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CHAPTER EIGHTEEN
Electrical Phenomena: Forces, Charges, Currents
In Chapter 4, we introduced the idea of interactions at a distance or
equivalently of action-at-a-distance forces: gravitational,
electrical or electrostatic, and magnetic. We have treated
one of these, the gravitational force, in considerable
detail. But although gravitational forces may be far
more conspicuous in your direct experience, electrical forces are every bit as pervasive in the universe. This was true even before the electronic
age—indeed, even before the emergence of life
on Earth—because electrical forces are central
not only to the operation of electronic devices
but to the fabric of matter itself.
In this chapter we will develop qualitatively
an underlying model that will enable us to explain
a range of electrical behaviors. In the chapters that follow, we will formulate these ideas quantitatively.
“. . . electrical forces are central not only to the operation of
electronic devices but to the fabric of matter itself.”
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544 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
18-1 Developing an Underlying Model
to Account for the Observations
The ancient Greeks made the first known observations of electrostatic effects. Just
as you may observe that a comb run through your hair attracts bits of tissue
paper, the ancient Greeks found that a briskly rubbed piece of amber would
attract small bits of various materials. The Greek word for amber is elektron, so
the forces were called electric or electrical.
Englishman William Gilbert (1540–1603) found that a variety of materials,
when rubbed, would display this same property: sulfur, wax, resinous substances
such as amber, glass, and precious stones. In the seventeenth and eighteenth centuries, such materials were called electrics, because they were amber-like in their
behavior. Numerous modern materials display the same behavior, among them
cellophane, Styrofoam, the polyurethane of plastic bags, Mylar, audio or video
tape, and synthetic fabrics with their well-known static cling.
In the late 1600s, Otto von Guericke of Magdeburg (in what is now Germany)
discovered that a body, after being attracted to an electric, might later be repelled
by it and not be attracted again until it had come in contact with yet another
body. The following sequence of events repeats his observations with everyday
materials.
Case 18-1
◆
Comb and Foil: Some Observations in Need of an Explanation
Tape
Important: Although the following steps are
fully described, reading a description cannot
Hair
substitute for making the observations for Sticky
yourself. You are strongly urged to do this as side in
1 cm × 1 cm
an On-the-Spot Activity.
2
Aluminum foil
Materials needed: a plastic comb, a
(b) (after running comb
(c) a few seconds later
human hair (about 5 to 10 cm long) or fine (a) (Press halves together)
through your hair)
thread, a small piece of aluminum foil about
Figure 18-1 Evidence of electrical forces in simple materials.
1 cm 12 cm, a little glue or substitute (see
below), and an inch of tape.
contact with the comb anywhere from a few
Apply some glue to one side of the aluminum
seconds to a minute or more (Figure 18-1b).
foil—or make it sticky by wiping it against a freshly
Step 3: But then, without your doing anything more,
licked stamp or hard candy—and fold it in half around
the foil will jump sharply away from the comb
one end of the hair, with the sticky side in (Figure
(Figure 18-1c). If you move the comb slightly
18-1a). Press the halves firmly together. You are now
toward the foil at this stage, the foil will edge
fully equipped.
further away from the comb.
Step 1: Use the tape to hang the hair by the free end
Step 4: Touch the aluminum foil firmly with the fingers
so that the aluminum foil at the other end danof your other hand (the one without the comb).
gles freely. Then run the comb briskly through
Maintain this contact for a couple of seconds,
your hair.
then release it so that the foil once again dangles freely from the hair. Bring the comb close
Step 2: Bring the comb, teeth forward, to within a cm
to the foil again. You will observe that the foil
of the foil. You will observe the foil attracted
is once again attracted.
strongly toward the comb. It may remain in
How can we explain what we observed in Case 18-1? You could readily verify with a refrigerator magnet that aluminum does not respond to magnets, so
the forces involved here are not magnetic forces. Your massive physics book
doesn’t attract the foil either; gravitational forces between objects this size are far
too weak to produce these effects. So the electrostatic force is clearly a different
kind of force.
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18-1 Developing an Underlying Model to Account for the Observations ◆ 545
To what is it due? Much as we assumed that a property of matter, called gravitational mass, is responsible for the gravitational force, we might assume there
is some other property of matter or substance within matter giving rise to the
electrical or electrostatic force. In older English usage, a charge meant a load carried by anything, whether the carrier was a cannon or a horse. Because this property or substance was “carried” by matter, it was called the electric charge. This
doesn’t tell us what was being carried. We could as well have called it the electric whatsit; calling it charge doesn’t mean we understand its nature. In fact, for
the same reason, we could equally well have referred to gravitational mass as
gravitational charge. Some modern authors have used this term to stress the conceptual similarity, but its use is not common practice.
Gravitational forces are always attractive, but our observations show evidence
of both attractive and repulsive electrostatic forces. One kind of charge, always
behaving the same way, could not account for both. A simple assumption consistent with the evidence is that there are two kinds of charge: We call these positive and negative. We can account for our observation of both attraction and
repulsion by supposing that opposite charges attract each other, and like charges
repel each other. For further evidence of this, work through Problems 18-1, 18-2,
and 18-3.
STOP&Think Suppose there are equal amounts of positively and negatively
charged matter in the universe. How would this matter tend to rearrange itself over
time if like charges attracted and opposites repelled? What if opposite charges didn’t
react to each other at all (as gravitational charge doesn’t react to electric charge),
but instead charges of one kind (say, positive) were mutually attractive and charges
of the other kind were mutually repulsive? ◆
Most objects show no evidence of exerting electrostatic forces on each other.
We call such matter neutral.
Because the comb doesn’t attract the foil until we rub it, it does not seem
to be charged until that point. But we didn’t do anything to the foil. Why should
it have become charged? Or did it?
Our model so far has made two assumptions:
• Matter ordinarily contains equal amounts of positive () and negative () charge.
• Opposite charges attract; like charges repel.
Negatively
charged
–
–––
––
––
–––
––
––
––
––
–
+ –
+ –
+ –
(a)
–– – –
–––––
–
–––––
–
– –––
–––
Suppose we now make two further assumptions:
± –
± –
± –
(b)
• Charge can neither be created nor destroyed.
• Charge can move through matter.
The first of the new assumptions is called the law of conservation of electric
charge. It fits with the evidence that the appearance of positive charge in one
place is always accompanied by the appearance of equal negative charge somewhere else. The last assumption provides a way that the usual neutral situation
can be altered if we can’t “create” charge. The negatively charged comb attracts
the positive charge and repels the negative charge in the neutral aluminum foil.
If either kind of charge can move, this causes a charge separation (Figure 18-2a),
with more of the negative charge further from the comb. (We will see later that
in metals, only the electrons, which are negative, can move.) But if there is repulsion as well as attraction, why is the aluminum foil attracted to the comb? We
must add yet another assumption to the model:
• Electrostatic forces decrease with distance.
–
–––
–
–
––
–––
––
––
––
––
–
–
–
–
(c)
–
–
–
(d)
Figure 18-2 Charge configuration
diagrams for Case 18-1.
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546 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
For WebLink 18-1:
A Model to Explain
Electrical Attractions
and Repulsions, go to
www.wiley.com/college/touger
With this assumption, if the negative charges are further from the comb, they will
be repelled less strongly than the positive charges are attracted. The total force
is then toward the comb, and the foil is attracted to it. But the negative charges
on the comb also repel one another. Once the foil is touching the comb, some
of these negative charges can move onto the aluminum foil. Now both bodies
have net negative charges, and they repel each other. We have now explained
Steps 1 to 3 of Case 18-1. For a graphic step-by-step presentation of the reasoning that explains these observations, go WebLink 18-1.
When you bring your fingers in contact with the foil (Step 4 and Figure
18-2d ) after it has gained negative charge from the comb and been repelled,
mutually repelling negative charges on the foil can now get farther from one
another by traveling into your body and possibly spreading from there to the
ground or Earth. So little charge remains on the foil that it is once again effectively neutral. This explanation makes yet another assumption—namely, that
charges could travel through your finger and body much more readily than
through the hair connected to the foil. We therefore add another assumption to
our model:
• Materials differ as to how readily they permit the passage of charge.
We will shortly consider other evidence of this.
Figure 18-2 diagrams the arrangements or configurations of charge at different stages of the observations in Case 18-1. After each new action, we try to
show the system when there is no longer any net movement of charge. At that
stage, we say that the system is in electrostatic equilibrium. The changes in
configuration from one diagram to the next are governed by our assumptions
about how charges behave. Drawing these diagrams is important for visualizing
what is going on in the underlying model, which we adopt because it explains
the behaviors that we actually observe. We are again in the business of looking
for the basic rules by which the game of nature is played.
PROCEDURE 18-1
Charge Configuration Diagrams
1. Diagrams should show the distribution of charges on each body. Plus 12
or minus 12 signs in a region indicate an excess of positive or negative
charge in a region. Regions that are neutral and have a uniform mix of positive and negative charges are unmarked.
2. In each diagram, the distribution of charges will be governed by the nature
of electrostatic forces and the extent to which the charges can move in
response to those forces:
a. Opposite charges attract and like charges repel each other.
b. Like charges will therefore move as far from one another as they can if
paths are available.
c. Charges exert weaker forces on one another when they are further
apart.
d. Charges will move in response to these forces if there is a path by which
they can travel.
3. For sequences of events, you should draw a sequence of diagrams in
which the progression from one to the next is clearly determined by
factors 2a–d.
4. Arrows (in contrasting color) indicate how charge has moved.
The diagrams in Figure 18-2 illustrate point 3. Example 18-1 illustrates the significance of point 2d.
