interactive Textbook

CO

NCEP

TCH

ECK

......

CO

NCEP

TCH

ECK

......

Dem

on

stratio

nD

em

on

stratio

n

CO

NCEP

TCH

ECK

......

CO

NCEP

TCH

ECK

......

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CH

APTER 32

ELECTRO

STATICS 653

32.6 Charging by Induction

If a charged object is brought near a conducting surface, even w

ithout physical contact, electrons will m

ove in the conducting surface. In Figure 32.8a, the uncharged insulated m

etal spheres touch each other, so in effect they form

a single noncharged conductor. In Figure 32.8b, a negatively charged rod is held near sphere A

. Electrons in the m

etal are repelled by the rod, and excess negative charge has m

oved onto sphere B, leaving sphere A

with excess positive charge.

The charge on the tw

o spheres has been redistributed, or induced. In Figure 32.8c, the spheres are separated w

hile the rod is still pres-ent. In Figure 32.8d, the rod has been rem

oved, and the spheres are charged equally and oppositely. T

hey have been charged by induction, w

hich is the charging of an object without direct contact. Since the

charged rod never touched them, it retains its initial charge.

A single sphere can be charged sim

ilarly by induction. Consider

a metal sphere that hangs from

a nonconducting string. In Figure 32.9a, the net charge on the m

etal sphere is zero. In Figure 32.9b, a charge redistribution is induced by the presence of the charged rod. T

he net charge on the sphere is still zero. In Figure 32.9c, touching the sphere rem

oves electrons by contact. In Figure 32.9d, the sphere is left positively charged. In Figure 32.9e, the sphere is attracted to the negative rod; it sw

ings over to it and touches it. Now

electrons m

ove onto the sphere from the rod. T

he sphere has been negatively charged by contact. In Figure 32.9f, the negative sphere is repelled by the negative rod.

FIGU

RE 32.8 !C

harging by induction can be illustrated using tw

o insulated m

etal spheres.

FIGU

RE 32.9 "C

harge induction by grounding can be illus-trated using a m

etal sphere hanging from

a nonconducting string.

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32.6 Charging by Induction

Ke

y Te

rms

ind

uced

, ind

uctio

n, g

rou

nd

ing

Ask W

hy is the charge distribution in Figure 32.8d not uniform

? The ch

arges are clo

ser to

geth

er in facin

g h

alves of

the co

nd

uctin

g sp

here d

ue to

in

du

ction

. If the sp

heres w

ere m

uch

farther ap

art and

ind

uctio

n

betw

een th

em w

ere neg

ligib

le, th

e charg

e distrib

utio

n o

n each

w

ou

ld b

e un

iform

.

Ch

arge an

electrop

ho

rus,

place an

insu

lated m

etal d

isk on

top

of it, an

d sh

ow

th

at the d

isk is no

t charg

ed

wh

en rem

oved

and

bro

ug

ht

near a ch

arged

pith

ball.

The in

sulatin

g su

rface of th

e electro

ph

oru

s has m

ore g

rab

on

the electro

ns th

an th

e m

etal plate. R

est the p

late on

th

e electrop

ho

rus ag

ain an

d

tou

ch th

e top

of th

e plate.

This g

rou

nd

s it. No

w b

ring

th

e plate n

ear the p

ith b

all an

d sh

ow

that it is ch

arged

b

y no

ting

the flash

of lig

ht

pro

du

ced w

hen

the ch

arged

m

etal plate is to

uch

ed to

th

e end

of a g

as d

ischarg

e tu

be o

r a flu

orescen

t lamp

.

Dem

on

stratio

nD

em

on

stratio

n

Notice that one idea is related

to the next in this sequence—very im

portant, as the ideas of electricity are usually difficult to grasp the first tim

e through. Be sure to take care in m

oving through this sequence of dem

onstrations and their explanations.

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654

When w

e touch the metal surface w

ith a finger, as illustrated in Figure 32.9c, charges that repel each other have a conducting path to a practically infinite reservoir for electric charge—

the ground. When

we allow

charges to move off (or onto) a conductor by touching it, it

is comm

on to say that we are grounding it. C

hapter 34 returns to this idea of grounding in the discussion of electric currents.

