Electrical Phenomena: Forces, Charges, Currents

CHAPTER EIGHTEEN

Electrical Phenomena: Forces, Charges, Currents

In Chapter 4, we introduced the idea of interactions at a distance orequivalently of action-at-a-distance forces: gravitational,electrical or electrostatic, and magnetic. We have treatedone of these, the gravitational force, in considerabledetail. But although gravitational forces may be farmore conspicuous in your direct experience, electri-cal forces are every bit as pervasive in the uni-verse.This was true even before the electronicage—indeed, even before the emergence of lifeon Earth—because electrical forces are centralnot only to the operation of electronic devicesbut to the fabric of matter itself.

In this chapter we will develop qualitativelyan underlying model that will enable us to explaina range of electrical behaviors. In the chapters that fol-low, we will formulate these ideas quantitatively.

“. . . electrical forces are central not only to the operation ofelectronic devices but to the fabric of matter itself.”

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18-1 Developing an Underlying Model to Account for the Observations

The ancient Greeks made the first known observations of electrostatic effects. Justas you may observe that a comb run through your hair attracts bits of tissuepaper, the ancient Greeks found that a briskly rubbed piece of amber wouldattract small bits of various materials. The Greek word for amber is elektron, sothe 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 substancessuch as amber, glass, and precious stones. In the seventeenth and eighteenth cen-turies, such materials were called electrics, because they were amber-like in theirbehavior. Numerous modern materials display the same behavior, among themcellophane, Styrofoam, the polyurethane of plastic bags, Mylar, audio or videotape, 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 repelledby it and not be attracted again until it had come in contact with yet anotherbody. The following sequence of events repeats his observations with everydaymaterials.

How can we explain what we observed in Case 18-1? You could readily ver-ify with a refrigerator magnet that aluminum does not respond to magnets, sothe forces involved here are not magnetic forces. Your massive physics bookdoesn’t attract the foil either; gravitational forces between objects this size are fartoo weak to produce these effects. So the electrostatic force is clearly a differentkind of force.

544 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents

Important: Although the following steps arefully described, reading a description cannotsubstitute for making the observations foryourself. You are strongly urged to do this asan On-the-Spot Activity.

Materials needed: a plastic comb, ahuman hair (about 5 to 10 cm long) or finethread, a small piece of aluminum foil about

a little glue or substitute (seebelow), and an inch of tape.

Apply some glue to one side of the aluminumfoil—or make it sticky by wiping it against a freshlylicked stamp or hard candy—and fold it in half aroundone end of the hair, with the sticky side in (Figure18-1a). Press the halves firmly together. You are nowfully equipped.

Step 1: Use the tape to hang the hair by the free endso that the aluminum foil at the other end dan-gles freely. Then run the comb briskly throughyour hair.

Step 2: Bring the comb, teeth forward, to within a cmof the foil. You will observe the foil attractedstrongly toward the comb. It may remain in

contact with the comb anywhere from a fewseconds to a minute or more (Figure 18-1b).

Step 3: But then, without your doing anything more,the foil will jump sharply away from the comb(Figure 18-1c). If you move the comb slightlytoward the foil at this stage, the foil will edgefurther away from the comb.

Step 4: Touch the aluminum foil firmly with the fingersof your other hand (the one without the comb).Maintain this contact for a couple of seconds,then release it so that the foil once again dan-gles freely from the hair. Bring the comb closeto the foil again. You will observe that the foilis once again attracted.

1 cm � 12 cm,

Case 18-1 ◆ Comb and Foil: Some Observations in Need of an Explanation

(a) (Press halves together) (b) (after running comb through your hair)

(c) a few seconds later

1 cm × cmAluminum foil

12

Hair

Tape

Stickyside in

Figure 18-1 Evidence of electrical forces in simple materials.

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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 grav-itational mass, is responsible for the gravitational force, we might assume thereis some other property of matter or substance within matter giving rise to theelectrical or electrostatic force. In older English usage, a charge meant a load car-ried by anything, whether the carrier was a cannon or a horse. Because this prop-erty or substance was “carried” by matter, it was called the electric charge. Thisdoesn’t tell us what was being carried. We could as well have called it the elec-tric whatsit; calling it charge doesn’t mean we understand its nature. In fact, forthe same reason, we could equally well have referred to gravitational mass asgravitational charge. Some modern authors have used this term to stress the con-ceptual similarity, but its use is not common practice.

Gravitational forces are always attractive, but our observations show evidenceof both attractive and repulsive electrostatic forces. One kind of charge, alwaysbehaving the same way, could not account for both. A simple assumption con-sistent with the evidence is that there are two kinds of charge: We call these posi-tive and negative. We can account for our observation of both attraction andrepulsion by supposing that opposite charges attract each other, and like chargesrepel 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 negativelycharged matter in the universe. How would this matter tend to rearrange itself overtime if like charges attracted and opposites repelled? What if opposite charges didn’treact 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 chargesof 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 seemto be charged until that point. But we didn’t do anything to the foil. Why shouldit 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.

Suppose we now make two further assumptions:

• 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 electriccharge. It fits with the evidence that the appearance of positive charge in oneplace is always accompanied by the appearance of equal negative charge some-where else. The last assumption provides a way that the usual neutral situationcan be altered if we can’t “create” charge. The negatively charged comb attractsthe 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 thatin metals, only the electrons, which are negative, can move.) But if there is repul-sion as well as attraction, why is the aluminum foil attracted to the comb? Wemust add yet another assumption to the model:

• Electrostatic forces decrease with distance.

��

+++

–––

–––

–

Negativelycharged

––––

––––––––––

––

±±±

–––

–– – ––––––––––––– –––––––

–––

–––––

––––––––––

–

–

–––

–––

Figure 18-2 Charge configurationdiagrams for Case 18-1.

(a)

(b)

(c)

(d)

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With this assumption, if the negative charges are further from the comb, they willbe repelled less strongly than the positive charges are attracted. The total forceis then toward the comb, and the foil is attracted to it. But the negative chargeson the comb also repel one another. Once the foil is touching the comb, someof these negative charges can move onto the aluminum foil. Now both bodieshave net negative charges, and they repel each other. We have now explainedSteps 1 to 3 of Case 18-1. For a graphic step-by-step presentation of the reason-ing that explains these observations, go WebLink 18-1.

When you bring your fingers in contact with the foil (Step 4 and Figure18-2d) after it has gained negative charge from the comb and been repelled,mutually repelling negative charges on the foil can now get farther from oneanother by traveling into your body and possibly spreading from there to theground or Earth. So little charge remains on the foil that it is once again effec-tively neutral. This explanation makes yet another assumption—namely, thatcharges could travel through your finger and body much more readily thanthrough the hair connected to the foil. We therefore add another assumption toour 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 differ-

ent stages of the observations in Case 18-1. After each new action, we try toshow the system when there is no longer any net movement of charge. At thatstage, we say that the system is in electrostatic equilibrium. The changes inconfiguration from one diagram to the next are governed by our assumptionsabout how charges behave. Drawing these diagrams is important for visualizingwhat is going on in the underlying model, which we adopt because it explainsthe behaviors that we actually observe. We are again in the business of lookingfor the basic rules by which the game of nature is played.

The diagrams in Figure 18-2 illustrate point 3. Example 18-1 illustrates the sig-nificance of point 2d.

PROCEDURE 18-1Charge Configuration Diagrams

1. Diagrams should show the distribution of charges on each body. Plus or minus signs in a region indicate an excess of positive or negativecharge in a region. Regions that are neutral and have a uniform mix of pos-itive and negative charges are unmarked.

2. In each diagram, the distribution of charges will be governed by the natureof electrostatic forces and the extent to which the charges can move inresponse 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 byfactors 2a–d.

4. Arrows (in contrasting color) indicate how charge has moved.

1�21� 2

For WebLink 18-1:A Model to Explain Electrical Attractionsand Repulsions, go towww.wiley.com/college/touger

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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 ona thread or wire. A negatively charged rubber rod is briefly brought in contactwith the other end of the rod and then removed. This procedure is repeatedfor three different instances:

Horizontal rod made of . . . and hung from . . .