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18-1 Developing an Underlying Model to Account for the Observations ◆ 547
Example 18-1
Conducting and Insulating Rods
For a guided interactive solution, go to Web Example 18-1 at
www.wiley.com/college/touger
A horizontal rod is suspended at its center from a metal ceiling (Figure 18-3a).
At one end, the rod is in contact with a piece of aluminum foil that hangs on
a thread or wire. A negatively charged rubber rod is briefly brought in contact
with the other end of the rod and then removed. This procedure is repeated
for three different instances:
Horizontal rod made of . . .
and hung from . . .
metal
glass
metal
nylon thread
nylon thread
copper wire
Instance I
Instance II
Instance III
Metal ceiling
–––
–– ––
–
–
–– ––
–– Metal
Nylon
threads
rod
Touch
charged
rubber and
metal rod
Aluminum
foil
– –––– –––
–
––– Copper
––
–– wire
–
–
–
–
– ––– –– ––
–
–
– ––
––
Touching
(a)
Nylon
thread
Symbolic representation
of grounding in (b)
(b)
(c)
Figure 18-3 Grounding a conductor. If the aluminum foil in this arrangement were
suspended by an insulating thread (a), negative charge would spread from the rubber
rod through the metal rod to the aluminum foil. The negatively charged metal rod and
aluminum foil would repel each other. But in (b), the copper wire allows the negative
charge to spread over a much larger conducting region, preventing enough concentration
of charge to produce a visible repulsion. Preventing an accumulation of charge in this
way is called grounding.
STOP&Think Before continuing, see if you can figure out what will happen to
the piece of foil in each case. ◆
In instance I, the piece of foil is immediately repelled by the horizontal
rod and remains repelled when the rubber rod is removed. In instances II and
III, no repulsion is observed. Use charge configuration diagrams to explain
these behaviors.
Brief Solution
Choice of approach. The mutual repulsion of like charges and mutual attraction of opposite charges must govern the behavior that we see.
Diagrams and reasoning. If two bodies repel, there must be like charge on
them. The only source of excess charge is the rubber rod. If the metal rod
permits the passage of charge, the mutually repelling negative charges that start
out on the rubber in Figure 18-3a will get as far away from one another as
they can and thus distribute themselves over the metal rod and the foil. Once
rod and foil are both negatively charged, they will repel each other. We therefore must assume that the metal rod permits the passage of charge very quickly.
The only difference between instance II and instance I is that the horizontal rod is made of glass. If no repulsion takes place, we must infer that
excess negative charge has not spread to the far end of the rod and to the
foil, and therefore glass does not readily permit the passage of charge.
In instance III there is no repulsion even though the rod is metal. Why?
In instances I and II, we didn’t consider the thread supporting the rod as a
possible path for the excess charges. Like glass, nylon does not permit the passage of charge. But copper is a metal. The charges can therefore get farther
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548 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
EXAMPLE 18-1 continued
away from one another by going up the copper wire and spreading out over
the metal ceiling (recall point 2b in Procedure 18-1), as in Figure 18-3b. The
excess charge becomes so spread out that the excess negative charge in any
one location is insufficient to produce visible repulsions.
◆ Related homework: Problems 18-12 through 18-15.
+
+
+
+
+
+
In the example we see that some materials, such as metals, permit the passage
of charge very quickly. A material that does this is called a conductor. Metals
are good conductors. Other materials, such as glass, do not readily permit the
passage of charge. A material of this type is called an insulator. Like conductor, insulator is not an absolute term. Materials may be conducting or insulating
to various degrees. Until we make these ideas quantitative, we will make do by
speaking of good or poor conductors and insulators.
A wire connected to the ground or Earth would have the same effect as the
copper wire in the above example or in the similar situation in Figure 18-3a and
b, so any large body where excess charge can spread out when connected by a
wire is called ground (the British call this earth). Connecting an object to ground
is called grounding. When you use jumper cables to start your car, one terminal must always be connected to the engine block or car frame, which serves as
ground, to prevent a dangerous build-up of excess charge. The usual symbol for
ground in diagrams is
(Figure 18-3c). It is possible to charge an object connected to ground by bringing an already charged object near it, without transferring any charge from that second object. (For the details of this process, called
Conductor
charging by induction, see Problem 18-46.)
+ + + + + +
In Case 18-1 (Figure 18-2), we looked at situations in which electrostatic forces
(a)
– – – – – –
produce a separation of charge. Figure 18-4 shows that this separation can result
– charge shifts to left
either from positive charge moving one way or negative charge
Both movements result
+ + + + + +
moving the opposite way. Because it is a pain in the neck to
– – – – –
(b)
in the same net negative
–
be worrying about minus signs all the time, physicists often
charge on the left and
+ charge shifts to right
the same net positive
take advantage of this fact to describe situations in terms of the
+
charge on the right.
+ + + + +
(c)
movement of positive charge, even when negative charge is
– – – – – –
(highlighted areas neutral)
moving the other way. We have not yet established whether
Summary charge
one or both kinds of charge are able to move in various con–
+
(d )
configuration for
ducting materials. So in the following example, for instance, in
either (b) or (c)
which positive charge is effectively transferred to a region of a
Figure 18-4 A flow of negative
conducting sphere, it may actually be that negative charge is being transferred away
charge in one direction is equivafrom that region or that both are occurring.
lent to a flow of positive charge
in the other.
Example 18-2
Charge Distributions on Conductors, I
Figure 18-5a shows an isolated conducting sphere. Some positive charge is
effectively transferred to a small region of the sphere at some instant. How is
the charge distributed when the sphere reaches electrostatic equilibrium?
STOP&Think Attempt to do the reasoning yourself before reading the solution. ◆
Solution
Choice of approach. We can apply point 2b of Procedure 18-1.
Diagrams and reasoning. The excess positive charges repel one another, so
that the charge spreads out as far as the conducting material permits. It thus
ends up distributed uniformly over the surface of the sphere (Figure 18-5b).
For the same reason, any excess charge on a conducting body in equilibrium
will always be located on the surface, although not always distributed uniformly.
◆ Related homework: Problem 18-16.
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18-1 Developing an Underlying Model to Account for the Observations ◆ 549
+
++ +
++
++++
+
+
+
–
+
–
+
–
+
–
+
(b) Electrostatic
equilibrium
Conducting sphere
Example 18-3
––
––
+
+
(a) Instant charge
added
++
+
+
+
(c) Instant charge
added
(d ) Electrostatic
equilibrium
Parallel conducting plates
Figure 18-5 Figures for Examples
18-2 and 18-3.
Charge Distributions on Conductors, II
Figure 18-5c shows an edge view of two thin conducting metal plates (the
thickness is exaggerated in the diagrams) separated by a nonconducting gap.
Equal and opposite amounts of charge are effectively transferred to small
regions of the plates at some instant. How is this charge distributed when the
system reaches electrostatic equilibrium? STOP&Think Once again, try to do
the reasoning yourself before reading the solution. ◆
Solution
Choice of approach. We can again apply Procedure 18-1.
Diagrams and reasoning. As in Example 18-2, and for the same reason, the
excess charge on each conductor spreads out over its surface, but this time
not uniformly over the entire surface. Because the opposite charges on the two
plates attract each other, they will move as close to each other as they can.
Thus nearly all the excess charge will end up on the inner faces of the two
plates (Figure 18-5d ). The distribution will be essentially uniform over the inner
faces, except near the edges.
◆ Related homework: Problem 18-17.
If the charges in Figure 18-5d are truly in equilibrium, there must be constraining forces on the charges that are equal and opposite to the forces that the
positive and negative charges exert on each other. The constraining forces are
exerted either by the conducting surfaces or the intervening medium; we will not
concern ourselves with the details. If the two opposite concentrations of charge
become sufficiently large, the electrostatic forces on the charges will exceed the
maximum constraining forces, and charges will jump across the gap between the
charged objects. This happens when charges build up on clouds, causing an opposite buildup of charge on Earth’s surface, until finally there is the discharge that
we know as lightning.
The forces that individual charges exert on each other are directed toward
each other if attractive, away from each other if repulsive. When like charges are
on a flat or gently curving surface of a conductor, the repulsive forces they exert
are essentially along the surface (Figure 18-6a), causing the charge to spread out
on the surface. On a needle-like projection (Figure 18-6b), the forces those same
charges exert on each other would be essentially perpendicular to the surface
and thus would not contribute significantly to spreading. Consequently, on irregularly shaped conducting bodies, charge tends to concentrate at sharp projections.
It is for this reason that lightning tends to strike tall trees or lightning rods rather
than flat expanses of ground or roof.
++
+
(a)
+
(b)
Figure 18-6 Repulsive forces that
surface charges on conductors
exert on each other. (a) Forces
mostly parallel to gently rounded
surface. (b) Forces mostly perpendicular to the surface of a sharp point.
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18-2
Charge Carriers
In addition to the terms we’ve defined so far to describe our underlying model,
we will also suppose (and later provide evidence) that there are charge carriers:
Charge carriers: Particles that have the property of charge as an inherent and unalterable trait. As the carriers move, their charge goes with them.
➥A note on language: Although
electric current has sometimes been
called electricity, the word electricity in common usage has a variety
of related meanings, such as the
study of all electrical phenomena.
To avoid confusion, we introduce a
less ambiguous term.
➥A note on language: We use the
term electrostatic forces even when
charge carriers are in motion, because
unless their speeds exceed 0.1c, the
electrical forces on them are essentially the same as when they are stationary or static. This is not a concern
in electric circuits.
(a)
In general, we will refer to the movement or flow of charge from one place
to another as an electric current, or simply a current. This definition is preliminary. Later we will define current quantitatively, but we will retain the notion
that there is a flow of charge if and only if there is a flow of charge carriers.