Charging by induction occurs during thunderstorm

s. The nega-

tively charged bottoms of clouds induce a positive charge on the

surface of Earth below, as seen in Figure 32.10. B

enjamin Franklin

was the first to dem

onstrate this in his famous kite-flying experim

ent, in w

hich he proved that lightning is an electrical phenomenon. 32.6

Most lightning is an electrical discharge betw

een oppositely charged parts of clouds. T

he kind of lightning we are m

ost familiar w

ith is the electrical discharge betw

een the clouds and the oppositely charged ground below

.

Franklin also found that charge flows readily to or from

sharp points, and fashioned the first lightning rod. If the rod is placed above a building connected to the ground, the point of the rod col-lects electrons from

the air, preventing a large buildup of positive charge on the building by induction. T

his continual “leaking” of charge prevents a charge buildup that m

ight otherwise lead to a

sudden discharge between the cloud and the building. T

he primary

purpose of the lightning rod, then, is to prevent a lightning discharge from

occurring. If for any reason sufficient charge does not leak from

the air to the rod, and lightning strikes anyway, it m

ay be attracted to the rod and short-circuited to the ground, sparing the building.

CON

CEPT

CHECK

......What hap

pens w

hen a charged

object is p

laced

near a conducting

surface?

Why does the negative

rod in Figure 32.8 have the sam

e charge before and after the spheres are charged, but not w

hen charging takes place as in Figure 32.9?Answ

er: 32.6

thin

k!

FIGU

RE 32.10 !The bottom

of the negatively charged cloud induces a positive charge at the surface of the ground below

.

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4

Explain

the sim

ilarity of

a Wh

imsh

urst m

achin

e (electro

static gen

erator) to

a ro

tating

electrop

ho

rus. Sh

ow

sp

arks jum

pin

g b

etween

th

e sph

eres of th

e mach

ine

and

so fo

rth, an

d d

iscuss th

e sizes (rad

ii of cu

rvature) o

f th

e sph

eres in term

s of th

eir cap

acity for sto

ring

charg

e. (Th

e amo

un

t of ch

arge

that can

be sto

red b

efore

disch

arge

into

the air

is directly

pro

po

rtion

al to

the rad

ius

of th

e sph

ere.)

" Teach

ing

Tip D

iscuss th

e lig

htn

ing

rod

as a preven

ter o

f ligh

ting

wh

ile sho

win

g

the sim

ilar fun

ction

of th

e m

etal po

ints attach

ed to

the

Wh

imsh

urst m

achin

e.

Wh

en sh

ow

ing

the lo

ng

sparks

that ju

mp

from

the d

om

e of

the V

an d

e Graaff g

enerato

r to

the sm

aller gro

un

ded

sp

here, h

old

a ligh

tnin

g ro

d

(any sh

arp p

oin

ted co

nd

ucto

r) in

the vicin

ity of th

e do

me an

d

the sp

arking

will sto

p. B

ring

th

e ligh

tnin

g ro

d farth

er away

and

the freq

uen

t sparkin

g w

ill resu

me. Set a cu

p o

f pu

ffed

rice or p

uffed

wh

eat on

top

of

the V

an d

e Graaff g

enerato

r. Y

ou

r stud

ents w

ill like the

fou

ntain

that resu

lts wh

en yo

u

charg

e it. Or,

place a stack

of alu

min

um

pie

plates o

n th

e do

me

and

watch

them

levitate and

fly aw

ay on

e by o

ne.

Dem

on

stratio

nD

em

on

stratio

n

Dem

on

stratio

nD

em

on

stratio

n

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CH

APTER 32

ELECTRO

STATICS 655

32.7 Charge Polarization

Charging by induction is not restricted to conductors.

Charge

polarization can occur in insulators that are near a charged object. W

hen a charged rod is brought near an insulator, there areno free electrons to m

igrate throughout the insulating material.