Instance I metal nylon thread

Instance II glass nylon thread

Instance III metal copper wire

STOP&Think Before continuing, see if you can figure out what will happen tothe piece of foil in each case. ◆

In instance I, the piece of foil is immediately repelled by the horizontalrod and remains repelled when the rubber rod is removed. In instances II andIII, no repulsion is observed. Use charge configuration diagrams to explainthese behaviors.

Brief SolutionChoice of approach. The mutual repulsion of like charges and mutual attrac-tion of opposite charges must govern the behavior that we see.

Diagrams and reasoning. If two bodies repel, there must be like charge onthem. The only source of excess charge is the rubber rod. If the metal rodpermits the passage of charge, the mutually repelling negative charges that startout on the rubber in Figure 18-3a will get as far away from one another asthey can and thus distribute themselves over the metal rod and the foil. Oncerod and foil are both negatively charged, they will repel each other. We there-fore 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 hori-zontal rod is made of glass. If no repulsion takes place, we must infer thatexcess negative charge has not spread to the far end of the rod and to thefoil, 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 apossible path for the excess charges. Like glass, nylon does not permit the pas-sage of charge. But copper is a metal. The charges can therefore get farther

Metal ceiling

Aluminumfoil

Touching

Nylonthreads

Metal rod

Touchchargedrubber andmetal rod

Symbolic representationof grounding in (b)

–––––––– ––––

–––

Nylonthread

Copperwire

––––– ––––

––––––––––––––––––––

––––– –

(a) (b) (c)

Figure 18-3 Grounding a conductor. If the aluminum foil in this arrangement weresuspended by an insulating thread (a), negative charge would spread from the rubberrod through the metal rod to the aluminum foil. The negatively charged metal rod andaluminum foil would repel each other. But in (b), the copper wire allows the negativecharge to spread over a much larger conducting region, preventing enough concentrationof charge to produce a visible repulsion. Preventing an accumulation of charge in thisway is called grounding.

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away from one another by going up the copper wire and spreading out overthe metal ceiling (recall point 2b in Procedure 18-1), as in Figure 18-3b. Theexcess charge becomes so spread out that the excess negative charge in anyone 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 passageof charge very quickly. A material that does this is called a conductor. Metalsare good conductors. Other materials, such as glass, do not readily permit thepassage of charge. A material of this type is called an insulator. Like conduc-tor, insulator is not an absolute term. Materials may be conducting or insulatingto various degrees. Until we make these ideas quantitative, we will make do byspeaking of good or poor conductors and insulators.

A wire connected to the ground or Earth would have the same effect as thecopper wire in the above example or in the similar situation in Figure 18-3a andb, so any large body where excess charge can spread out when connected by awire is called ground (the British call this earth). Connecting an object to groundis called grounding. When you use jumper cables to start your car, one termi-nal must always be connected to the engine block or car frame, which serves asground, to prevent a dangerous build-up of excess charge. The usual symbol forground in diagrams is (Figure 18-3c). It is possible to charge an object con-nected to ground by bringing an already charged object near it, without trans-ferring any charge from that second object. (For the details of this process, calledcharging by induction, see Problem 18-46.)

In Case 18-1 (Figure 18-2), we looked at situations in which electrostatic forcesproduce a separation of charge. Figure 18-4 shows that this separation can result

either from positive charge moving one way or negative chargemoving the opposite way. Because it is a pain in the neck tobe worrying about minus signs all the time, physicists oftentake advantage of this fact to describe situations in terms of themovement of positive charge, even when negative charge ismoving the other way. We have not yet established whetherone or both kinds of charge are able to move in various con-ducting materials. So in the following example, for instance, inwhich positive charge is effectively transferred to a region of a

conducting sphere, it may actually be that negative charge is being transferred awayfrom that region or that both are occurring.

–+–

+–

+–

+–

++–

+––

+–

+–

+–

+–

+

+–

+–

+–

+–

+–

+–

Both movements resultin the same net negativecharge on the left andthe same net positivecharge on the right.(highlighted areas neutral)

Summary chargeconfiguration foreither (b) or (c)

+ charge shifts to right

– charge shifts to left

Conductor

(a)

(b)

(c)

(d )

+ +

+ +

– ++ +

–+–

+–

+–

+–

++–

+––

+–

+–

+–

+–

+ Both movements resultin the same net negativecharge on the left andthe same net positivecharge on the right.(highlighted areas neutral)

Summary chargeconfiguration foreither (b) or (c)

+ charge shifts to right

charge shifts to left

(b)

(c)

(d )

+ +

+ +

– ++ +

Example 18-2 Charge Distributions on Conductors, I

Figure 18-5a shows an isolated conducting sphere. Some positive charge iseffectively transferred to a small region of the sphere at some instant. How isthe charge distributed when the sphere reaches electrostatic equilibrium?STOP&Think Attempt to do the reasoning yourself before reading the solution. ◆

SolutionChoice of approach. We can apply point 2b of Procedure 18-1.

Diagrams and reasoning. The excess positive charges repel one another, sothat the charge spreads out as far as the conducting material permits. It thusends up distributed uniformly over the surface of the sphere (Figure 18-5b).For the same reason, any excess charge on a conducting body in equilibriumwill always be located on the surface, although not always distributed uniformly.

◆ Related homework: Problem 18-16.

Figure 18-4 A flow of negativecharge in one direction is equiva-lent to a flow of positive chargein the other.

EXAMPLE 18-1 continued

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Instant chargeadded

(a) Electrostaticequilibrium

(b) Instant chargeadded

(c) Electrostaticequilibrium

(d )

+ +++

++++

++

+

+

+

+

––––++++

–+

–+

–+

–++

+

Conducting sphere Parallel conducting platesFigure 18-5 Figures for Examples18-2 and 18-3.

Example 18-3 Charge Distributions on Conductors, II

Figure 18-5c shows an edge view of two thin conducting metal plates (thethickness is exaggerated in the diagrams) separated by a nonconducting gap.Equal and opposite amounts of charge are effectively transferred to smallregions of the plates at some instant. How is this charge distributed when thesystem reaches electrostatic equilibrium? STOP&Think Once again, try to dothe reasoning yourself before reading the solution. ◆

SolutionChoice of approach. We can again apply Procedure 18-1.

Diagrams and reasoning. As in Example 18-2, and for the same reason, theexcess charge on each conductor spreads out over its surface, but this timenot uniformly over the entire surface. Because the opposite charges on the twoplates 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 twoplates (Figure 18-5d ). The distribution will be essentially uniform over the innerfaces, except near the edges.

◆ Related homework: Problem 18-17.

If the charges in Figure 18-5d are truly in equilibrium, there must be con-straining forces on the charges that are equal and opposite to the forces that thepositive and negative charges exert on each other. The constraining forces areexerted either by the conducting surfaces or the intervening medium; we will notconcern ourselves with the details. If the two opposite concentrations of chargebecome sufficiently large, the electrostatic forces on the charges will exceed themaximum constraining forces, and charges will jump across the gap between thecharged objects. This happens when charges build up on clouds, causing an oppo-site buildup of charge on Earth’s surface, until finally there is the discharge thatwe know as lightning.

The forces that individual charges exert on each other are directed towardeach other if attractive, away from each other if repulsive. When like charges areon a flat or gently curving surface of a conductor, the repulsive forces they exertare essentially along the surface (Figure 18-6a), causing the charge to spread outon the surface. On a needle-like projection (Figure 18-6b), the forces those samecharges exert on each other would be essentially perpendicular to the surfaceand thus would not contribute significantly to spreading. Consequently, on irreg-ularly 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 ratherthan flat expanses of ground or roof.

Figure 18-6 Repulsive forces thatsurface charges on conductorsexert on each other. (a) Forcesmostly parallel to gently roundedsurface. (b) Forces mostly perpendi-cular to the surface of a sharp point.