Strictly speaking, a flow of charge doesn’t require us to assume the existence
of charge-carrying particles. The 1771 Encyclopaedia Britannica, reflecting the
prevalent views of the time, described electricity as a “very subtile fluid . . . capable of uniting with almost every body.” Whether it be fluid or particles, we assume
it gets set in motion because an electrostatic force is exerted on it. If we also
assume that the relationship between forces and motion is always governed by
Newton’s second law of motion, we must attribute inertial mass as well as electric charge to whatever is moving.
Subsequent experimentation validated viewing electrical phenomena in terms
of forces and motion. Eighteenth-century investigators found that by rapidly rotating a large glass globe against a suitable rubbing surface using a wheel and belt
mechanism (Figure 18-7a), the rubbing would result in a very substantial charge
on the globe. A modern device that makes more sophisticated use of a continuous belt conveyor to develop charge on a metallic globe is the Van de Graaff
generator (Figure 18-7b), invented by Robert J. Van de Graaff in 1929. A conductor brought in contact with the globe also becomes charged (Figure 18-8).
Investigators using either device have found that when a large enough charge is
developed on the globe and a conducting body is brought sufficiently close, a
visible and audible spark jumps from the globe to the conducting body (Figure
18-7b), much as lightning jumps from clouds to Earth. The charges that remain
after the spark are found to be reduced, indicating that charge has jumped the
gap, and providing evidence of motion brought about by electrostatic forces.
(b)
Figure 18-7 Devices for generating large build-ups of electric charge. (a) 18th century:
Joseph Priestly’s electrical machine (plate 73 of vol. 2 of 1771 Encyclopaedia Brittanica).
(b) 20th century: The giant Van de Graaff generator at the Boston Museum of Science.
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18-2 Charge Carriers ◆ 551
STOP&Think Why won’t the spark jump
to an insulator? Draw diagrams showing
the configuration of charges on the conductor before and after it is brought near
a positively charged sphere. Does your
“after” configuration account for a force
that could cause charge to jump the gap?
Why can’t you get the same “after” configuration for the insulator? ◆
Uncharged
electroscope
+ + +
++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+
+ + +
+
+
+
Metallic leaves
of electroscope
become positively
charged and repel
each other.
By the late nineteenth century, investigators were able to obtain not just brief
sparks but sustained “rays” or beams
between two conducting terminals on
which opposite charges were continuously replenished. These beams were produced within sealed glass chambers and caused a glow where they struck the
fluorescent material coating the glass surface at one end (Figure 18-9). Because
the negatively charged terminal was called a cathode, the beams were called
cathode rays, and the glass chambers cathode ray tubes. These were the primitive ancestors of most television, personal computer, and oscilloscope tubes
(before widespread use of liquid crystal displays), in which, by rapidly varying
the direction of the beam, a pattern of light is produced on the end of the tube
that the viewer sees.
English physicist J. J. Thomson (1856–1940) observed that when oppositely
charged plates were positioned above and below the beam, the beam deflected
toward the positive plate, indicating that the beam itself was negatively charged.
Moreover, for any given amount of charge on the plates, the beam deflected a
fixed amount; there was no spreading out of the beam. Thomson reasoned as
follows: (1) Imagine the beam to be a stream of separate tiny particles. Thomson called these particles “cathode corpuscles.” (2) The electrostatic force will be
the same on all particles having the same charge. (3) The force will produce an
acceleration, and thus a deflection y 12 at2, perpendicular to the beam direction.
(4) But by Newton’s second law, the acceleration varies inversely as the mass.
(5) Thus, if there were no relationship between charge and mass, that is, if particles having equal charge could have different masses, the particles would
undergo different accelerations. They would therefore deflect by different amounts,
and there would be a spread. (6) But there is no spread. So particles with the
same charge must have the same mass (and vice versa), and so the ratio of charge
to mass must have a fixed value.
Thomson’s cathode corpuscles are today called electrons, and for establishing its charge-to-mass ratio (treated in Chapter 24), Thomson is generally credited with being the electron’s discoverer. His reasoning established clearly that a
given amount of charge moves with a fixed amount of mass. This supports our
idea of charge carriers. Thomson further surmised that his particles were fundamental components of all matter, as we now know electrons to be.
But there is nothing in this reasoning that logically requires the carriers to be
separate particles rather than a continuous flow of matter. (People knew there
...which are
accelerated
through cathode
Heated anode (–)
emits electrons...
Figure 18-8 Transfer of charge
from Van de Graaff generator to
conducting bodies.
Plates to deflect
beam horizontally
– +
Plates to deflect
beam vertically
Beam
Glow where
beam strikes
fluoresent
coating
Figure 18-9 The cathode ray tube.
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552 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
Nerve cells or neurons. An electric
current consisting of a flow of ions
from neuron to neuron is the signal
that carries information in the nervous system. The neurons here are
magnified 2500 times by a scanning
electron microscope.
was a fixed ratio of hydrogen to oxygen in water long before they knew that
what we experience as a continuous fluid was made up of individual molecules,
each containing two hydrogen atoms and one oxygen atom.) The particle nature
was confirmed, however, by American physicist Robert A. Millikan (1865–1953).
In his famous oil drop experiment (1910–1913), Millikan put oil in an atomizer to obtain tiny individual droplets that could acquire electric charge from contact with ions in the air. By allowing the droplets to enter a region between oppositely charged plates, he could measure their terminal velocities. Knowing all the
other forces on each droplet, he could determine the electrostatic force on it and
from that its charge. He found that the charges on the droplets were always integer multiples of the same value, which he inferred must be the smallest possible
“chunk” of charge. This he took to be the charge of the electron. Charge, then,
was made up of pieces of fixed size, and if the ratio of mass to charge was constant, then the fixed amounts of charge must be carried by pieces of matter with
fixed amounts of mass, in other words, particles.
Experiments such as these began to shape our present-day ideas about the
structure of matter. Atoms contain positive nuclei surrounded by negative electrons. The nuclei are in turn made up of positive protons and neutral neutrons.
The positive and negative particles exert electrostatic forces on one another. Under
some circumstances, an outer electron of an atom may be more attracted to the
positive nucleus of a neighbor atom than to its own, and will be pulled to the
other nucleus, giving its new home atom a net negative charge and leaving its
previous home atom with a net positive charge. Atoms charged in this way are
called positive and negative ions.
Moving ions are also charge carriers. Electric currents in liquids generally
involve the movement of ions. This is the case in many processes that you are
likely to encounter in more detail in your chemistry course, such as electrolysis,
electroplating, and the operation of certain types of batteries. In your own body
and in all living things, which are mostly water, some kinds of ions can pass
through particular cell membranes more readily than others (the membrane is said
to be permeable to these ions). This can result in net positive and negative charges
on opposite sides of a membrane. Such charge distributions have great importance for biological systems. In neurons (nerve cells), for example, the properties
of a membrane may change in response to a stimulus such as heat or light or a
signal from a neighboring neuron. This “information” to the cell membrane may
itself take the form of the arrival of charge carriers to the membrane, which in
turn can react chemically with components of the membrane. When the membrane changes properties, its permeability for different ions changes, and there is
an ion flow across the membrane. This flow, or current, passed on from neuron
to neuron, is the signal that carries information in the nervous system.
Chemical reactions are likewise the result of electrostatic forces. In ionic bonding, ions of opposite charge attract each other electrostatically; in covalent bonding, electrostatic forces are exerted on shared electrons by more than one nucleus.
Roughly speaking, chemical reactions—changes in the bonding situation—are a
change in the configuration of charge carriers (positive nuclei and negative electrons) in response to electrostatic forces. (We will need to refine this description
in Chapter 27.) This is true both of the simplest reaction between two atoms and
all the multistep reactions among complex molecules that make up the processes
of life. (The totality of all these reactions in a living thing is called its metabolism.)
In certain very large molecules, shared electrons can move among many
atoms that make up the molecule. This is true, for example, in pigment molecules, such as rhodopsin in the rods and cones of the human eye and chlorophyll in green plants. In a sense, over distances smaller than their total size,
these molecules are conductors, and this property is critical to their role in vision
or in photosynthesis.
Metals carry this property to an extreme. The outermost electrons are shared
by all the atoms making up a piece of metal and so can travel throughout the
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18-3 The Electron Gas and the Effect of Uneven Charge Distributions ◆ 553
–
+
– +
+
–
+
–
+
– +
– +–
+ –
+ –
– +
– + +
–
+ + –
+
+ – +
–
+ – +– – – +
–
(a)
–
–
–
–
–
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–
–
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–
–
–
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–
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–
–
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
+ –
(b)
metal. This is why metals are conductors. The rest of each atom—a positive ion—
remains stationary. To fit with this picture, we must refine the model we have
developed so far. The charge carriers in metals, and therefore in the wires of
ordinary electrical devices, are electrons. When electrons move from a region,
they leave positive ions behind. Thus, if a negatively charged object is brought
near a piece of metal, the nearest part of the metal’s surface becomes positive
not because positive charge carriers move onto that part but because electrons
leave it. For a step-by-step graphic presentation of this reasoning, work through
WebLink 18-2.
Because most electrical devices use metal wires in which the carriers are electrons, the currents we deal with most often turn out to be flows of negative charge.
But as Figure 18-4 showed, a flow of negative charge in one direction is equivalent in its effect to a flow of positive charge in the other. The flow of positive charge
is called a conventional current (conventional means it is something that we
agree on) and is usually what is meant by current in quantitative treatments.