Instead, as shown in Figure 32.11a, there is a rearrangem

ent of the positions of charges w

ithin the atoms and m

olecules themselves.

One side of the atom

or molecule is induced to be slightly m

ore positive (or negative) than the opposite side, and the atom

or mol-

ecule is said to be electrically polarized. If the charged rod is nega-tive, say, then the positive side of the atom

or molecule is tow

ard the rod, and the negative side of the atom

or molecule is aw

ay from it. T

he atom

s or molecules near the surface all becom

e aligned this way, as

seen in Figure 32.11b.

Is the Water That C

omes O

ut of Your Faucet Charg

ed?

1.C

harge a comb by running it through your hair. This w

ill work

especially well if the w

eather is dry.2.

Now

bring the comb near som

e tiny bits of paper. Explain your observations.

3.N

ext, place the charged comb near a thin stream

of water from

the faucet.

4.Is there an electrical interaction betw

een the comb and

the stream?

5.Think

Does this m

ean the stream of w

ater is charged? Why

or why not?

disco

ver!

FIGU

RE 32.11 !a. W

hen an external negative charge is brought closer from the

left, the charges within a neutral atom

or molecule rearrange.

b. All the atom

s or molecules near the surface of the insulator

become electrically polarized.

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655

disco

ver!M

ATE

RIA

LS com

b, p

aper,

faucet

EX

PE

CTE

D OU

TCO

ME Stu

den

ts w

ill ob

serve an electrical

interactio

n b

etween

the co

mb

an

d th

e stream o

f water.

THIN

K The stream

of w

ater h

as a net ch

arge o

f zero b

ut

the ch

arges are rearran

ged

an

d th

e stream b

ecom

es electrically p

olarized

.

If a ch

arged

ob

ject is b

rou

gh

t near a

con

du

cting

surface, even

with

ou

t p

hysical co

ntact, electro

ns w

ill m

ove in

the co

nd

uctin

g su

rface.

Te

ac

hin

g R

es

ou

rc

es

• Reading and Study W

orkbook• Concept-D

evelopment

Practice Book 32-2• Transparencies 76, 77• Presentation

EXPR

ESS

• Interactive Textbook

32.7 Charge Polarization

Ke

y Te

rmelectrically p

olarized

" Teach

ing

Tip D

efine

po

larization

by exp

lainin

g

Figu

res 32.11 thro

ug

h 32.14

in th

e text. Sho

w th

e effect of

po

larization

wh

en a ch

arged

b

alloo

n sticks to

a wall.

CON

CEPT

CHECK

......

CON

CEPT

CHECK

......

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656

Exam

ples of Charge Polarization T

his explains why elec-

trically neutral bits of paper are attracted to a charged object, such as the com

b shown in Figure 32.12. M

olecules are polarized in the paper, w

ith the oppositely charged sides of molecules closest to the

charged object. Closeness w

ins, and the bits of paper experience a net attraction. Som

etimes they w

ill cling to the charged object and sud-denly fly off. T

his indicates that charging by contact has occurred; the paper bits have acquired the sam

e sign of charge as the charged object and are then repelled.

Rub an inflated balloon on your hair and it becom

es charged. Place the balloon against the w

all and it sticks. As show

n in Figure 32.13, the charge on the balloon induces an opposite surface charge on the w

all. Closeness w

ins, for the charge on the balloon is slightly closer to the opposite induced charge than to the charge of the sam

e sign.

Electric Dipoles M

any molecules—

H2 O

, for example—

are elec-trically polarized in their norm

al states. The distribution of electric

charge is not perfectly even. As illustrated in Figure 32.14, there is a

little more negative charge on one side of the m

olecule than on the other. Such m

olecules are said to be electric dipoles.

+

––

+

FIGU

RE 32.14 !A

n H2 O

molecule is an

electric dipole.

FIGU

RE 32.13 "The negatively charged bal-loon polarizes m

olecules in the w

ooden wall and cre-

ates a positively charged surface, so the balloon sticks to the w

all.