++

++

(a) (b)

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18-2 Charge CarriersIn 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 unal-terable trait. As the carriers move, their charge goes with them.

In general, we will refer to the movement or flow of charge from one placeto another as an electric current, or simply a current. This definition is pre-liminary. Later we will define current quantitatively, but we will retain the notionthat 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 existenceof charge-carrying particles. The 1771 Encyclopaedia Britannica, reflecting theprevalent views of the time, described electricity as a “very subtile fluid . . . capa-ble of uniting with almost every body.” Whether it be fluid or particles, we assumeit gets set in motion because an electrostatic force is exerted on it. If we alsoassume that the relationship between forces and motion is always governed byNewton’s second law of motion, we must attribute inertial mass as well as elec-tric charge to whatever is moving.

Subsequent experimentation validated viewing electrical phenomena in termsof forces and motion. Eighteenth-century investigators found that by rapidly rotat-ing a large glass globe against a suitable rubbing surface using a wheel and beltmechanism (Figure 18-7a), the rubbing would result in a very substantial chargeon the globe. A modern device that makes more sophisticated use of a continu-ous belt conveyor to develop charge on a metallic globe is the Van de Graaffgenerator (Figure 18-7b), invented by Robert J. Van de Graaff in 1929. A con-ductor brought in contact with the globe also becomes charged (Figure 18-8).Investigators using either device have found that when a large enough charge isdeveloped on the globe and a conducting body is brought sufficiently close, avisible and audible spark jumps from the globe to the conducting body (Figure18-7b), much as lightning jumps from clouds to Earth. The charges that remainafter the spark are found to be reduced, indicating that charge has jumped thegap, and providing evidence of motion brought about by electrostatic forces.

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.

➥A note on language: Althoughelectric current has sometimes beencalled electricity, the word electric-ity in common usage has a varietyof related meanings, such as thestudy of all electrical phenomena.To avoid confusion, we introduce aless ambiguous term.

➥A note on language: We use theterm electrostatic forces even whencharge carriers are in motion, becauseunless their speeds exceed 0.1c, theelectrical forces on them are essen-tially the same as when they are sta-tionary or static. This is not a concernin electric circuits.

(a) (b)

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18-2 Charge Carriers ◆ 551

STOP&Think Why won’t the spark jumpto an insulator? Draw diagrams showingthe configuration of charges on the con-ductor before and after it is brought neara positively charged sphere. Does your“after” configuration account for a forcethat could cause charge to jump the gap?Why can’t you get the same “after” con-figuration for the insulator? ◆

By the late nineteenth century, inves-tigators were able to obtain not just briefsparks but sustained “rays” or beamsbetween two conducting terminals onwhich opposite charges were continuously replenished. These beams were pro-duced within sealed glass chambers and caused a glow where they struck thefluorescent material coating the glass surface at one end (Figure 18-9). Becausethe negatively charged terminal was called a cathode, the beams were calledcathode rays, and the glass chambers cathode ray tubes. These were the prim-itive ancestors of most television, personal computer, and oscilloscope tubes(before widespread use of liquid crystal displays), in which, by rapidly varyingthe direction of the beam, a pattern of light is produced on the end of the tubethat the viewer sees.

English physicist J. J. Thomson (1856–1940) observed that when oppositelycharged plates were positioned above and below the beam, the beam deflectedtoward the positive plate, indicating that the beam itself was negatively charged.Moreover, for any given amount of charge on the plates, the beam deflected afixed amount; there was no spreading out of the beam. Thomson reasoned asfollows: (1) Imagine the beam to be a stream of separate tiny particles. Thom-son called these particles “cathode corpuscles.” (2) The electrostatic force will bethe same on all particles having the same charge. (3) The force will produce anacceleration, and thus a deflection 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 par-ticles having equal charge could have different masses, the particles wouldundergo different accelerations. They would therefore deflect by different amounts,and there would be a spread. (6) But there is no spread. So particles with thesame charge must have the same mass (and vice versa), and so the ratio of chargeto mass must have a fixed value.

Thomson’s cathode corpuscles are today called electrons, and for establish-ing its charge-to-mass ratio (treated in Chapter 24), Thomson is generally cred-ited with being the electron’s discoverer. His reasoning established clearly that agiven amount of charge moves with a fixed amount of mass. This supports ouridea of charge carriers. Thomson further surmised that his particles were funda-mental components of all matter, as we now know electrons to be.

But there is nothing in this reasoning that logically requires the carriers to beseparate particles rather than a continuous flow of matter. (People knew there

y � 12 at2,

+

++

+

++

++

++

+++

++

+

+++++++++++

+

+ +

Unchargedelectroscope

Metallic leavesof electroscopebecome positivelycharged and repeleach other.

++

+++

+ + +

Figure 18-8 Transfer of chargefrom Van de Graaff generator toconducting bodies.

Figure 18-9 The cathode ray tube.

Heated anode (–)emits electrons...

...which areacceleratedthrough cathode

Plates to deflectbeam vertically

Plates to deflectbeam horizontally

Glow wherebeam strikesfluoresentcoating

Beam

+–

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was a fixed ratio of hydrogen to oxygen in water long before they knew thatwhat we experience as a continuous fluid was made up of individual molecules,each containing two hydrogen atoms and one oxygen atom.) The particle naturewas confirmed, however, by American physicist Robert A. Millikan (1865–1953).

In his famous oil drop experiment (1910–1913), Millikan put oil in an atom-izer to obtain tiny individual droplets that could acquire electric charge from con-tact with ions in the air. By allowing the droplets to enter a region between oppo-sitely charged plates, he could measure their terminal velocities. Knowing all theother forces on each droplet, he could determine the electrostatic force on it andfrom that its charge. He found that the charges on the droplets were always inte-ger 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 con-stant, then the fixed amounts of charge must be carried by pieces of matter withfixed amounts of mass, in other words, particles.

Experiments such as these began to shape our present-day ideas about thestructure of matter. Atoms contain positive nuclei surrounded by negative elec-trons. The nuclei are in turn made up of positive protons and neutral neutrons.The positive and negative particles exert electrostatic forces on one another. Undersome circumstances, an outer electron of an atom may be more attracted to thepositive nucleus of a neighbor atom than to its own, and will be pulled to theother nucleus, giving its new home atom a net negative charge and leaving itsprevious home atom with a net positive charge. Atoms charged in this way arecalled positive and negative ions.

Moving ions are also charge carriers. Electric currents in liquids generallyinvolve the movement of ions. This is the case in many processes that you arelikely to encounter in more detail in your chemistry course, such as electrolysis,electroplating, and the operation of certain types of batteries. In your own bodyand in all living things, which are mostly water, some kinds of ions can passthrough particular cell membranes more readily than others (the membrane is saidto be permeable to these ions). This can result in net positive and negative chargeson opposite sides of a membrane. Such charge distributions have great impor-tance for biological systems. In neurons (nerve cells), for example, the propertiesof a membrane may change in response to a stimulus such as heat or light or asignal from a neighboring neuron. This “information” to the cell membrane mayitself take the form of the arrival of charge carriers to the membrane, which inturn can react chemically with components of the membrane. When the mem-brane changes properties, its permeability for different ions changes, and there isan ion flow across the membrane. This flow, or current, passed on from neuronto neuron, is the signal that carries information in the nervous system.

Chemical reactions are likewise the result of electrostatic forces. In ionic bond-ing, ions of opposite charge attract each other electrostatically; in covalent bond-ing, electrostatic forces are exerted on shared electrons by more than one nucleus.Roughly speaking, chemical reactions—changes in the bonding situation—are achange in the configuration of charge carriers (positive nuclei and negative elec-trons) in response to electrostatic forces. (We will need to refine this descriptionin Chapter 27.) This is true both of the simplest reaction between two atoms andall the multistep reactions among complex molecules that make up the processesof 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 manyatoms that make up the molecule. This is true, for example, in pigment mole-cules, such as rhodopsin in the rods and cones of the human eye and chloro-phyll 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 visionor in photosynthesis.