Figure 18-10 Polarization: a model
to explain the attraction of nonconducting materials to charged
bodies. (Adapted from A. Arons,
Development of Concepts in Physics,
Addison-Wesley, 1965.) (a) Thermal
motion ordinarily keeps dipole molecules randomly oriented. (b) But they
partially align in the presence of a
charged object. (Thermal agitation
prevents complete alignment.)
For WebLink 18-2:
Movement of Charge
in Metals, go to
www.wiley.com/college/touger
✦POLARIZATION We mentioned earlier that after you run a comb through your
hair, it attracts small bits of paper. But paper is not a conductor. Placing paper
between copper wires prevents current from passing from one to the other. Cardboard cylinders serve as insulators in the bulb sockets of older light fixtures. In
explaining why aluminum foil is attracted to the comb, we assumed that a separation of charge could occur in the aluminum (Figure 18-2b) because charge can
move through a conductor. Then what happens in the paper?
Understanding that molecules have both positive and negative parts enables
us to propose a satisfactory model of what goes on in this case. We suppose that
although the molecule is neutral overall, it may have more of its positive charge
at one end and more of its negative charge at the other. Because it has two oppositely charged “poles,” it is called an electric dipole.
Like other atoms and molecules, these dipoles will jiggle about in thermal
motion, and will ordinarily be randomly oriented (Figure 18-10a). But a charged
rod brought near them causes them to pivot into alignment with the oppositely
charged poles drawn towards the rod and the like charged poles repelled (Figure 18-10b). The resulting separation between the average positions of the positive and negative constituents is called polarization. Because the positive charges
on average are slightly closer to the rod, there is a small net attraction.
➥Some molecules (called polar
molecules) are dipolar even in electrically neutral surroundings; others
become polarized only if another
charged body exerts opposite electrical forces on their positive and
negative components.
++
++
–
–
An image that physicists sometimes find useful in describing metals is that of a
negative electron gas pervading a connected lattice of positive ions (Figure 18-11).
The electrons are pictured as mobile in somewhat the same way that molecules
in an ordinary gas are mobile, and, like the molecules in an ordinary gas, the electrons move around randomly when there is no net flow overall.
–
–
++
18-3 The Electron Gas and the Effect
of Uneven Charge Distributions
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Figure 18-11 Simple model of a
metal: lattice of positive ions electron gas.
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554 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
Like an ordinary gas, an electron gas can also be made to flow in some direction, but the causes of the flow are different. In an ordinary gas, molecules flow
from regions where there is a greater density of molecules to regions of lesser
density. The gas thus flows from higher to lower pressure (the pressure is a collective effect of molecules colliding with one another and with their surroundings). In an electron gas, electrons flow from regions where there is a greater
density of electrons to regions of lesser density. What drives the motion is not a
pressure difference but electrostatic forces. Electrons will be repelled by regions
where there is a surplus of electrons and attracted toward regions where a deficit
of electrons leaves unbalanced positive charges.
Net flow in ordinary gases is affected by differences in density; the excess
molecules in regions of higher pressure are distributed throughout the region’s
volume. Net flow in an electron gas is affected by differences in charge density.
But excess charges on a conductor are always located on its surface—never in
the interior—because mutual repulsion keeps them as far apart as possible (recall
Examples 18-2 and 18-3). So the charge density that affects flow is a surface
charge density. These surface charges exert forces on the electrons in the interior of the conductor and may cause a flow of the interior electrons, but the flow
occurs in such a way that the charge density remains zero throughout the interior. The next chapter details how this happens.
For WebLink 18-3:
Pumps and Batteries,
go to
www.wiley.com/college/touger
✦PUMPS AND BATTERIES If two gas-filled chambers are connected (Figure
18-12a), the pressure will be uniform throughout. It is possible to increase the
pressure in one chamber and decrease the pressure in the other by connecting
them through an air pump (Figure 18-12b). If we then open a valve connecting
the two chambers, there is a rush of gas from the higher-pressure chamber to
the lower (Figure 18-12c).
If we similarly connect two identical conducting wires (Figure 18-12d), charge
will distribute uniformly over both. If we then connect a battery between the two
wires (Figure 18-12e) and bring the free ends of the wires together (Figure 18-12f ),
there will be a flow of electrons. If the contact is broken, we may observe a
spark across the gap. We have already noted that a spark is evidence of a flow
of charge. The two systems in Figure 18-12 are analogous. To explore the analogy more fully, work through WebLink 18-3.
In Figure 18-12e, the two wires provide very little surface on which to place
excess charge, so the charge density becomes sufficient to oppose the pumping
Excess
molecules
here
Closed
valve
Closed
valve
Pump
Open
valve
Deficit of
molecules
here
(a)
Figure 18-12 Comparing the
effect of a pump and a battery.
±
±
±
±
±
±
±
±
±
±
(d )
Flow of
molecules
(b)
Excess
electrons
here
Deficit of
electrons
here
–
–
–
–
–
–
–
–
–
–
–
+
+
+
+
+
+
+
+
+
+
+
(e)
(c)
–
–
– –
– –
–
–
–
+
+ +
+ +
+
+
(f)
Spark when
contact is broken
Flow of
electrons when
contact is secure
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18-3 The Electron Gas and the Effect of Uneven Charge Distributions ◆ 555
Conducting
surfaces
Rolled and inserted
into container
Conducting
wires
Conducting
wires
Final
product
Figure 18-13 What goes into a
typical commercial capacitor.
Non-conducting
layers
of further charge when only a tiny amount of charge has been pumped from one
wire to the other. At this stage, the charges already on either wire exert a total
electrostatic force on any further charge that is equal and opposite to the force
exerted by the battery. Because the latter force results from the battery’s chemistry, we call it a non-electrostatic force.
Suppose we now take the free ends of the two wires in Figure 18-12a and
connect them to the plates in Example 18-3. We now have a mechanism, the battery, that can transfer charge from one plate to another to produce the charge
configuration in Figure 18-5d. The plates, because of their extended surface areas,
can take on much more excess charge before the charge density builds up sufficiently to oppose the pumping effect of the battery. Because of this greater
capacity to hold charge, any device consisting of two conducting surfaces separated by a small nonconducting gap is called a capacitor.
The capacitor in Example 18-3 is called a parallel plate capacitor. In many
commercial capacitors (Figure 18-13), the conducting layers or plates and the intervening nonconducting layers are rolled together and put into a cylindrical container to provide large surface areas within a small space. The extent to which a
capacitor can store charge is called its capacitance (we will provide a quantitative definition later on). Large surface areas are clearly an important factor contributing to large capacitance.
Now let’s see what happens when we string together some of the objects we
have discussed. An unbroken loop of these objects is called an electric circuit,
because it is a path around which charge carriers can circulate or move in circles.
If the loop includes a capacitor, it is not in the strictest sense a circuit because
charge cannot pass across the nonconducting layer or gap, but in ordinary usage
we call it a circuit anyway for lack of a better term. The first circuit we look at
will consist of a battery, a capacitor with large capacitance, connecting wires, and
in addition, a small bulb and socket. To understand how charge can move through
the bulb, it is important for you to understand the connections that make up the
conducting path (Figure 18-14).
In a bulb, the filament is a
fine conducting wire that
connects between the
lower tip and the screw
threads. These two
terminals are separated
by an insulator.
Insulator
The threads of the
socket connect to
the threads of the
bulb.
Using a defibrillator. A defibrillator
is a medical device that applies an
electric shock to restore the rhythm
of a heart that is not beating properly. The shock is provided by the
discharge of a large-capacitance
capacitor in the defibrillator.
So the charge
follows this overall
path through bulb
and socket.
The base of the socket
connects to the lower
tip of the bulb.
(a)
Figure 18-14 Conducting path through a light bulb.
(b)
(c)
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556 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
or
Element
–
or
Capacitor
or
+
Battery
Symbol
–
Wire
+
Note: Bends in the
wire do not affect its
role as a conductor.
Figure 18-15 Standard symbols
for circuit elements.
Miniature
bulb
Clip A
+
Clip B
+
–
Clip A
–
Metal alligator
clips for firm
contacts
Bulb
+
Very large
capacitance
capacitor
Actual circuit
Clip B
–
Schematic
(a)
–
Actual circuit
+
Schematic
(b)
Figure 18-16 Circuit for Case 18-2.
Physicists usually draw electrical circuits using stylized symbols. Figure 18-15
shows the circuit elements (the building blocks of the circuit) we have discussed
so far and their usual symbols. Figure 18-16a shows these elements connected to
form a circuit. The accompanying symbolic drawing of the circuit is called a
schematic diagram, or simply a schematic.
Case 18-2
◆
Using Batteries to Charge and Discharge Large Capacitance Capacitors
If you have the materials shown in Figure 18-16a available to you, you should do the following steps for
yourself as an On-the-Spot Activity. Then, keeping in
mind the ability of the two plates of a capacitor to store
opposite charges, you should try to figure out how our
underlying model can account for what you observe.
You will be more likely to “own” the reasoning if you
can work it out for yourself.
Step 1: Assemble the circuit in Figure 18-16a, but leave
clip B unconnected. STOP&Think What do you
expect to happen when you connect clip B to
the battery? Will the bulb light up? Will it remain
lit? ◆ Now connect clip B to see what happens.
Step 2: Suppose that after all contacts have been in place
for a couple of minutes, you disconnect clips A
and B from the battery and bring them together
as in Figure 18-16b (eliminating the battery from
the circuit). STOP&Think What do you expect
to happen? Will the bulb light up? Will it remain
lit? ◆ Now do it to see what happens.
Step 3: After all contacts have again been in place for a
couple of minutes, replace the bulb (call it bulb
A) with a different bulb B (e.g., one having a
different wattage) and repeat steps 1 and 2.