FIGU

RE 32.12 !A

charged comb attracts an uncharged piece of paper

because the force of attraction for the closer charge is greater than the force of repulsion for the farther charge.

If you rub a balloon on your hair, you w

ill find that the balloon w

ill stick to a w

all.

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6

Sho

w th

e effects of electrical

force an

d ch

argin

g b

y in

du

ction

by h

old

ing

a ch

arged

rod

near th

e end

s of a

wo

od

en 2 3

4. The 2 3

4 mu

st b

e mo

re than

a meter lo

ng

, an

d it m

ust b

alance an

d ro

tate easily sid

eways at its m

idp

oin

t o

n a p

rotru

sion

such

as the

bo

ttom

of a m

etal spo

on

. Yo

u

can easily set th

e massive p

iece o

f wo

od

in m

otio

n. Th

is is q

uite im

pressive!

" Teach

ing

Tip Th

e dem

o w

ith

the 2 3

4 piece o

f wo

od

is an

examp

le of ch

arge p

olarizatio

n.

Wh

en th

e charg

es are free to

mo

ve we h

ave ind

uctio

n; w

hen

th

ey’re on

ly free to rep

ositio

n

in fixed

atom

s, we h

ave charg

e p

olarizatio

n.

Ru

b a b

alloo

n o

n yo

ur h

air an

d sh

ow

that it sticks to

the

wall. Sketch

Figu

re 32.13 on

th

e bo

ard an

d sh

ow

that th

e attractin

g ch

arges are slig

htly

closer th

an th

e repellin

g

charg

es. Clo

seness w

ins an

d

the b

alloo

n sticks to

the w

all!

Dem

on

stratio

nD

em

on

stratio

n

Dem

on

stratio

nD

em

on

stratio

n

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CH

APTER 32

ELECTRO

STATICS 657

In summ

ary, objects are electrically charged in three ways.

1. B

y friction, when electrons are transferred by friction from

one object to another.

2. B

y contact, when electrons are transferred from

one object to another by direct contact w

ithout rubbing. A charged rod placed

in contact with an uncharged piece of m

etal, for example, w

ill transfer charge to the m

etal.

3. B

y induction, when electrons are caused to gather or disperse by

the presence of nearby charge (even without physical contact).

A charged rod held near a m

etal surface, for example, repels

charges of the same sign as those on the rod and attracts oppo-

site charges. The result is a redistribution of charge on the object

without any change in its net charge. If the m

etal surface is dis-charged by contact, w

ith a finger for example, then a net charge

will be left.

Ifthe object is an insulator, on the other hand, then a realignment

of charge rather than a migration of charge occurs. T

his is charge polarization, in w

hich the surface near the charged object becomes

oppositely charged. This occurs w

hen you stick a charged balloon to a w

all.

CON

CEPT

CHECK

......What hap

pens w

hen an insulator is in the presence

of a charged

object?

Microw

ave Cooking

Imagine an enclosure filled w

ith table-tennis balls am

ong a few batons, all at rest. N

ow im

agine the batons suddenly flipping back and forth like sem

i-rotating propellers, striking neighboring table-tennis balls. Alm

ost imm

ediately most table-tennis

balls are energized, vibrating in all directions. A m

icrowave oven w

orks similarly. The batons are

water m

olecules that flip back and forth in rhythm

with m

icrowaves in the enclosure. The table-tennis

balls are nonwater m

olecules that make up the

bulk of material being cooked.

H2 O

molecules are polar, w

ith opposite charges on opposite sides. W

hen an electric field is imposed

on them, they align w

ith the field like a compass

aligns with a m

agnetic field. Microw

aves are an electric field that oscillates, so H

2 O m

olecules oscillate also—

and quite energetically. Food is cooked by a sort of “kinetic friction” as flip-flopping H

2 O m

olecules increase the thermal

motion of surrounding food m

olecules.

A microw

ave oven wouldn’t w

ork without the

presence of the electric dipoles in the food (usually, but not alw

ays, water). That’s w

hy microw

aves pass through foam

, paper, or ceramic plates w

ith no effect. M

icrowaves also reflect and bounce

off conductors with no effect. They do, how

ever, energize w

ater molecules.