Metals carry this property to an extreme. The outermost electrons are sharedby all the atoms making up a piece of metal and so can travel throughout the

Nerve cells or neurons. An electriccurrent consisting of a flow of ionsfrom neuron to neuron is the signalthat carries information in the nerv-ous system. The neurons here aremagnified 2500 times by a scanningelectron microscope.

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18-3 The Electron Gas and the Effect of Uneven Charge Distributions ◆ 553

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 havedeveloped so far. The charge carriers in metals, and therefore in the wires ofordinary electrical devices, are electrons. When electrons move from a region,they leave positive ions behind. Thus, if a negatively charged object is broughtnear a piece of metal, the nearest part of the metal’s surface becomes positivenot because positive charge carriers move onto that part but because electronsleave it. For a step-by-step graphic presentation of this reasoning, work throughWebLink 18-2.

Because most electrical devices use metal wires in which the carriers are elec-trons, 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 equiva-lent in its effect to a flow of positive charge in the other. The flow of positive chargeis called a conventional current (conventional means it is something that weagree on) and is usually what is meant by current in quantitative treatments.

✦POLARIZATION We mentioned earlier that after you run a comb through yourhair, it attracts small bits of paper. But paper is not a conductor. Placing paperbetween copper wires prevents current from passing from one to the other. Card-board cylinders serve as insulators in the bulb sockets of older light fixtures. Inexplaining why aluminum foil is attracted to the comb, we assumed that a sep-aration of charge could occur in the aluminum (Figure 18-2b) because charge canmove through a conductor. Then what happens in the paper?

Understanding that molecules have both positive and negative parts enablesus to propose a satisfactory model of what goes on in this case. We suppose thatalthough the molecule is neutral overall, it may have more of its positive chargeat one end and more of its negative charge at the other. Because it has two oppo-sitely charged “poles,” it is called an electric dipole.

Like other atoms and molecules, these dipoles will jiggle about in thermalmotion, and will ordinarily be randomly oriented (Figure 18-10a). But a chargedrod brought near them causes them to pivot into alignment with the oppositelycharged poles drawn towards the rod and the like charged poles repelled (Fig-ure 18-10b). The resulting separation between the average positions of the posi-tive and negative constituents is called polarization. Because the positive chargeson average are slightly closer to the rod, there is a small net attraction.

18-3 The Electron Gas and the Effect of Uneven Charge Distributions

An image that physicists sometimes find useful in describing metals is that of anegative electron gas pervading a connected lattice of positive ions (Figure 18-11).The electrons are pictured as mobile in somewhat the same way that moleculesin an ordinary gas are mobile, and, like the molecules in an ordinary gas, the elec-trons move around randomly when there is no net flow overall.

For WebLink 18-2:Movement of Charge

in Metals, go towww.wiley.com/college/touger

➥Some molecules (called polarmolecules) are dipolar even in elec-trically neutral surroundings; othersbecome polarized only if anothercharged body exerts opposite elec-trical forces on their positive andnegative components.

Figure 18-10 Polarization: a modelto explain the attraction of non-conducting materials to chargedbodies. (Adapted from A. Arons,Development of Concepts in Physics,Addison-Wesley, 1965.) (a) Thermalmotion ordinarily keeps dipole mole-cules randomly oriented. (b) But theypartially align in the presence of acharged object. (Thermal agitationprevents complete alignment.)

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Figure 18-11 Simple model of ametal: lattice of positive ions electron gas.

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Like an ordinary gas, an electron gas can also be made to flow in some direc-tion, but the causes of the flow are different. In an ordinary gas, molecules flowfrom regions where there is a greater density of molecules to regions of lesserdensity. The gas thus flows from higher to lower pressure (the pressure is a col-lective effect of molecules colliding with one another and with their surround-ings). In an electron gas, electrons flow from regions where there is a greaterdensity of electrons to regions of lesser density. What drives the motion is not apressure difference but electrostatic forces. Electrons will be repelled by regionswhere there is a surplus of electrons and attracted toward regions where a deficitof electrons leaves unbalanced positive charges.

Net flow in ordinary gases is affected by differences in density; the excessmolecules in regions of higher pressure are distributed throughout the region’svolume. 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 inthe interior—because mutual repulsion keeps them as far apart as possible (recallExamples 18-2 and 18-3). So the charge density that affects flow is a surfacecharge density. These surface charges exert forces on the electrons in the inte-rior of the conductor and may cause a flow of the interior electrons, but the flowoccurs in such a way that the charge density remains zero throughout the inte-rior. The next chapter details how this happens.

✦PUMPS AND BATTERIES If two gas-filled chambers are connected (Figure18-12a), the pressure will be uniform throughout. It is possible to increase thepressure in one chamber and decrease the pressure in the other by connectingthem through an air pump (Figure 18-12b). If we then open a valve connectingthe two chambers, there is a rush of gas from the higher-pressure chamber tothe lower (Figure 18-12c).

If we similarly connect two identical conducting wires (Figure 18-12d), chargewill distribute uniformly over both. If we then connect a battery between the twowires (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 aspark across the gap. We have already noted that a spark is evidence of a flowof charge. The two systems in Figure 18-12 are analogous. To explore the anal-ogy more fully, work through WebLink 18-3.

In Figure 18-12e, the two wires provide very little surface on which to placeexcess charge, so the charge density becomes sufficient to oppose the pumping

Figure 18-12 Comparing theeffect of a pump and a battery.

Deficit ofmoleculeshere

Flow ofmolecules

Flow ofelectrons whencontact is secure

Spark whencontact is broken

Excessmoleculeshere

Deficit ofelectronshere

Excesselectronshere

Closedvalve

Pump Closedvalve

Openvalve

±±±±±

±±±±±

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(a) (b) (c)

(d ) (e) ( f )

For WebLink 18-3:Pumps and Batteries,go towww.wiley.com/college/touger

0540T_c18_543-565.qxd 9/22/04 15:10 Page 554 EQA


of further charge when only a tiny amount of charge has been pumped from onewire to the other. At this stage, the charges already on either wire exert a totalelectrostatic force on any further charge that is equal and opposite to the forceexerted by the battery. Because the latter force results from the battery’s chem-istry, we call it a non-electrostatic force.

Suppose we now take the free ends of the two wires in Figure 18-12a andconnect them to the plates in Example 18-3. We now have a mechanism, the bat-tery, that can transfer charge from one plate to another to produce the chargeconfiguration 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 suf-ficiently to oppose the pumping effect of the battery. Because of this greatercapacity to hold charge, any device consisting of two conducting surfaces sepa-rated by a small nonconducting gap is called a capacitor.

The capacitor in Example 18-3 is called a parallel plate capacitor. In manycommercial capacitors (Figure 18-13), the conducting layers or plates and the inter-vening nonconducting layers are rolled together and put into a cylindrical con-tainer to provide large surface areas within a small space. The extent to which acapacitor can store charge is called its capacitance (we will provide a quantita-tive definition later on). Large surface areas are clearly an important factor con-tributing to large capacitance.

Now let’s see what happens when we string together some of the objects wehave 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 becausecharge cannot pass across the nonconducting layer or gap, but in ordinary usagewe call it a circuit anyway for lack of a better term. The first circuit we look atwill consist of a battery, a capacitor with large capacitance, connecting wires, andin addition, a small bulb and socket. To understand how charge can move throughthe bulb, it is important for you to understand the connections that make up theconducting path (Figure 18-14).

Conductingwires

Finalproduct

Conductingwires

Conductingsurfaces

Non-conductinglayers

Rolled and inserted into container

Figure 18-13 What goes into atypical commercial capacitor.

Using a defibrillator. A defibrillatoris a medical device that applies anelectric shock to restore the rhythmof a heart that is not beating prop-erly. The shock is provided by thedischarge of a large-capacitancecapacitor in the defibrillator.