The Observations (see if these agree with yours)
For Step 1: When clip B is connected, the bulb
glows briefly, gradually dying out. The glow may last
anywhere from less than a second to over half a
minute, depending on the specific capacitor, bulb, and
battery used.
For Step 2: Here, too, we observe that the bulb
glows briefly and then dies out!
For Step 3: In each of steps 1 and 2, bulb B glows
more brightly but dims more quickly. (Or, if we chose
a bulb that was initially less bright, it would dim more
slowly.)
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18-3 The Electron Gas and the Effect of Uneven Charge Distributions ◆ 557
How can our model account for the observations?
Check your own reasoning against the following.
In step 1: When the battery is connected, it pumps
electrons from the positive to the negative capacitor
plate. When enough electrons are concentrated on the
negative plate to repel the arrival of further charge, and
enough of an electron deficit is created on the positive
plate so that a net positive charge holds back the remaining electrons there, the flow ceases. The bulb, it appears,
glows when there is charge flowing through it.
In step 2: If the glow indicates a flow of charge—
a current—how can the bulb glow again after the battery is removed? Doesn’t the battery supply the current?
The charge imbalance between the two plates can be
maintained only as long as the battery is pumping to
maintain it. When the pump is removed, the mutual
repulsion of electrons on one plate will cause electrons
to flow back to the plate where there is an electron
deficit. That electrostatic repulsion was also there when
the battery was there, but now it is no longer opposed
by the non-electrostatic force that the battery exerted.
A battery “pumps” charge along; it does not supply the
charge carriers that make up the current. Current will flow
whenever an uneven distribution of charge exerts a net
force on available charge carriers, whether caused by a
battery or not.
In step 3: We see that when the light is dimmer—
less is given off each second—it is emitted for more
seconds. In developing our model, we may surmise
that the battery “pump” is building up the same total
amount of charge on the capacitor plate, but is doing
it more slowly through bulb B. Bulb B seems to be
more resistant than A to charge passing through it, so
the charge passes through it more gradually. This is
similar to what happens when you allow water to pass
through two paper coffee filters rather than one: The
water seeps through more slowly, but ultimately you
end up with the same amount of water collected in
your pot. In this case, the same amount of charge ultimately passes through the bulb to collect on the capacitor plate.
Pattern of charge behavior
Charge flowing
through bulb each
second (current)
Bulb A
Bulb B
more
less
A 100 W bulb is brighter than a 15 W bulb. Watts
are a unit of power, the rate of energy use. The brightness of a bulb is associated with its power rating, the
Duration
of flow
less
more
more
less
Comparing the above patterns, we infer that a
bulb’s brightness indicates the rate at which charge
flows through it, not how much total charge passes
through. The rate of charge flow is what we call current. A bulb that is more resistant to the passage of
same
same
amount of energy it draws and emits each second. We
begin to see that the pattern of energy emission reflects
the pattern of charge behavior:
Corresponding pattern of energy emission
Bulb brightness
(power, or energy
Duration
emitted each second)
of glow
Bulb A
Bulb B
Total
accumulation of
charge on plates
less
more
Total
energy use
same
same
charge carriers glows less brightly (we refer to this property as resistance). Thus, if bulbs are placed one at a
time in the circuit in Figure 18-16, the bulb with higher
resistance will permit a smaller current to pass through.
(Much of Case 18-2 is adapted from the work of Melvin Steinberg.)
We saw that there is less current through a higher-resistance bulb when each
is connected individually to the battery, so that the same difference in surface
charge density is maintained between the ends of each bulb filament. But it is
not true when the two bulbs are placed in the same circuit one after the other,
as in Figure 18-17. Now the two bulbs are along the same conducting path. What
passes through one must also pass through the other, so the current through both
must be the same. But the total change in surface charge density from the beginning of one filament to the end of the other is not distributed equally between
the two filaments. The higher-resistance bulb can sustain a greater charge density
difference between its two ends, so most of the change is across this bulb. In fact,
A
B
RB > RA
–
Flow of
electrons
+
Flow of
conventional (+)
current
Figure 18-17 Bulbs along same
conducting path (“in series”).
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558 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
+
+
+
+
Attracted toward
+ region with more
positive surface
+ charge
+
+
–
–
–
–
–
– Repelled by
region with more
– negative surface
charge
–
–
Figure 18-18 The changing
charge distribution (charge
density gradient) along a wire’s
surface results in a net electrostatic force on electrons in the
wire’s interior.
it takes a greater electrostatic force to move charge carriers through the higherresistance bulb. The greater charge density difference is necessary to exert this
greater electrostatic force. Because charge carriers must be pushed harder through
this bulb, the rate of energy expenditure (power) is greater. Thus, the higher
resistance bulb glows more brightly when the same current passes through both.
In a circuit with no capacitor, and therefore no nonconducting gap, the battery can pump charge continuously around the resulting loop. The simplest such
circuit consists of a battery with a wire connected between its terminals (Figure
18-12f ). (The wire should be made of a fairly high-resistance alloy, such as
nichrome, to avoid rapid depletion of the battery.) When the circuit is closed, the
surface charge density along the wire, instead of occurring abruptly as in Figure
18-12e, tends to be very gradual (Figure 18-12f ).
In the steady state, when the current is not changing, the charge density changes
uniformly along the length of the wire. We call this a constant charge density gradient. The direction of decrease is the direction of the negative gradient. A gas will
flow in the direction of a negative pressure or density gradient. Positive charge or
conventional current will flow in the direction of a negative surface charge density
gradient. Electrons, in contrast, flow in the direction of the positive gradient.
With no resistance in the wire, the configuration of surface charge in Figure 18-18 would exert a nonzero force on electrons in the wire’s interior, and
they would accelerate in the direction of increasingly positive surface charge. But
because there is resistance, they do not accelerate unhindered. Obstacles or conditions that they encounter in their path recurrently slow them down, so they
level off to a certain average velocity, called their drift velocity. STOP&Think
If electrons are drifting through the interior of a current carrying wire, does that
mean the wire’s interior has a net charge? ◆
Along a closed conducting path, electrons leaving any region are replaced by
electrons entering it, so the net charge in the interior of a conductor remains
zero, even when there is a current. The predominant movement of charge is
through the neutral interior of the circuit, with each tiny region contributing the
electrons that drift into the next. The drifting electrons that constitute the current
come from sites all along the conducting path, from the bulb filament and the
connecting wires as well as the interior of the battery.
✦SUM M ARY✦
In this chapter, we developed an underlying model to explain
a range of observed behaviors. The model involves a number
of key ideas:
Electrostatic forces are a class of action-at-a-distance
forces, both attractive and repulsive, that bodies exert on one
another, which are demonstrably not gravitational or magnetic.
We call these forces electrostatic because they occur even
when there is no motion of the charge carriers responsible
for the forces. The forces are weaker when the bodies are further apart.
Electric charge is a property we attribute to matter that
exerts electrostatic forces (just as gravitational mass is responsible for gravitational forces). We postulate that it comes in two
varieties, positive and negative. Oppositely charged bodies
attract each other, and bodies of like charge repel each other.
Neutral bodies contain equal amounts of positive and negative charge.
We can explain certain observations by supposing that
charge can move through some matter in response to electrostatic forces. We developed specific vocabulary for describing
this motion.
Electric current, or simply current, is the rate of
movement or flow of chargea from one place to another
(later we will make this quantitative). Electrostatic equilibrium is the state or condition of a body or system in
which there is no net movement of charge (and consequently
no net current).
Conductors are materials that permit a current to pass
through them. Insulators are materials that in contrast to conductors do not permit the passage of a current. Conductor and
insulator are not absolute terms. Materials may be conducting
or insulating to various degrees. Ground refers to a conducting body (such as the Earth) that is large in comparison to the
other bodies in a situation, so that charge may flow onto it or
from it without apparent limit.
To put these concepts together in a coherent, connected
picture, it is useful to try to explain behaviors by means of
charge configuration diagrams (see Procedure 18-1).
Charge carriers are particles that have the property of
charge as an inherent and unalterable trait. In a current, as the
carriers move, their charge goes with them.
Experiments such as Thomson’s cathode ray experiment and Millikan’s oil drop experiment led to a model
of matter in which atoms are understood to be made up of
positive nuclei and negative electrons. In metals, which are
conductors, the mobile charge carriers are electrons.
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Qualitative and Quantitative Problems ◆ 559
Conventional current is a flow of positive charge equal
and opposite to the flow of charge carried by electrons.
A useful model of a metal is one in which a negative
electron gas is free to move about a lattice of positive
nuclei. Excess charge always ends up on the surfaces of
conductors.
Conventional current will flow from higher to lower surface charge density. When positive charges concentrate in one
region, their mutual repulsion will produce a net movement
away from this region—a flow of charge or current—if a conducting path is available.
In explaining the behavior of circuits, we looked at several common circuit elements:
Batteries set up a surface charge density difference by
exerting non-electrostatic forces to “pump” charge from one terminal to the other. The resulting charge distributions in turn exert
electrostatic forces on carriers in regions where there is a charge
density gradient, causing them to reach a certain average drift
velocity.
Current will flow whenever there is a net force on available
charge carriers due to an uneven distribution of charge,
whether caused by a battery or not.
Capacitors are charge storage devices consisting of two
conducting surfaces separated by a nonconducting gap. Capacitance is a measure of the extent to which they can hold charge.
Bulbs contain filaments that glow visibly when sufficient
current passes through them. The filaments are characterized
by their resistance to the passage of current. If two bulbs are
connected one at a time between the same charge density difference, the higher-resistance bulb will allow charge to pass
through at a lesser rate, and will glow less brightly (see Case
18-2). But if the two bulbs are connected so that the same
current passes through them sequentially, most of the charge
density difference will be across the higher-resistance bulb, so
more work will be done and energy will be dissipated at a
greater rate in that bulb, and it will glow more brightly.