Ph

ysics in

the K

itchen

Be glad that water

is an electric dipole. If its opposite ends didn’t attract different ions, alm

ost all the chem

istry that occurs in aqueous solutions w

ould be impossible.

Three cheers for the electric dipole nature of the w

ater molecule!

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657

Place a charg

ed ro

d n

ear a th

in stream

of fallin

g w

ater. Th

e stream w

ill be attracted

to

the ro

d d

ue to

the d

ipo

le n

ature o

f water m

olecu

les—th

ey are po

sitive on

the

hyd

rog

en sid

e and

neg

ative o

n th

e oxyg

en sid

e. The w

ater m

olecu

les align

alon

g th

e electric field

of th

e charg

ed

rod

, regard

less of its ch

arge.

Dem

on

stratio

nD

em

on

stratio

n

Conclude the chapter by going back to the Van de Graaff generator. Introduce the idea of electric field—

that space near the generator dom

e is altered, as you can dem

onstrate by snuffing out a m

atch held near the charged dom

e. This will be the focus of the next chapter.

C

harg

e po

larization

can o

ccur in

in

sulato

rs that are n

ear a charg

ed

ob

ject.

Te

ac

hin

g R

es

ou

rc

es

• Reading and Study W

orkbook• Presentation

EXPR

ESS

• Interactive Textbook• N

ext-Time Q

uestion 32-3

CON

CEPT

CHECK

......

CON

CEPT

CHECK

......

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658

3REV

IEW

Conce

pt Su

mm

ary

•••

••

•

•

Like charges repel and opposite charges attract.

•

An object that has unequal num

bers of electrons and protons is electrically charged.

•

Coulom

b’s law states that for charged

particles or objects that are small com

-pared w

ith the distance between them

, the force betw

een the charges varies directly as the product of the charges and inversely as the square of the distance betw

een 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 w

ill move in

the conducting surface.

•

Charge polarization can occur in insula-

tors that are near a charged object.

Key Te

rms

•••

••

•

electrostatics (p. 644)

electrical forces(p. 645)

charge (p. 645)

conservation of charge (p. 647)

Coulom

b’s law(p. 648)

coulomb (p. 649)

conductor (p. 651)

insulator (p. 651)

semiconductor

(p. 652)

induced (p. 653)

induction (p. 653)

grounding (p. 654)

electrically polarized (p. 655)

32.2 W

hen your rubber- or plastic-soled shoes drag across the rug, they pick up electrons from

the rug in the same w

ay you charge a rubber or plastic rod by rubbing it w

ith a cloth. You have m

ore electrons after you scuff your shoes, so you are negatively charged (and the rug is positively charged).

32.3.1 T

he small value of G

indicates that gravity is a w

eak force; the large value of k indi-cates that the electrical force is enorm

ous in com

parison.

32.3.2a. In accord w

ith the inverse-square law,

at twice the distance the force w

ill be one-fourth as m

uch. b. Since there is a force of attraction, the charges m

ust be opposite in sign, so the charged particle is positive.

32.6 In the charging process of Figure 32.8, no contact w

as made betw

een the negative rod and either of the spheres. In the charging process of Figure 32.9, how

ever, the rod touched the sphere w

hen it was positively

charged. A transfer of charge by contact

reduced the negative charge on the rod.

thin

k!

Answ

ers

For:Visit:W

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Self-Assessment

PHSchool.com

csa 3200

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8

R

EVIEW

Te

ac

hin

g R

es

ou

rc

es

• TeacherEXPR

ESS

• Virtual Physics Lab 29

• Conceptual Physics Alive!

DV

Ds Electro

statics

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SSESS

CH

APTER 32

ELECTRO

STATICS 659

Check

Conce

pts

•••

••

•

Section 32.1 1. W

hich force—gravitational or electrical—

repels as well as attracts?

2. Gravitational forces depend on the prop-

erty called mass. W

hat comparable property

underlies electrical forces?