Figure 18-14 Conducting path through a light bulb.

(a) (b) (c)

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.

The threads of the socket connect to the threads of the bulb.

So the charge follows this overall path through bulb and socket.

Insulator

The base of the socket connects to the lower tip of the bulb.

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Physicists usually draw electrical circuits using stylized symbols. Figure 18-15shows the circuit elements (the building blocks of the circuit) we have discussedso far and their usual symbols. Figure 18-16a shows these elements connected toform a circuit. The accompanying symbolic drawing of the circuit is called aschematic diagram, or simply a schematic.

Figure 18-15 Standard symbolsfor circuit elements.

Capacitor

Symbol

Element

Battery Wire

or

or

Bulb

or

+–

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Note: Bends in the wire do not affect its role as a conductor.

+ –

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+ –Miniaturebulb

Clip A Clip BClip A Clip B

Very largecapacitancecapacitor

Actual circuit Schematic Actual circuit Schematic

Metal alligatorclips for firmcontacts

+–

(a) (b)

Figure 18-16 Circuit for Case 18-2.

Case 18-2 ◆ Using Batteries to Charge and Discharge Large Capacitance Capacitors

If you have the materials shown in Figure 18-16a avail-able to you, you should do the following steps foryourself as an On-the-Spot Activity. Then, keeping inmind the ability of the two plates of a capacitor to storeopposite charges, you should try to figure out how ourunderlying model can account for what you observe.You will be more likely to “own” the reasoning if youcan work it out for yourself.

Step 1: Assemble the circuit in Figure 18-16a, but leaveclip B unconnected. STOP&Think What do youexpect to happen when you connect clip B tothe battery? Will the bulb light up? Will it remainlit? ◆ Now connect clip B to see what happens.

Step 2: Suppose that after all contacts have been in placefor a couple of minutes, you disconnect clips Aand B from the battery and bring them togetheras in Figure 18-16b (eliminating the battery fromthe circuit). STOP&Think What do you expect

to happen? Will the bulb light up? Will it remainlit? ◆ Now do it to see what happens.

Step 3: After all contacts have again been in place for acouple of minutes, replace the bulb (call it bulbA) with a different bulb B (e.g., one having adifferent 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 lastanywhere from less than a second to over half aminute, depending on the specific capacitor, bulb, andbattery used.

For Step 2: Here, too, we observe that the bulbglows briefly and then dies out!

For Step 3: In each of steps 1 and 2, bulb B glowsmore brightly but dims more quickly. (Or, if we chosea bulb that was initially less bright, it would dim moreslowly.)

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We saw that there is less current through a higher-resistance bulb when eachis connected individually to the battery, so that the same difference in surfacecharge density is maintained between the ends of each bulb filament. But it isnot 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. Whatpasses through one must also pass through the other, so the current through bothmust be the same. But the total change in surface charge density from the begin-ning of one filament to the end of the other is not distributed equally betweenthe two filaments. The higher-resistance bulb can sustain a greater charge densitydifference between its two ends, so most of the change is across this bulb. In fact,

How can our model account for the observations?Check your own reasoning against the following.

In step 1: When the battery is connected, it pumpselectrons from the positive to the negative capacitorplate. When enough electrons are concentrated on thenegative plate to repel the arrival of further charge, andenough of an electron deficit is created on the positiveplate so that a net positive charge holds back the remain-ing 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 bat-tery is removed? Doesn’t the battery supply the current?The charge imbalance between the two plates can bemaintained only as long as the battery is pumping tomaintain it. When the pump is removed, the mutualrepulsion of electrons on one plate will cause electronsto flow back to the plate where there is an electrondeficit. That electrostatic repulsion was also there whenthe battery was there, but now it is no longer opposedby the non-electrostatic force that the battery exerted.

A battery “pumps” charge along; it does not supply thecharge carriers that make up the current. Current will flowwhenever an uneven distribution of charge exerts a netforce on available charge carriers, whether caused by abattery or not.

In step 3: We see that when the light is dimmer—less is given off each second—it is emitted for moreseconds. In developing our model, we may surmisethat the battery “pump” is building up the same totalamount of charge on the capacitor plate, but is doingit more slowly through bulb B. Bulb B seems to bemore resistant than A to charge passing through it, sothe charge passes through it more gradually. This issimilar to what happens when you allow water to passthrough two paper coffee filters rather than one: Thewater seeps through more slowly, but ultimately youend up with the same amount of water collected inyour pot. In this case, the same amount of charge ulti-mately passes through the bulb to collect on the capac-itor plate.

Pattern of charge behaviorCharge flowing Total

through bulb each � Duration � accumulation ofsecond (current) of flow charge on plates

Bulb A more less same

Bulb B less more same

A 100 W bulb is brighter than a 15 W bulb. Wattsare a unit of power, the rate of energy use. The bright-ness of a bulb is associated with its power rating, the

amount of energy it draws and emits each second. Webegin to see that the pattern of energy emission reflectsthe pattern of charge behavior:

Corresponding pattern of energy emissionBulb brightness

(power, or energy Duration Totalemitted each second)

�of glow

�energy use

Bulb A more less same

Bulb B less more same

Comparing the above patterns, we infer that abulb’s brightness indicates the rate at which chargeflows through it, not how much total charge passesthrough. The rate of charge flow is what we call curr-ent. A bulb that is more resistant to the passage of

charge carriers glows less brightly (we refer to this prop-erty as resistance). Thus, if bulbs are placed one at atime in the circuit in Figure 18-16, the bulb with higherresistance will permit a smaller current to pass through.(Much of Case 18-2 is adapted from the work of Melvin Steinberg.)

+–

Flow ofconventional (+)current

Flow ofelectrons

A B

RB > RA

Figure 18-17 Bulbs along sameconducting path (“in series”).

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it takes a greater electrostatic force to move charge carriers through the higher-resistance bulb. The greater charge density difference is necessary to exert thisgreater electrostatic force. Because charge carriers must be pushed harder throughthis bulb, the rate of energy expenditure (power) is greater. Thus, the higherresistance bulb glows more brightly when the same current passes through both.

In a circuit with no capacitor, and therefore no nonconducting gap, the bat-tery can pump charge continuously around the resulting loop. The simplest suchcircuit consists of a battery with a wire connected between its terminals (Figure18-12f ). (The wire should be made of a fairly high-resistance alloy, such asnichrome, to avoid rapid depletion of the battery.) When the circuit is closed, thesurface charge density along the wire, instead of occurring abruptly as in Figure18-12e, tends to be very gradual (Figure 18-12f ).

In the steady state, when the current is not changing, the charge density changesuniformly along the length of the wire. We call this a constant charge density grad-ient. The direction of decrease is the direction of the negative gradient. A gas willflow in the direction of a negative pressure or density gradient. Positive charge orconventional current will flow in the direction of a negative surface charge densitygradient. Electrons, in contrast, flow in the direction of the positive gradient.

With no resistance in the wire, the configuration of surface charge in Fig-ure 18-18 would exert a nonzero force on electrons in the wire’s interior, andthey would accelerate in the direction of increasingly positive surface charge. Butbecause there is resistance, they do not accelerate unhindered. Obstacles or con-ditions that they encounter in their path recurrently slow them down, so theylevel off to a certain average velocity, called their drift velocity. STOP&ThinkIf electrons are drifting through the interior of a current carrying wire, does thatmean the wire’s interior has a net charge? ◆

Along a closed conducting path, electrons leaving any region are replaced byelectrons entering it, so the net charge in the interior of a conductor remainszero, even when there is a current. The predominant movement of charge isthrough the neutral interior of the circuit, with each tiny region contributing theelectrons that drift into the next. The drifting electrons that constitute the currentcome from sites all along the conducting path, from the bulb filament and theconnecting wires as well as the interior of the battery.

Figure 18-18 The changingcharge distribution (chargedensity gradient) along a wire’ssurface results in a net electro-static force on electrons in thewire’s interior.