✦ Q U A L I TAT I V E A N D Q U A N T I TAT I V E P R O B L E M S ✦
Hands-On Activities and Discussion Questions
The questions and activities in this group are particularly suitable for
in-class use.
attract or repel each other? What does this tell you about
the way like charges respond to each other?
In doing the activities in Problems 18-1 to 18-3, try to forget
anything you know ahead of time about how like or opposite charges
affect each other. The goal of these activities is to deduce what they
do from what you observe. To do these activities you will need several
strips of ordinary transparent sticky tape (Magic Scotch tape works
best) about 10 cm (4 in) in length, with one end of each doubled over
(Figure 18-19a) to provide a nonstick handle. These should be used
just after being torn off the roll. Use fresh strips for each question.
(These activities are adapted from A. Arons, A Guide to
Introductory Physics Teaching [Wiley, 1990] and The Electrostatics
Workshop [AAPT, 1991], with additional helpful suggestions
by Robert Morse.)
18-2. Hands-On Activity. See instructions before Problem 18-1.
Attach the two strips of tape to each other front to back (sticky
side to nonsticky side) for their entire lengths, handles excepted.
Run your fingers along them to remove any surplus charge, so
that you can start out knowing the pair of strips is neutral.
a. If you were now to pull the two strips apart (don’t do it
yet), could they both end up with the same charge? Could
they end up with opposite charges? What does “neutral” tell
you about the charges that are initially present?
b. Now quickly separate the two strips of tape, and then bring
them close together. Do they attract or repel each other?
Does this demonstrate anything about how opposite charges
respond to each other? If so, what?
18-1. Hands-On Activity. Attach two strips of tape (described
above) in different locations on a smooth, flat, clean, dry surface (Formica and plastic surfaces work especially well) so that
the entire length of each strip except for the “handle” is stuck
flat to the surface. Run your thumbnail over the strips to ensure
good uniform contact.
a. Suppose you were to take both strips by their handles and
pull them quickly off the surface in the same way (don’t
do it yet). Should the two strips have like or opposite
charges? Explain.
b. Now pull the strips off by their handles and bring the free
ends very close (less than a cm) to each other. Do they
Fold over to produce
non-stick handle
Shown sticky
side up
(a)
Tape as
“electroscope”
leaf
(b)
Figure 18-19 Problems 18-1, 18-2, and 18-3
18-3. Hands-On Activity. See instructions before Problem
18-1. In this activity you will rub two suitable objects together
to charge them. A comb and your hair, a Styrofoam cup and
your hair, a plastic (polyethylene) bag and a garment made of
synthetic fabric are good possibilities. But first, produce two
oppositely charged strips of tape as in Problem 18-2, and suspend both from a table edge about a foot apart.
a. Suppose you brought a charged object near each of the two
strips in turn without touching and both responded in the
same way (attraction or repulsion). Could the object have the
same charge as either strip of tape? What would you have to
conclude about whether there are just two kinds of charge?
b. Now let’s see if the behavior we hypothesized in a actually
occurs. Rub various objects to charge them and bring each
object near (but never touching) each strip in turn. (If you
spend much time on this, you may have to replace the tape
strips with a fresh pair produced in the same way.) How
do the two strips respond to each object? Do they ever
respond in the same way to the same object?
c. Is there any evidence in your observations for a third kind
of charge?
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560 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
18-4. Discussion Question.
1
9
2
Figure 18-20 shows a loop of
A
3
8
conducting wire. The wire is
B
neutral, but nine typical con7
4
duction electrons, equally
5
6
spaced, have been singled
out for your attention.
Figure 18-20 Problem 18-4
a. Suppose something (such
as a battery) exerts a non-electrostatic force on electron 1
and moves it from point A to point B. How does moving
electron 1 affect the total force on electron 2? How does
electron 2 move in response?
b. How does moving electron 1 affect the total force on electron 9? How does electron 9 move in response?
c. Are electrons 2 and 9 slow to respond to the motion of electron 1, or is the response more nearly instantaneous? Explain.
d. When electrons 2 and 9 move, how does that in turn affect
electrons 3 and 8?
e. Are electrons 4 and 7 ultimately affected? Are 5 and 6?
Sketch the resulting arrangement of all nine electrons on the
loop.
f. Suppose a battery between A and B continues to pump
electrons from A to B. How do the electrons elsewhere in
the loop respond?
g. Suppose now that all the electrons are drifting slowly in the
direction shown by the arrow. Suppose the resistance
between A and B is increased. How would that affect the
motion of electron 1?
h. Because electron 1 contributes to the total electrostatic force
on electrons 2 and 9, how is the motion of those electrons
affected? How, in turn, is the motion of the remaining electrons affected?
i. What effect does increasing the resistance between A and
B have on the current in the loop? Is the current more
affected in one part of the loop than in another? Explain.
j. Would any of your reasoning be changed if instead of a
flow of electrons, you considered a conventional current of
positive charges moving the other way? Briefly explain.
18-5. Discussion Question. Popular descriptions of science
are not always accurate and may generate confusion when you
wish to use concepts carefully for orderly reasoning. A staff
member of a major science museum in a large U.S. city made
the following statement when introducing their electricity show
to a large audience: “When positive and negative attract, the
force generated in that process is electricity.”
a. What inaccuracies can you detect in this statement? First try to
answer this without going on to the specific hints in part b.
b. Is a force something different than an attraction or a repulsion? Does it mean anything to say that an attraction “generates” a force? Is electricity a force, or charge, or a current,
or what? Which of these terms have we defined carefully?
Did we define electricity ?
c. How many different meanings can you find for the word
electricity in ordinary (non-physics) usage?
d. Can you suggest any incorrect conclusions to which the staff
member’s statement might lead a listener?
Review and Practice
Section 18-1 Developing an Underlying Model
to Account for the Observations
18-6. A positively charged rod is brought toward two small
conducting spheres suspended by insulating cords. Sphere A
is attracted to the rod; sphere B is repelled by it. Indicate
whether each of the following statements about the total
charges on the spheres is definitely true, possibly true, or false:
a. A is positively charged.
d. A is neutral.
b. B is positively charged.
e. B is neutral.
c. A is negatively charged.
18-7. SSM Suppose two objects A and B start out neutral, but
when they are rubbed together, object A becomes negatively
charged.
a. If charge cannot be created or destroyed, where does A’s
charge come from?
b. What is the effect of this on object B?
c. Does a neutral object contain any positive charge? Does it
contain any negative charge? Briefly explain.
18-8. In Figure 18-2c, what happens to the arrangement of
charge on the piece of foil if the foil is carried far from the
comb without being brought in contact with a conductor?
18-9. In Step 2 of Case 18-1, the comb is replaced by a bar
magnet with its north pole forward. How will the piece of aluminum foil be affected when the magnet is brought near it?
SSM Solution is in the Student Solutions Manual
18-10. After you run a comb through your hair, the comb will
attract tiny bits of both newspaper and aluminum foil. If the
bits are of equal mass, which would you expect to be attracted
more strongly to the comb? Briefly explain.
18-11. Suppose you have tiny bits of aluminum foil and scraps
of newspaper all having the same mass. You charge a plastic
comb by running it through your hair. What could you do experimentally to determine which is more strongly attracted to the
comb? Be very specific about your procedure and how it permits
you to make distinguishable observations for the two situations.
18-12.
a. Describe a situation that will cause electrons to flow onto
a neutral object when it is grounded. What will the resulting charge on the object be?
b. Describe a situation that will cause electrons to flow away
from a neutral object when it is grounded. What will the
resulting charge on the object be?
18-13. SSM A negatively charged rod is brought near a conducting sphere suspended by a copper wire from a metal ceiling. The sphere is attracted to the rod.
a. Was the sphere initially positively charged, negatively charged,
or neutral ? Briefly explain.
b. The piece of aluminum foil in Case 18-1 was subsequently
repelled by the rod. Will the same thing happen to the conducting sphere in this situation? Briefly explain.
WWW Solution is at http://www.wiley.com/college/touger
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Qualitative and Quantitative Problems ◆ 561
18-14. A conducting metal rod is suspended by an insulating
nylon wire (Figure 18-21). A small, lightweight metal ball suspended by a nylon thread is very close to one end of the rod
but not touching it. If a positively charged rod is briefly
touched to the other end of the metal rod, what will happen
to the ball if it is initially a. has a small positive charge (compared to the charge on the rod)? b. has a small negative
charge? c. is neutral?
Nylon
threads
Positively
charged
+
++
rod
++
Metal rod
Metal
ball
Figure 18-21 Problem 18-14
18-15. Sketch charge configuration diagrams to explain what
is happening in each part of Problem 8-14.
18-16. A negatively charged rod is held a small distance to the
left of a positively charged solid conducting sphere. Because
the sphere is conducting, the excess charge on the sphere will
be mostly ____ (within the left half of the sphere; on the surface of the left half of the sphere; within the right half of the
sphere; on the surface of the right half of the sphere).
18-17. SSM Two flat metal plates are initially very far apart.
Plate A is positively charged; plate B is neutral. Plate B is then
moved until it is parallel to A and very close to it. Sketch the
initial and final charge configurations on both plates.
18-18. Use our underlying model for electrostatic forces to
explain in detail why the hair of the person in Figure 18-8b
appears as it does.
18-19.
a. Why are you at greater risk of being struck by lightning if
you are standing in the middle of an open field?
b. If you cannot quickly get to cover, what could you do to
reduce the risk?
