Physics For Scientists And Engineers 6E - part 177

Electricity and

Magnetism

e now study the branch of physics concerned with electric and magnetic phe-
nomena. The laws of electricity and magnetism have a central role in the oper-
ation of such devices as radios, televisions, electric motors, computers,

high-energy accelerators, and other electronic devices. More fundamentally, the in-
teratomic and intermolecular forces responsible for the formation of solids and liq-
uids are electric in origin. Furthermore, such forces as the pushes and pulls between
objects and the elastic force in a spring arise from electric forces at the atomic level.

Evidence in Chinese documents suggests that magnetism was observed as early

as 2000

. The ancient Greeks observed electric and magnetic phenomena possi-

bly as early as 700

. They found that a piece of amber, when rubbed, becomes

electrified and attracts pieces of straw or feathers. The Greeks knew about magnetic
forces from observations that the naturally occurring stone magnetite (Fe

) is at-

tracted to iron. (The word electric comes from elecktron, the Greek word for “amber.”
The word magnetic comes from Magnesia, the name of the district of Greece where
magnetite was first found.) In 1600, the Englishman William Gilbert discovered that
electrification is not limited to amber but rather is a general phenomenon. In the
years following this discovery, scientists electrified a variety of objects. Experiments
by Charles Coulomb in 1785 confirmed the inverse-square law for electric forces.

It was not until the early part of the nineteenth century that scientists established

that electricity and magnetism are related phenomena. In 1819, Hans Oersted dis-
covered that a compass needle is deflected when placed near a circuit carrying an
electric current. In 1831, Michael Faraday and, almost simultaneously, Joseph Henry
showed that when a wire is moved near a magnet (or, equivalently, when a magnet is
moved near a wire), an electric current is established in the wire. In 1873, James
Clerk Maxwell used these observations and other experimental facts as a basis for
formulating the laws of electromagnetism as we know them today. (Electromagnet-
ism is a name given to the combined study of electricity and magnetism.) Shortly
thereafter (around 1888), Heinrich Hertz verified Maxwell’s predictions by producing
electromagnetic waves in the laboratory. This achievement led to such practical de-
velopments as radio and television.

Maxwell’s contributions to the field of electromagnetism were especially signifi-

cant because the laws he formulated are basic to all forms of electromagnetic phe-
nomena. His work is as important as Newton’s work on the laws of motion and the
theory of gravitation.

P A R T

Lightning is a dramatic example of electrical phenomena occurring in nature. While we

are most familiar with lightning originating from thunderclouds, it can occur in other
situations, such as in a volcanic eruption (here, the Sakurajima volcano, Japan). (M. Zhilin/
M. Newman/Photo Researchers, Inc.)

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Chapter 23

Electric Fields

C H A P T E R O U T L I N E

23.1 Properties of Electric Charges

23.2 Charging Objects By

Induction

23.3 Coulomb’s Law

23.4 The Electric Field

23.5 Electric Field of a Continuous

Charge Distribution

23.6 Electric Field Lines

23.7 Motion of Charged Particles

in a Uniform Electric Field

706

▲

Mother and daughter are both enjoying the effects of electrically charging their bodies.

Each individual hair on their heads becomes charged and exerts a repulsive force on the
other hairs, resulting in the “stand-up’’ hairdos that you see here. (Courtesy of Resonance
Research Corporation)

707

he electromagnetic force between charged particles is one of the fundamental forces

of  nature.  We  begin  this  chapter  by  describing  some  of  the  basic  properties  of  one
manifestation  of  the  electromagnetic  force,  the  electric  force.  We  then  discuss
Coulomb’s law, which is the fundamental law governing the electric force between any
two  charged  particles.  Next,  we  introduce  the  concept  of  an  electric  field  associated
with a charge distribution and describe its effect on other charged particles. We then
show how to use Coulomb’s law to calculate the electric field for a given charge distrib-
ution. We conclude the chapter with a discussion of the motion of a charged particle
in a uniform electric field.

23.1 Properties of Electric Charges

A number of simple experiments demonstrate the existence of electric forces and
charges. For example, after running a comb through your hair on a dry day, you will
find that the comb attracts bits of paper. The attractive force is often strong enough to
suspend the paper. The same effect occurs when certain materials are rubbed together,
such as glass rubbed with silk or rubber with fur.