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Repelled by region with more negative surface charge

✦ S U M M A RY ✦

In this chapter, we developed an underlying model to explaina range of observed behaviors. The model involves a numberof key ideas:

Electrostatic forces are a class of action-at-a-distanceforces, both attractive and repulsive, that bodies exert on oneanother, which are demonstrably not gravitational or magnetic.We call these forces electrostatic because they occur evenwhen there is no motion of the charge carriers responsiblefor the forces. The forces are weaker when the bodies are fur-ther apart.

Electric charge is a property we attribute to matter thatexerts electrostatic forces (just as gravitational mass is respon-sible for gravitational forces). We postulate that it comes in twovarieties, positive and negative. Oppositely charged bodiesattract each other, and bodies of like charge repel each other.Neutral bodies contain equal amounts of positive and nega-tive charge.

We can explain certain observations by supposing thatcharge can move through some matter in response to electro-static forces. We developed specific vocabulary for describingthis motion.

Electric current, or simply current, is the rate ofmovement or flow of chargea from one place to another

(later we will make this quantitative). Electrostatic equi-librium is the state or condition of a body or system inwhich there is no net movement of charge (and consequentlyno net current).

Conductors are materials that permit a current to passthrough them. Insulators are materials that in contrast to con-ductors do not permit the passage of a current. Conductor andinsulator are not absolute terms. Materials may be conductingor insulating to various degrees. Ground refers to a conduct-ing body (such as the Earth) that is large in comparison to theother bodies in a situation, so that charge may flow onto it orfrom it without apparent limit.

To put these concepts together in a coherent, connectedpicture, it is useful to try to explain behaviors by means ofcharge configuration diagrams (see Procedure 18-1).

Charge carriers are particles that have the property ofcharge as an inherent and unalterable trait. In a current, as thecarriers move, their charge goes with them.

Experiments such as Thomson’s cathode ray experi-ment and Millikan’s oil drop experiment led to a modelof matter in which atoms are understood to be made up ofpositive nuclei and negative electrons. In metals, which areconductors, the mobile charge carriers are electrons.

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Conventional current is a flow of positive charge equaland opposite to the flow of charge carried by electrons.

A useful model of a metal is one in which a negativeelectron gas is free to move about a lattice of positivenuclei. Excess charge always ends up on the surfaces ofconductors.

Conventional current will flow from higher to lower surf-ace charge density. When positive charges concentrate in oneregion, their mutual repulsion will produce a net movementaway from this region—a flow of charge or current—if a con-ducting path is available.

In explaining the behavior of circuits, we looked at sev-eral common circuit elements:

Batteries set up a surface charge density difference byexerting non-electrostatic forces to “pump” charge from one ter-minal to the other. The resulting charge distributions in turn exertelectrostatic forces on carriers in regions where there is a chargedensity gradient, causing them to reach a certain average driftvelocity.

Current will flow whenever there is a net force on availablecharge carriers due to an uneven distribution of charge,whether caused by a battery or not.

Capacitors are charge storage devices consisting of twoconducting surfaces separated by a nonconducting gap. Capaci-tance is a measure of the extent to which they can hold charge.

Bulbs contain filaments that glow visibly when sufficientcurrent passes through them. The filaments are characterizedby their resistance to the passage of current. If two bulbs areconnected one at a time between the same charge density dif-ference, the higher-resistance bulb will allow charge to passthrough at a lesser rate, and will glow less brightly (see Case18-2). But if the two bulbs are connected so that the samecurrent passes through them sequentially, most of the chargedensity difference will be across the higher-resistance bulb, somore work will be done and energy will be dissipated at agreater rate in that bulb, and it will glow more brightly.

Qualitative and Quantitative Problems ◆ 559

attract or repel each other? What does this tell you aboutthe way like charges respond to each other?

18-2. Hands-On Activity. See instructions before Problem 18-1.Attach the two strips of tape to each other front to back (stickyside to nonsticky side) for their entire lengths, handles excepted.Run your fingers along them to remove any surplus charge, sothat 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? Couldthey end up with opposite charges? What does “neutral” tellyou about the charges that are initially present?

b. Now quickly separate the two strips of tape, and then bringthem close together. Do they attract or repel each other?Does this demonstrate anything about how opposite chargesrespond to each other? If so, what?

18-3. Hands-On Activity. See instructions before Problem18-1. In this activity you will rub two suitable objects togetherto charge them. A comb and your hair, a Styrofoam cup andyour hair, a plastic (polyethylene) bag and a garment made ofsynthetic fabric are good possibilities. But first, produce twooppositely charged strips of tape as in Problem 18-2, and sus-pend 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 thesame way (attraction or repulsion). Could the object have thesame charge as either strip of tape? What would you have toconclude about whether there are just two kinds of charge?

b. Now let’s see if the behavior we hypothesized in a actuallyoccurs. Rub various objects to charge them and bring eachobject near (but never touching) each strip in turn. (If youspend much time on this, you may have to replace the tapestrips with a fresh pair produced in the same way.) Howdo the two strips respond to each object? Do they everrespond in the same way to the same object?

c. Is there any evidence in your observations for a third kindof charge?Figure 18-19 Problems 18-1, 18-2, and 18-3

✦ Q UA L I TAT I V E A N D Q UA N T I TAT I V E P RO B L E M S ✦

H a n d s - O n A c t i v i t i e s a n d D i s c u s s i o n Q u e s t i o n sThe questions and activities in this group are particularly suitable forin-class use.

In doing the activities in Problems 18-1 to 18-3, try to forgetanything you know ahead of time about how like or opposite chargesaffect each other. The goal of these activities is to deduce what theydo from what you observe. To do these activities you will need severalstrips of ordinary transparent sticky tape (Magic Scotch tape worksbest) 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 usedjust after being torn off the roll. Use fresh strips for each question.

(These activities are adapted from A. Arons, A Guide toIntroductory Physics Teaching [Wiley, 1990] and The ElectrostaticsWorkshop [AAPT, 1991], with additional helpful suggestionsby Robert Morse.)

18-1. Hands-On Activity. Attach two strips of tape (describedabove) in different locations on a smooth, flat, clean, dry sur-face (Formica and plastic surfaces work especially well) so thatthe entire length of each strip except for the “handle” is stuckflat to the surface. Run your thumbnail over the strips to ensuregood 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’tdo it yet). Should the two strips have like or oppositecharges? Explain.

b. Now pull the strips off by their handles and bring the freeends very close (less than a cm) to each other. Do they

Fold over to produce non-stick handle

Tape as “electroscope” leaf

Shown sticky side up

(a) (b)

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18-4. Discussion Question.Figure 18-20 shows a loop ofconducting wire. The wire isneutral, but nine typical con-duction electrons, equallyspaced, have been singledout for your attention.a. Suppose something (such

as a battery) exerts a non-electrostatic force on electron 1and moves it from point A to point B. How does movingelectron 1 affect the total force on electron 2? How doeselectron 2 move in response?

b. How does moving electron 1 affect the total force on elec-tron 9? How does electron 9 move in response?

c. Are electrons 2 and 9 slow to respond to the motion of elec-tron 1, or is the response more nearly instantaneous? Explain.

d. When electrons 2 and 9 move, how does that in turn affectelectrons 3 and 8?

e. Are electrons 4 and 7 ultimately affected? Are 5 and 6?Sketch the resulting arrangement of all nine electrons on theloop.

f. Suppose a battery between A and B continues to pumpelectrons from A to B. How do the electrons elsewhere inthe loop respond?

g. Suppose now that all the electrons are drifting slowly in thedirection shown by the arrow. Suppose the resistancebetween A and B is increased. How would that affect themotion of electron 1?

h. Because electron 1 contributes to the total electrostatic forceon electrons 2 and 9, how is the motion of those electronsaffected? How, in turn, is the motion of the remaining elec-trons affected?

i. What effect does increasing the resistance between A andB have on the current in the loop? Is the current moreaffected in one part of the loop than in another? Explain.

j. Would any of your reasoning be changed if instead of aflow of electrons, you considered a conventional current ofpositive charges moving the other way? Briefly explain.