Section 18-2 Charge Carriers
18-20. When radioactivity was first discovered, three different
kinds of radioactive “rays” were identified; they were called
alpha (a), beta (b), and gamma (g) rays. When a beam of
each kind of ray was passed between oppositely charged
plates, the alpha ray beam bent very slightly toward the negative plate, the beta ray beam bent quite substantially toward
the positive plate, and the gamma ray beam passed through
without bending at all.
a. Which of these rays might possibly be made up of electrons? Briefly explain.
b. If the alpha and beta rays both turned out to be made up
of particles, which particles would you expect to have a
greater charge-to-mass ratio? Briefly explain.
18-21. Are the charge carriers always electrons when there is
an electric current? Briefly explain.
18-22. In your own words, tell what is meant by a conventional current.
18-23. If a conventional current flows from left to right along
a copper wire, which way are the electrons flowing?
18-24. Explain in your own words why a flow of electrons
with a certain total charge in one direction along a wire is
equivalent to the flow of an equal amount of positive charge
in the opposite direction.
18-25.
a. Compare the movement of charge carriers in large molecules such as pigments and in metals.
b. Comment on the validity of the idea that “what goes on in a
metal is like one giant covalent bond among all of its
atoms.”
18-26. Positive and negative electrodes are connected to the
two terminals of a battery and dipped into a tank containing a
solution of sodium chloride (table salt) in water. This means
there are equal numbers of positive sodium ions and negative
chloride ions in the water. When the electrodes are dipped into
opposite ends of the tank, a current flows between them. Suppose we could chemically remove all the chloride ions, leaving
the number of sodium ions the same as before. When the electrodes are dipped into the tank as before, it would produce
____ (a current greater than the current that occurred with both
kinds of ions present; a current equal to that current; a current
less than that current but not zero; no current at all). Briefly
explain.
18-27. How does the permeability of a cell membrane to various chemical species affect the electrical current crossing the
membrane?
Section 18-3 The Electron Gas and the Effect
of Uneven Charge Distributions
18-28. A student argues as follows: “Batteries are the source
of current in simple electric circuits. There is a certain amount
of current that the battery can provide, and when the battery
dies, or if I take the battery away, there is no more current.”
Comment on the correctness or incorrectness of this argument.
In your comments, be sure to address the question of whether
there can ever be a current when there is no battery in the
circuit.
18-29. SSM WWW Suppose you start out with two identical
capacitors and two bulbs, A and B. First you charge the capacitors, one at a time. Then you discharge one capacitor through
each bulb. What can you conclude about either the capacitors
or the bulbs if a. bulb A glows more brightly but for a shorter
time interval than bulb B? Briefly explain. b. A glows more
brightly and also for a longer time interval than B? Briefly
explain.
18-30. When you connect the ends of a wire to a battery so
that a current flows through the wire, does the total charge
on the wire remain zero or is the wire electrically charged?
Briefly explain.
18-31. It is common to speak of “charging a battery.” Are you
transferring any charge to the battery when you do this? Briefly
explain.
18-32.
a. When you “charge a capacitor” by connecting it to a battery,
where does the charge go, and where does it come from?
b. Does the battery act as a source or supplier of charge? Explain?
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562 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
18-33. When a battery is connected through a small bulb to
a capacitor, the fact that the bulb dims and goes out after a
brief interval is evidence that the capacitor plates do not keep
gaining charge indefinitely. Use what you know about electrostatic forces on electrons to explain why a. the negative
plate of the capacitor doesn’t keep getting more negative indefinitely. b. the positive plate of the capacitor doesn’t keep getting more positive indefinitely.
18-34. A team of students finds that in Case 18-2, when they
charge and discharge the capacitor through bulb A, the bulb
glows very brightly. When they charge and discharge it through
bulb B, this bulb glows less brightly. They hypothesize that
because bulb A glows more brightly, it is permitting more total
charge to pass through and be stored on the capacitor. To test
this hypothesis, they decide to charge the capacitor through
bulb B and discharge it through bulb A.
a. If their hypothesis is right, how would the brightness of
bulb A during discharge compare with its brightness during
discharge when the capacitor was also charged through bulb
A? Why?
b. When they do the test, they observe that when they discharge the capacitor through bulb A, it glows just as brightly
and for just as long as when the capacitor was charged
through bulb A. What can you conclude from this observation? (Adapted from M. Steinberg et al., Electricity Visualized, 1990.)
18-35. Suppose that in the circuit in Case 18-2, the capacitor
is replaced by one with plates that are twice as big. If nothing else is changed, how would this affect a. the maximum
brightness of the bulb? Use the underlying model to briefly
explain your answer. b. the time it takes to dim to half its
initial brightness? Use the underlying model to briefly explain
your answer.
18-36. After the circuit in Figure 18-16a has been connected
for a few minutes, does the battery produce a surface charge
density difference? What effect, if any, does this have on current flowing in the depicted circuit? Justify your answers by
sketching the location(s) of any excess charge.
18-37. When the last connection has just been made in the
circuit in Figure 18-16b and the capacitor is just beginning to
discharge, tell whether each of the following is positively
charged, negatively charged, or neutral:
a. the surface of the wire 1 cm from the positive plate of the
capacitor
b. the interior of the wire 1 cm from the positive plate of the
capacitor
c. the surface of the wire 1 cm from the negative plate of the
capacitor
d. the interior of the wire 1 cm from the negative plate of the
capacitor
e. the entire capacitor (consider the net overall charge)
f. the entire circuit (consider the net overall charge)
18-38. Figure 18-22 shows a simB
ple closed circuit consisting of a
bulb, a battery, and connecting
wires. Three points in the circuit
are labeled (point B is on the filament of the bulb). Rank the three
+
–
A
C
labeled points according to each
of the following, listing them in Figure 18-22 Problem
order from least to greatest and 18-38
indicating any equalities: a. the
density of surface charge at each point. b. the current at each
point.
18-39. Figure 18-23 shows a simple closed circuit consisting of a
two bulbs A and B, a battery
(labeled C for cell), and connecting wires. Rank the three circuit
elements in order, from least to
greatest, according to the current
that passes through each one.
Indicate any equalities.
Bulb A
Bulb B
RB > RA
Cell C
Figure 18-23 Problems
18-39 and 18-40
18-40.
a. In which of the two bulbs in Figure 18-23 is the rate of
energy expenditure greater? Briefly explain.
b. Which of the two bulbs will glow more brightly?
Going Further
The questions and problems in this group are not organized by section heading, so you must determine for yourself which ideas apply.
Some of them will be more challenging than the Review and Practice
questions and problems (especially those marked with a • or ••).
18-41. Suppose there are equal amounts of positively and negatively charged matter in the universe.
a. How would this matter tend to rearrange itself over time if
like charges attracted and opposites repelled? Does this
agree with or contradict what we actually observe in the
universe?
b. What if opposite charges didn’t react to each other at all
(as gravitational charge doesn’t react to electric charge), but
instead charges of one kind (say, positive) were mutually
attractive and charges of the other kind were mutually
repulsive? How would this matter tend to rearrange itself
over time? Does this agree with or contradict what we actually observe in the universe?
18-42. Two objects A and B are attracted to each other. When
a negatively charged body C is brought near them, both are
attracted to C. What can you conclude about the charges on
A and B?
•18-43. A student holds an iron bar magnet in her hand. If a
positively charged Styrofoam sphere is initially half a centimeter
from the north pole and is free to move, it will be ____
(attracted to the north pole; repelled by the north pole; attracted
then repelled; unaffected by the magnet).
18-44.
a. In Case 18-1, estimate the gravitational force that the comb
and the piece of aluminum foil exert on each other at a
separation of 0.01 m.
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Qualitative and Quantitative Problems ◆ 563
b. Estimate the time it takes for the piece of aluminum foil to
jump the gap to the comb and use this to find an approximate value for the average acceleration of the foil during
this interval.
c. Calculate the force necessary to produce this acceleration.
d. Compare the values you’ve obtained in a and c. Express
in a
the comparison as a ratio FF found
found in c . Briefly explain the significance of this comparison (or this ratio).
18-45. SSM WWW A common device for detecting electric
charge is the electroscope (Figure 18-24a). The metal knob at
the top is connected via the conducting metal post below it
to two metal foil leaves suspended from the bottom of the
post.
a. When a charge is transferred to the knob, what will happen to the foil leaves? Why? How does this compare to the
effect shown in Figure 18-8b?
b. Suppose you temporarily ground the electroscope by touching the knob with a finger to neutralize it. You then remove
your finger and bring a positively charged rod very near but
not touching the knob of the electroscope. What happens
to the leaves when the rod is close? Sketch a charge diagram to explain what happens. Is there a net charge on the
electroscope? How is it distributed?
c. What happens to the leaves when the rod is moved a little further from the knob? Explain your answer in terms of
the forces that charge carriers exert on one another.
Glass
Metal ball and
stem provide
conducting path
to leaves
+ + ++
+++
Metal foil
leaves
(a) Metal foil leaves of
electroscope hang
straight down
when uncharged
(b) A step in charging
the electroscope
by induction
Figure 18-24 Problems 18-45, 18-46, and 18-67
18-46. Charging by induction. A positively charged rod is
again brought close to the knob of a neutral electroscope without touching it, and the leaves respond as in Problem 18-45.
a. With the rod kept in this position, a student places her finger in contact with the knob, as in Figure 18-24b. What
happens to the foil leaves? Why? Draw a charge configuration diagram to support your explanation. Is there a net
charge on the electroscope? How is it distributed?
b. The student then removes her finger while the rod remains
in the same position. Now what happens to the foil leaves?