3. How

do protons and electrons differ in their electric charge?

4. Is an electron in a hydrogen atom the sam

e as an electron in a uranium

atom?

5. Which has m

ore mass—

a proton or an electron?

6. In a normal atom

, how m

any electrons are there com

pared with protons?

7. a. How

do like charges behave toward each

other?

b. How

do unlike charges behave toward

each other?

Section 32.2 8. H

ow does a negative ion differ from

a positive ion?

9. What does it m

ean to say that charge is conserved?

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. H

ow is C

oulomb’s law

similar to N

ewton’s

law of gravitation?

b. H

ow are the tw

o laws different?

12. The SI unit of m

ass is the kilogram. W

hat is the SI unit of charge?

13. The proportionality constant k in C

ou-lom

b’s law is huge in ordinary units,

whereas the proportionality constant G

in N

ewton’s law

of gravity is tiny. What does

this mean in term

s of the relative strengths of these tw

o forces?

Section 32.4 14. a. W

hy are metals good conductors?

b. W

hy are materials such as rubber and

glass good insulators?

15. What is a sem

iconductor?

Section 32.5 16. W

hich two m

ethods of charging objects involve touching?

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659

A

SSESS

Check

Conce

pts

1. Electrical; gravitational force

only attracts.

2. Charge

3. Sam

e magnitude, but

opposite charge

4. Y

es, all electrons are identical.

5. Proton—

more than 1800

times greater than the

electron

6. Sam

e number, no net charge

7. a. Repel each other

b. Attract each other

8. A

negative ion has extra electron(s); a positive ion has lost electron(s).

9. It is neither created nor

destroyed, only transferred.

10. a. Negatively

b. Positively 11. a. Both are inverse-square

laws.

b. One depends on m

ass, and one depends on charge; Coulom

b’s law com

prises both attractive and repulsive forces.

12. Coulomb

13. Electrical force is relatively m

uch greater.

14. a. Free electrons

b. Bound electrons

15. Material that can behave

as either an insulator or a conductor

16. Contact and friction

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SSESSA

SSESS(continued)

660

3Section 32.6 17. W

hich method of charging objects involves

no touching?

18. What is lightning?

19. What is the function of a lightning rod?

Section 32.7 20. W

hat does it mean to say an object is elec-

trically polarized?

21. When a charged object polarizes another,

why is there an attraction betw

een the objects?

22. What is an electric dipole?

Thin

k a

nd R

ank •

••

••

•

Rank each of the follow

ing 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 w

ith an equal sign. (e.g., A

! B

)

23. The three pairs of m

etal 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 m

oments the spheres

are separated. Rank from

greatest to least the total am

ount of charge on the pairs of spheres after separation.

24. Three separate pairs of uncharged m

etal spheres are in contact. A

(positively or negatively) charged rod is brought up to the sam

e distance from each set of spheres.

Rank the resulting charge on each sphere

from greatest positive to greatest negative.

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. T

he other, much larger, charges all

have the same m

agnitude and lie on a line that passes through P. N

ote some charges

are positive and some are negative. R

ank the arrangem

ents on the basis of the strength of the electric force on the test charge, from

strongest to w

eakest.

AB

C

AB

C

PP

P

AB

DEF

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0

17. Induction 18. Electrical discharge from

cloud to cloud or to ground

19. To prevent discharge and to

conduct charge to ground

20. Negative on one side, positive

on the other

21. The oppositely charged side is a little closer.

22. A m

olecule in which the

distribution of charge is uneven

Thin

k a

nd R

ank

23. A, C, B

24. B 5 E, C 5

D, A

5 F

25. C, B, A

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APTER 32

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STATICS 661

CH

APTER 32

ELECTRO

STATICS 661

26. Shown below

are three separate pairs of point charges, pairs A

, B, and C

. Assum

e the pairs interact only w

ith each other. Rank the

magnitudes of the force betw

een the pairs, from

largest to smallest.