18-5. Discussion Question. Popular descriptions of scienceare not always accurate and may generate confusion when youwish to use concepts carefully for orderly reasoning. A staffmember of a major science museum in a large U.S. city madethe following statement when introducing their electricity showto a large audience: “When positive and negative attract, theforce 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 repul-sion? Does it mean anything to say that an attraction “gene-rates” 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 wordelectricity in ordinary (non-physics) usage?

d. Can you suggest any incorrect conclusions to which the staffmember’s statement might lead a listener?

560 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents560 ◆ Chapter 18 Electrical Phenomena: Forces, Charges, Currents

R e v i e w a n d P ra c t i c eSection 18-1 Developing an Underlying Modelto Account for the Observations

18-6. A positively charged rod is brought toward two smallconducting spheres suspended by insulating cords. Sphere Ais attracted to the rod; sphere B is repelled by it. Indicatewhether each of the following statements about the totalcharges 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, butwhen they are rubbed together, object A becomes negativelycharged.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 itcontain any negative charge? Briefly explain.

18-8. In Figure 18-2c, what happens to the arrangement ofcharge on the piece of foil if the foil is carried far from thecomb without being brought in contact with a conductor?

18-9. In Step 2 of Case 18-1, the comb is replaced by a barmagnet with its north pole forward. How will the piece of alu-minum foil be affected when the magnet is brought near it?

18-10. After you run a comb through your hair, the comb willattract tiny bits of both newspaper and aluminum foil. If thebits are of equal mass, which would you expect to be attractedmore strongly to the comb? Briefly explain.

18-11. Suppose you have tiny bits of aluminum foil and scrapsof newspaper all having the same mass. You charge a plasticcomb by running it through your hair. What could you do exper-imentally to determine which is more strongly attracted to thecomb? Be very specific about your procedure and how it permitsyou 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 result-ing charge on the object be?

b. Describe a situation that will cause electrons to flow awayfrom a neutral object when it is grounded. What will theresulting charge on the object be?

18-13. SSM A negatively charged rod is brought near a con-ducting sphere suspended by a copper wire from a metal ceil-ing. 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 subsequentlyrepelled by the rod. Will the same thing happen to the con-ducting sphere in this situation? Briefly explain.

1 2

3

45

9

8

76

A B

Figure 18-20 Problem 18-4

SSM Solution is in the Student Solutions Manual WWW Solution is at http://www.wiley.com/college/touger

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18-14. A conducting metal rod is suspended by an insulatingnylon wire (Figure 18-21). A small, lightweight metal ball sus-pended by a nylon thread is very close to one end of the rodbut not touching it. If a positively charged rod is brieflytouched to the other end of the metal rod, what will happento the ball if it is initially a. has a small positive charge (com-pared to the charge on the rod)? b. has a small negativecharge? c. is neutral?

18-15. Sketch charge configuration diagrams to explain whatis happening in each part of Problem 8-14.

18-16. A negatively charged rod is held a small distance to theleft of a positively charged solid conducting sphere. Becausethe sphere is conducting, the excess charge on the sphere willbe mostly ____ (within the left half of the sphere; on the sur-face of the left half of the sphere; within the right half of thesphere; 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 thenmoved until it is parallel to A and very close to it. Sketch theinitial and final charge configurations on both plates.

18-18. Use our underlying model for electrostatic forces toexplain in detail why the hair of the person in Figure 18-8bappears 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 toreduce the risk?

Section 18-2 Charge Carriers

18-20. When radioactivity was first discovered, three differentkinds of radioactive “rays” were identified; they were calledalpha ( ), beta ( ), and gamma ( ) rays. When a beam ofeach kind of ray was passed between oppositely chargedplates, the alpha ray beam bent very slightly toward the neg-ative plate, the beta ray beam bent quite substantially towardthe positive plate, and the gamma ray beam passed throughwithout bending at all.a. Which of these rays might possibly be made up of elec-

trons? Briefly explain.

b. If the alpha and beta rays both turned out to be made upof particles, which particles would you expect to have agreater charge-to-mass ratio? Briefly explain.

18-21. Are the charge carriers always electrons when there isan electric current? Briefly explain.

18-22. In your own words, tell what is meant by a conven-tional current.

gba

18-23. If a conventional current flows from left to right alonga copper wire, which way are the electrons flowing?

18-24. Explain in your own words why a flow of electronswith a certain total charge in one direction along a wire isequivalent to the flow of an equal amount of positive chargein the opposite direction.

18-25.a. Compare the movement of charge carriers in large mole-

cules such as pigments and in metals.

b. Comment on the validity of the idea that “what goes on in ametal is like one giant covalent bond among all of itsatoms.”

18-26. Positive and negative electrodes are connected to thetwo terminals of a battery and dipped into a tank containing asolution of sodium chloride (table salt) in water. This meansthere are equal numbers of positive sodium ions and negativechloride ions in the water. When the electrodes are dipped intoopposite ends of the tank, a current flows between them. Sup-pose we could chemically remove all the chloride ions, leavingthe number of sodium ions the same as before. When the elec-trodes are dipped into the tank as before, it would produce____ (a current greater than the current that occurred with bothkinds of ions present; a current equal to that current; a currentless than that current but not zero; no current at all). Brieflyexplain.

18-27. How does the permeability of a cell membrane to var-ious chemical species affect the electrical current crossing themembrane?

Section 18-3 The Electron Gas and the Effectof Uneven Charge Distributions

18-28. A student argues as follows: “Batteries are the sourceof current in simple electric circuits. There is a certain amountof current that the battery can provide, and when the batterydies, 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 whetherthere can ever be a current when there is no battery in thecircuit.

18-29. SSM WWW Suppose you start out with two identicalcapacitors and two bulbs, A and B. First you charge the capac-itors, one at a time. Then you discharge one capacitor througheach bulb. What can you conclude about either the capacitorsor the bulbs if a. bulb A glows more brightly but for a shortertime interval than bulb B? Briefly explain. b. A glows morebrightly and also for a longer time interval than B? Brieflyexplain.

18-30. When you connect the ends of a wire to a battery sothat a current flows through the wire, does the total chargeon the wire remain zero or is the wire electrically charged?Briefly explain.

18-31. It is common to speak of “charging a battery.” Are youtransferring any charge to the battery when you do this? Brieflyexplain.

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?


Nylonthreads

Metal rod

Metalball

Positivelychargedrod

+++++


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18-33. When a battery is connected through a small bulb toa capacitor, the fact that the bulb dims and goes out after abrief interval is evidence that the capacitor plates do not keepgaining charge indefinitely. Use what you know about elec-trostatic forces on electrons to explain why a. the negativeplate of the capacitor doesn’t keep getting more negative indef-initely. b. the positive plate of the capacitor doesn’t keep get-ting more positive indefinitely.

18-34. A team of students finds that in Case 18-2, when theycharge and discharge the capacitor through bulb A, the bulbglows very brightly. When they charge and discharge it throughbulb B, this bulb glows less brightly. They hypothesize thatbecause bulb A glows more brightly, it is permitting more totalcharge to pass through and be stored on the capacitor. To testthis hypothesis, they decide to charge the capacitor throughbulb 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 duringdischarge when the capacitor was also charged through bulbA? Why?

b. When they do the test, they observe that when they dis-charge the capacitor through bulb A, it glows just as brightlyand for just as long as when the capacitor was chargedthrough bulb A. What can you conclude from this obser-vation? (Adapted from M. Steinberg et al., Electricity Visualized, 1990.)

18-35. Suppose that in the circuit in Case 18-2, the capacitoris replaced by one with plates that are twice as big. If noth-ing else is changed, how would this affect a. the maximumbrightness of the bulb? Use the underlying model to brieflyexplain your answer. b. the time it takes to dim to half itsinitial brightness? Use the underlying model to briefly explainyour answer.