Why? Again, draw a charge configuration diagram to support your explanation. Is there a net charge on the electroscope? How is it distributed?
c. Finally the rod is removed. At this point there is a net charge
on the electroscope. Is it positive or negative? How is this
charge distributed? What would you see as evidence that
the electroscope is charged?
d. This is called charging by induction. We say the final
charge on the electroscope was induced by the charged
rod because it was not transferred from the rod, but it was
caused by the presence of the rod. Where did the final
charge on the electroscope come from? Briefly explain.
18-47. Are fabrics that develop static cling conductors or insulators? Briefly explain how you can tell.
18-48. Golfers are frequent lightning victims. What are some
of the factors that contribute to this? (Assume golfers have as
much common sense as other people.)
18-49. A lightning rod always has a wire connected to its
lower end. To what should the other end of the wire be connected? Why?
18-50. Jumper cables are used to recharge a car battery by
connecting it to the battery of another car. It is possible (but
not safe) to do this by connecting one cable between the positive terminals of the two batteries and the other between the
negative terminals of the two batteries.
a. Why do the safety instructions tell you that instead, you
should connect an end of one cable to your engine block
or car frame?
b. What would happen if you ran each cable between the positive terminal of one battery and the negative terminal of
the other?
18-51. SSM A positively
Charge configuration before
rod is brought near
charged rod is brought
close to a grounded conducting sphere (Figure
+ – +
++++
+
18-25). Unlike the usual
+– + – +
– + – +–
charge configuration dia– + –
gram that shows only
excess charge, the figure shows representative
Ground
charges on the sphere in Figure 18-25 Problem 18-51
its initial (neutral) state.
Show what happens to these charges by drawing the resulting
charge configuration on the sphere
a. if only positive charges are free to move in conductors.
b. if only negative charges are free to move in conductors.
c. if both positive and negative charges are free to move in
conductors.
d. Now draw a usual charge configuration diagram showing
only the final distribution of excess charge for each of these
cases. Does the distribution of excess charge depend on
whether you think about a flow of electrons or about a conventional current of positive charge? Explain.
18-52. What advantage is gained by making the upper part of
the Van de Graaff generator spherical?
18-53. If the bottom of a small bulb is placed against one terminal of a battery, and no other connections are made, a. will
there be any flow of charge at any time? Briefly explain. b. will
the bulb light up? Briefly explain.
18-54. If the circuit in Figure 18-16a were assembled using a
capacitor with only a thousandth of the capacitance of the one
shown, a. would there still be a transient current through the
bulb? Briefly explain. b. would you still see the bulb light up?
Briefly explain.
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564 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents
A
18-55. In the circuit in
Figure 18-26, bulbs A and
B
B are connected between 1
2 (RB > RA)
the same points 1 and 2.
Bulb B has greater resist+ –
ance than bulb A.
a. Sketch a charge config- Figure 18-26 Problems 18-55,
uration diagram show- 18-56, and 18-57
ing the distribution of excess surface charge along this circuit at an instant when the capacitor has just begun to
charge (after the switch is closed).
b. Repeat a for an instant when the capacitor is fully charged.
18-56. In the circuit in Figure 18-26, bulbs A and B are connected between the same points 1 and 2. Bulb B has greater
resistance than bulb A.
a. At an instant when the capacitor has just begun to charge,
is the difference in surface charge density between the ends
of bulb A less than, equal to, or greater than the difference
between the ends of bulb B? Briefly explain your answer.
b. Through which bulb will more current flow? Briefly explain
your answer.
c. Which bulb will glow more brightly? Briefly explain your
answer.
d. Consider the extreme case in which the resistance of bulb
B’s filament is so great that the filament is in effect an insulator. In this case, through which bulb will more current flow?
e. In the case described in d, which bulb will glow more
brightly?
f. Are your answers to d and e the same as your answers to
b and c? Should they be? Briefly explain.
18-57. Compare and contrast the behavior of the circuits in
Figures 18-26 and 18-17.
18-58. Batteries make use of chemical reactions in which one
chemical species gives up electrons and another acquires them.
a. Why does a battery wear out when an external conducting
path is established between its terminals?
b. Why is it especially unwise to keep a very low-resistance
conductor like a short length of copper wire connected
between the terminals of the battery?
18-59. SSM The circuit in Figure 18-27
is identical to the circuit in Figure
18-16a, except that a second capacitor identical to the first one has been
connected between points 1 and 2.
a. Compare the brightness of the
bulbs in the two circuits just after
clip B is connected to complete
the circuit. Briefly explain.
b. Compare how long the bulbs in
the two circuits glow once clip B
is connected. Briefly explain.
Clip B
+
–
1
2
Figure 18-27 Problem
18-59
18-60. The circuit in Figure 18-28 has the
same elements as the circuit in Figure
18-16a, but they are arranged differently.
a. Compare the brightness of the bulbs
in the two circuits just after clip B is
connected to complete the circuit.
Briefly explain.
Clip B
+
b. Compare how quickly the capacitors in the two circuits
charge once clip B is connected. Briefly explain.
18-61. Draw the simplest schematic circuit diagram you can
for the circuit depicted in Figure 18-29.
+
– +
–
Figure 18-29 Problems 18-61
18-62. In a series of popular lectures in 1934, British Nobel
laureate W. L. Bragg proposed the following analogy: “Now
suppose I take the spare cash in my pocket and hand it over
to you. Ought I to say that a current of riches has passed from
me to you, or that a current of poverty has passed from you
to me? Unfortunately . . . it was as if everyone agreed to say
that the current of poverty passed from you to me, before it
was realized that the actual cash . . . went from pocket to
pocket in the opposite direction” (W. L. Bragg, Electricity, Macmillan,
New York, 1936, p. 57). To what situation in physics was Bragg
referring? What in the physics situation is like the cash in the
situation Bragg described? What in the physics situation is like
the “current of poverty” in this situation?
18-63. When a positively charged rod is brought near some
tiny shreds of newspaper, the shreds are attracted to the rod.
What would happen if the rod were negative instead? Why?
18-64. Suppose you have
only the bulb, battery, and
+
–
single piece of flexible conducting wire that are shown in
Figure 18-30. Very carefully
sketch a way of arranging
these circuit elements that
would make the bulb light. Be Figure 18-30 Problem 18-64
sure that your sketch shows
clearly where the wire is making contact with other objects.
18-65. A simple closed circuit consists of a battery connected
to a bulb by wires. Within the battery, does the conventional
current flow from the negative terminal to the positive terminal
or from the positive terminal to the negative terminal? Briefly
explain.
18-66. In each of two set-ups, a capacitor is charged by connecting its plates to the two terminals of a battery. The setups are identical, except that the wires in set-up B have greater
resistance than the wires in set-up A. Is the charge acquired
by the capacitor in A less than, equal to, or greater than the
charge acquired by the capacitor in B? Briefly explain.
–
Figure 18-28
Problem 18-60
18-67. The leaves of an electroscope (Figure 18-24a) spread
out when a positively charged rod is brought close to but not
touching the ball at the top. In this situation, the ball is ____
and the leaves ____. Briefly explain.
a. positively charged . . . are both negatively charged
b. negatively charged . . . are both positively charged
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Qualitative and Quantitative Problems ◆ 565
c. neutral . . . are both negatively charged
d. neutral . . . are both positively charged
e. neutral . . . have equal but opposite charges
18-68. In Case 18-1, we assumed that the suspended piece of
aluminum foil started out neutral before being attracted to the
negatively charged comb. We can best show that this is actually the case by bringing (a positively charged rod; other negatively charged objects; a second, identically treated piece of
aluminum foil) close to it and seeing what happens. Give a
reason for your choice.
18-69. If you think of your body’s circulatory system as being
analogous to an electric circuit, a. what in your circulatory system is analogous to a battery in the electric circuit? b. what in
the circuit is analogous to blood pressure in your circulatory
system?
18-70. Example 18-2 (Figure 18-5) involved an effective transfer of positive charge. Suppose that the conducting sphere is
metallic, so that the charge carriers that are free to move are
actually negative electrons. How do the electrons move? Sketch
diagrams showing the stages of the motion.
18-71. A positively charged rod is held a small distance to the
left of a neutral solid conducting sphere. Because the sphere
is conducting, there will be excess electrons ____ (within the
left half of the sphere; on the surface of the left half of the
sphere; within the right half of the sphere; on the surface of the
right half of the sphere).
P r o b l e m s o n We b L i n k s
18-72. Suppose you wanted to show that the piece of aluminum foil involved in the observations in WebLink 18-1
started out neutral.
a. Could you accomplish this by putting it next to a charged
object to see what happened? If so, tell whether the object
should be positively or negatively charged. If not, briefly
explain why not.
b. Could you accomplish this by putting it next to an identical piece of aluminum foil to see what happened? Briefly
explain.
18-73. Which (one or more) of the following ideas is necessary to explain why the aluminum foil is attracted to the
charged comb in WebLink 18-1?
a. Opposite charges attract.
b. Like charges repel.
c. The foil acquires an opposite charge from the comb.
d. Charge can travel in conductors.
e. Charges exert less force on each other when further apart.
18-74. Suppose the aluminum foil in WebLink 18-2 is replaced
by a kind of metal foil that has only one conduction electron
contributed by each atom. Just before the foil actually touches
the comb, is the number of conduction electrons in the part
of foil furthest from the comb less than, equal to, or greater
than the number of positive ions in that part of the foil?
18-75. In WebLink 18-3, the conduction electrons on the lower
wire surface don’t all get “pumped” to the upper wire surface
because as more electrons accumulate on the upper wire ____
(the battery runs down; the electrostatic force they exert on
other electrons increases; the pressure builds up; the battery
runs out of electrons).