Another simple experiment is to rub an inflated balloon with wool. The balloon

then adheres to a wall, often for hours. When materials behave in this way, they are
said to be electrified

or to have become

electrically charged. You can easily electrify

your  body  by  vigorously  rubbing  your  shoes  on  a  wool  rug.  Evidence  of  the  electric
charge  on  your  body  can  be  detected  by  lightly  touching  (and  startling)  a  friend.
Under the right conditions, you will see a spark when you touch, and both of you will
feel  a  slight  tingle.  (Experiments  such  as  these  work  best  on  a  dry  day  because  an
excessive amount of moisture in the air can cause any charge you build up to “leak”
from your body to the Earth.)

In a series of simple experiments, it was found that there are two kinds of electric

charges, which were given the names

positive and negative by Benjamin Franklin

(1706–1790). We identify negative charge as that type possessed by electrons and posi-
tive charge as that possessed by protons. To verify that there are two types of charge,
suppose  a  hard  rubber  rod  that  has  been  rubbed  with  fur  is  suspended  by  a  sewing
thread,  as  shown  in  Figure  23.1.  When  a  glass  rod  that  has  been  rubbed  with  silk  is
brought  near  the  rubber  rod,  the  two  attract  each  other  (Fig.  23.1a).  On  the  other
hand, if two charged rubber rods (or two charged glass rods) are brought near each
other, as shown in Figure 23.1b, the two repel each other. This observation shows that
the rubber and glass have two different types of charge on them. On the basis of these
observations,  we  conclude  that

charges of the same sign repel one another and

charges with opposite signs attract one another.

Using the convention suggested by Franklin, the electric charge on the glass rod is

called positive and that on the rubber rod is called negative. Therefore, any charged
object attracted to a charged rubber rod (or repelled by a charged glass rod) must

have a positive charge, and any charged object repelled by a charged rubber rod (or at-
tracted to a charged glass rod) must have a negative charge.

Attractive electric forces are responsible for the behavior of a wide variety of com-

mercial products. For example, the plastic in many contact lenses, etafilcon, is made up
of molecules that electrically attract the protein molecules in human tears. These
protein molecules are absorbed and held by the plastic so that the lens ends up being
primarily composed of the wearer’s tears. Because of this, the lens does not behave as a
foreign object to the wearer’s eye, and it can be worn comfortably. Many cosmetics also
take advantage of electric forces by incorporating materials that are electrically
attracted to skin or hair, causing the pigments or other chemicals to stay put once they
are applied.

Another important aspect of electricity that arises from experimental observa-

tions is that

electric charge is always conserved in an isolated system. That is,

when one object is rubbed against another, charge is not created in the process. The
electrified  state  is  due  to  a  transfer  of  charge  from  one  object  to  the  other.  One
object gains some amount of negative charge while the other gains an equal amount
of  positive  charge.  For  example,  when  a  glass  rod  is  rubbed  with  silk,  as  in  Figure
23.2,  the  silk  obtains  a  negative  charge  that  is  equal  in  magnitude  to  the  posi-
tive charge on the glass rod. We now know from our understanding of atomic struc-
ture that electrons are transferred from the glass to the silk in the rubbing process.
Similarly, when rubber is rubbed with fur, electrons are transferred from the fur to
the  rubber,  giving  the  rubber  a  net  negative  charge  and  the  fur  a  net  positive
charge.  This  process  is  consistent  with  the  fact  that  neutral,  uncharged  matter
contains  as many  positive  charges  (protons  within  atomic  nuclei)  as  negative
charges (electrons).

In 1909, Robert Millikan (1868–1953) discovered that electric charge always

occurs as some integral multiple of a fundamental amount of charge e (see Section
25.7). In modern terms, the electric charge q is said to be

quantized, where q is the

standard symbol used for charge as a variable. That is, electric charge exists as
discrete “packets,” and we can write q ! Ne, where N is some integer. Other experi-
ments in the same period showed that the electron has a charge " e and the proton
has a charge of equal magnitude but opposite sign # e. Some particles, such as
the neutron, have no charge.

From our discussion thus far, we conclude that electric charge has the following im-

portant properties:

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C H A P T E R 2 3 • Electric Fields

Electric charge is conserved

Rubber

(a)

(b)

Rubber

– – –

– –

– – –

– –

–

– –

+ + +

+ +

Glass

–

Figure 23.1 (a) A negatively charged rubber rod suspended by a thread is attracted

to a positively charged glass rod. (b) A negatively charged rubber rod is repelled by

another negatively charged rubber rod.

–

Figure 23.2 When a glass rod is

rubbed with silk, electrons are

transferred from the glass to the

silk. Because of conservation of

charge, each electron adds nega-

tive charge to the silk, and an equal

positive charge is left behind on

the rod. Also, because the charges

are transferred in discrete bundles,

the charges on the two objects are
$

e, or $ 2e, or $ 3e, and so on.

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