Thin

k a

nd Ex

pla

in •

•••

••

27. Electrical forces between charges are enor-

mous relative to gravitational forces. Yet,

we norm

ally don’t sense electrical forces betw

een us and our environment, w

hile 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. T

he charge on the other remains the sam

e.

a. How

much stronger is the force betw

een them

?

b. How

does the force change if the charges of both particles are doubled?

29. How

will the forces betw

een two charged

particles compare w

hen one particle has ten tim

es as much charge as the other? D

efend your answ

er.

30. If electrons were positive and protons nega-

tive, would C

oulomb’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 m

ov-ing electrons in a penny repel one another. W

hy 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, w

hy does the plastic bag have exactly the sam

e amount of opposite charge?

34. Why do clothes often cling together after

tumbling in a clothes dryer?

35. Why w

ill dust be attracted to a CD

wiped

with a dry cloth?

36. When one m

aterial is rubbed against an-other, electrons jum

p readily from one to

the other, but protons do not. Why is this?

(Think in atom

ic terms.)

37. Plastic wrap becom

es electrically charged w

hen pulled from its container. D

oes the charged w

rap stick better to glass bowls or

metal bow

ls?

38. Explain how an object that is electrically

neutral can be attracted to an object that is charged.

-4q+2q

+3q+3q

+2q-2q

xxx/2

ABC

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661

26. C, B, A

Thin

k a

nd Ex

pla

in 27. Charges can cancel, w

hile m

asses cannot. 28. a. D

oubling the charge on one of the particles produces tw

ice the force.

b. Doubling the charge on

both particles produces 4 tim

es the force. 29. The forces w

ill be equal in m

agnitude in accord with

New

ton’s third law.

30. The same; Coulom

b’s law

does not distinguish between

positive and negative charges. 31. Positive; negative 32. The electrons are attracted to

the same num

ber of protons in the penny.

33. Charge is transferred. No

net charge is ever created or destroyed.

34. Static charge is built up by rubbing.

35. Static charge is built up by rubbing.

36. Protons are locked into the nuclei of atom

s but electrons are not.

37. Plastic wrap sticks better

to the non-conducting glass. It sticks poorly to the conducting m

etal. 38. The side having the opposite

sign of charge is closer to the charged object. The attraction betw

een the opposite charges is greater than the repulsion betw

een the like charges.

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SSESSA

SSESS(continued)

662

3 39. An electroscope is a sim

ple device. It con-sists of a m

etal ball that is attached by a conductor to tw

o fine gold leaves that are protected from

air disturbances in a jar, as show

n in the sketch. When the ball is

touched by a charged object, the leaves that norm

ally hang straight down spring apart.

Why? (Electroscopes are useful not only

as charge detectors, but also for measur-

ing the amount of charge: the m

ore charge transferred to the ball, the m

ore the leaves diverge.)

40. Would it be necessary for a charged object

to actually touch the leaves of an electro-scope (see Q

uestion 39) for the leaves to diverge? D

efend your answer.

41. Figure 32.12 shows a negatively charged

plastic comb attracting bits of paper w

ith no net charge. If the com

b were positively

charged, would it attract the sam

e bits of paper? D

efend your answer.

42. When a car is m

oved 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. W

hat does the phenom-

enon of polarization have to do with this?

43. Imagine a proton at rest a certain distance

from a negatively charged plate. It is released

and collides with the plate. T

hen imagine

the similar case of an electron at rest the

same distance aw

ay from a plate of equal

and opposite charge. In which case w

ould the m

oving particle have the greater speed w

hen the collision occurs? Why?

44. Consider a pair of particles w

ith equal charges. W

hen released, they fly apart from

each other. Your teacher asks how the

speeds will com

pare when they are ten tim

es farther apart than w

hen first released. Jess says that since the force on the particles decreases w

ith distance, their speeds will be

less. Marie says no, the speed of the repelled

particles increases as long as they interact w

ith each other. With w

hom do you agree

or disagree, and why?

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2

39. The leaves have like charges, and repel each other.

40. No, charging by induction w

ill also charge the leaves.

41. Yes, either a positive or

negative charge will polarize

and attract the paper.

42. The paint is polarized and

attracted to the conducting

surface.

43. Electron; the force on both

will be the sam

e but the electron w

ill have more

acceleration and therefore m

ore speed because of its lesser m

ass.

44. Disagree w

ith Jess and agree w

ith Marie. A

cceleration, not speed, decreases w

ith

increasing distance.

45. Sophia is correct about equal forces but not equal accelerations. Sandra is correct and should add

that the greater m

ass of the protons m

eans less acceleration for the sam

e force.

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CH

APTER 32

ELECTRO

STATICS 663

CH

APTER 32

ELECTRO

STATICS 663

45. A pair of isolated protons w

ill fly apart from

each other. The sam

e is true for a pair of isolated electrons. Your teacher asks w

hich has the greater initial acceleration if the initial distance betw

een the particles is the sam

e. Sophia says the initial accelerations w

ill be equal because the forces are equal. Sandra says no, that the electrons w

ill accelerate m

ore—but can’t explain w

hy. B

oth look to you for your input. What is

your thinking?

Thin

k a

nd So

lve •

••

••

•

46. The charge on an electron is 1.6 !

10"

19 C.

How

many electrons m

ake a charge of 1 C?

47. By how

much is the electrical force betw

een a pair of ions reduced w

hen their separation distance is doubled? Tripled?

48. Two pellets, each w

ith 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 m

etal spheres are brought together into contact. O

riginally one had a charge of #

40m

C and the other a charge of

"10m

C. W

hat is the charge on each after contact?

50. Consider tw

o small charged objects, one

with a charge of 15 m

C and the other of un-

known charge. W

hen 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 am

ount of electrostatic force betw

een them.

a. If the charge on one coin w

ere halved, w

hat would happen to the force betw

een them

?

b. If the charges on both coins were dou-

bled, what w

ould happen to the force betw

een them?

c. If the distance betw

een the coins were

tripled, what w

ould happen to the force betw

een them?

d. If the distance betw

een them w

ere re-duced to one-fourth the original distance, w

hat would happen to the force betw

een them

?

e. If the charge on each object were doubled

and the distance between them

were

doubled, what w

ould happen to the force betw

een them?

52. Two spherical inflated rubber balloons each

have the same am

ount of charge spread uniform

ly 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.

More Problem

-Solving PracticeA

ppendix F

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663

Thin

k a

nd So

lve

46. Total charge 4 (charge per

electron) 5 (1 C) 4

(1.6 3

102

19 C) 5

6.25 3 10

18 electrons

47. To 1/4; to 1/9 48. F 5

kq1 q

2 /d2 5

(9 3

109 N

·m2/C

2) 3

(1 3 10

26 C) 2/(0.30 m

) 2 5

0.1 N

49. 140 m

C 2 10 m

C 5 30 m

C; half on each 5

15 mC

50. From F 5

kq1 q

2 /d2,

q2 5

Fd2/kq

1 5 (2.8 N

) 3

(1.2 m) 2/(9 3

109 N

·m2/C

2 3

15 3 10

26 C) 5

3.0 3 10

25 C

5

30 mC

51. a. Force is proportional to

each charge, so the force w

ould be halved.

b. Force is proportional to the product of the charges, so the force w

ould be quadrupled.

c. Force is proportional to

the inverse of the distance squared, so the force w

ould

be 1/9 its original value.

d. Force is proportional to

the inverse of the distance squared. The inverse of (1/4) 2 is 16, so the force w

ould be 16 tim

es its original value.

e. D

oubling both charges w

ould multiply the force by

four. Doubling the distance

would m

ultiply the force by one-quarter. So there w

ould

be no change in force.

52. From F 5

kq1 q

2 /d2 5

kq2/d

2, q 5

d 3 V

F/k 5 0.30 m

3

V(2.5 N

)/(9 3 10

9 N·m

2/C2) 5

5.0 3

102

6 C 5 5.0 m

C

Te

ac

hin

g R

es

ou

rc

es

• Computer Test Bank

• Chapter and Unit Tests

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