18-36. After the circuit in Figure 18-16a has been connectedfor a few minutes, does the battery produce a surface chargedensity difference? What effect, if any, does this have on cur-rent flowing in the depicted circuit? Justify your answers bysketching the location(s) of any excess charge.

18-37. When the last connection has just been made in thecircuit in Figure 18-16b and the capacitor is just beginning to

discharge, tell whether each of the following is positivelycharged, 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 thecapacitor

c. the surface of the wire 1 cm from the negative plate of thecapacitor

d. the interior of the wire 1 cm from the negative plate of thecapacitor

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 sim-ple closed circuit consisting of abulb, a battery, and connectingwires. Three points in the circuitare labeled (point B is on the fil-ament of the bulb). Rank the threelabeled points according to eachof the following, listing them inorder from least to greatest andindicating any equalities: a. thedensity of surface charge at each point. b. the current at eachpoint.

18-39. Figure 18-23 shows a sim-ple closed circuit consisting of atwo bulbs A and B, a battery(labeled C for cell), and connect-ing wires. Rank the three circuitelements in order, from least togreatest, according to the currentthat passes through each one.Indicate any equalities.

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?


G o i n g F u r t h e rThe questions and problems in this group are not organized by sec-tion heading, so you must determine for yourself which ideas apply.Some of them will be more challenging than the Review and Practicequestions and problems (especially those marked with a • or ••).

18-41. Suppose there are equal amounts of positively and neg-atively charged matter in the universe.a. How would this matter tend to rearrange itself over time if

like charges attracted and opposites repelled? Does thisagree with or contradict what we actually observe in theuniverse?

b. What if opposite charges didn’t react to each other at all(as gravitational charge doesn’t react to electric charge), butinstead charges of one kind (say, positive) were mutuallyattractive and charges of the other kind were mutuallyrepulsive? How would this matter tend to rearrange itself

over time? Does this agree with or contradict what we actu-ally observe in the universe?

18-42. Two objects A and B are attracted to each other. Whena negatively charged body C is brought near them, both areattracted to C. What can you conclude about the charges onA and B?

•18-43. A student holds an iron bar magnet in her hand. If apositively charged Styrofoam sphere is initially half a centimeterfrom the north pole and is free to move, it will be ____

(attracted to the north pole; repelled by the north pole; attractedthen 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 aseparation of 0.01 m.

+ –A C

B

Figure 18-22 Problem18-38

RB > RA

Cell C

Bulb A Bulb B

Figure 18-23 Problems18-39 and 18-40

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b. Estimate the time it takes for the piece of aluminum foil tojump the gap to the comb and use this to find an approx-imate value for the average acceleration of the foil duringthis interval.

c. Calculate the force necessary to produce this acceleration.

d. Compare the values you’ve obtained in a and c. Expressthe comparison as a ratio Briefly explain the sig-nificance of this comparison (or this ratio).

18-45. SSM WWW A common device for detecting electriccharge is the electroscope (Figure 18-24a). The metal knob atthe top is connected via the conducting metal post below itto two metal foil leaves suspended from the bottom of thepost.a. When a charge is transferred to the knob, what will hap-

pen to the foil leaves? Why? How does this compare to theeffect shown in Figure 18-8b?

b. Suppose you temporarily ground the electroscope by touch-ing the knob with a finger to neutralize it. You then removeyour finger and bring a positively charged rod very near butnot touching the knob of the electroscope. What happensto the leaves when the rod is close? Sketch a charge dia-gram to explain what happens. Is there a net charge on theelectroscope? How is it distributed?

c. What happens to the leaves when the rod is moved a lit-tle further from the knob? Explain your answer in terms ofthe forces that charge carriers exert on one another.

F found in aF found in c.

Figure 18-24 Problems 18-45, 18-46, and 18-67

18-46. Charging by induction. A positively charged rod isagain brought close to the knob of a neutral electroscope with-out touching it, and the leaves respond as in Problem 18-45.a. With the rod kept in this position, a student places her fin-

ger in contact with the knob, as in Figure 18-24b. Whathappens to the foil leaves? Why? Draw a charge configura-tion diagram to support your explanation. Is there a netcharge on the electroscope? How is it distributed?

b. The student then removes her finger while the rod remainsin the same position. Now what happens to the foil leaves?Why? Again, draw a charge configuration diagram to sup-port your explanation. Is there a net charge on the elec-troscope? How is it distributed?

c. Finally the rod is removed. At this point there is a net chargeon the electroscope. Is it positive or negative? How is thischarge distributed? What would you see as evidence thatthe electroscope is charged?

d. This is called charging by induction. We say the finalcharge on the electroscope was induced by the chargedrod because it was not transferred from the rod, but it wascaused by the presence of the rod. Where did the finalcharge on the electroscope come from? Briefly explain.

18-47. Are fabrics that develop static cling conductors or insu-lators? Briefly explain how you can tell.

18-48. Golfers are frequent lightning victims. What are someof the factors that contribute to this? (Assume golfers have asmuch common sense as other people.)

18-49. A lightning rod always has a wire connected to itslower end. To what should the other end of the wire be con-nected? Why?

18-50. Jumper cables are used to recharge a car battery byconnecting it to the battery of another car. It is possible (butnot safe) to do this by connecting one cable between the pos-itive terminals of the two batteries and the other between thenegative terminals of the two batteries.

a. Why do the safety instructions tell you that instead, youshould connect an end of one cable to your engine blockor car frame?

b. What would happen if you ran each cable between the pos-itive terminal of one battery and the negative terminal ofthe other?

18-51. SSM A positivelycharged rod is broughtclose to a grounded con-ducting sphere (Figure18-25). Unlike the usualcharge configuration dia-gram that shows onlyexcess charge, the fig-ure shows representativecharges on the sphere inits initial (neutral) state.Show what happens to these charges by drawing the resultingcharge configuration on the spherea. 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 inconductors.

d. Now draw a usual charge configuration diagram showingonly the final distribution of excess charge for each of thesecases. Does the distribution of excess charge depend onwhether you think about a flow of electrons or about a con-ventional current of positive charge? Explain.

18-52. What advantage is gained by making the upper part ofthe Van de Graaff generator spherical?

18-53. If the bottom of a small bulb is placed against one ter-minal of a battery, and no other connections are made, a. willthere be any flow of charge at any time? Briefly explain. b. willthe bulb light up? Briefly explain.

18-54. If the circuit in Figure 18-16a were assembled using acapacitor with only a thousandth of the capacitance of the oneshown, a. would there still be a transient current through thebulb? Briefly explain. b. would you still see the bulb light up?Briefly explain.


(a) Metal foil leaves of electroscope hang straight down when uncharged

Metal foilleaves

Glass

(b) A step in charging the electroscope by induction

Metal ball andstem provideconducting pathto leaves +

++++++

Charge configuration beforerod is brought near

Ground

+++++ + – +– + –+ –

+–

+– +

– + –


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18-55. In the circuit inFigure 18-26, bulbs A andB are connected betweenthe same points 1 and 2.Bulb B has greater resist-ance than bulb A.a. Sketch a charge config-

uration diagram show-ing the distribution of excess surface charge along this cir-cuit at an instant when the capacitor has just begun tocharge (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 con-nected between the same points 1 and 2. Bulb B has greaterresistance than bulb A.a. At an instant when the capacitor has just begun to charge,

is the difference in surface charge density between the endsof bulb A less than, equal to, or greater than the differencebetween the ends of bulb B? Briefly explain your answer.

b. Through which bulb will more current flow? Briefly explainyour answer.

c. Which bulb will glow more brightly? Briefly explain youranswer.

d. Consider the extreme case in which the resistance of bulbB’s filament is so great that the filament is in effect an insu-lator. In this case, through which bulb will more current flow?

e. In the case described in d, which bulb will glow morebrightly?

f. Are your answers to d and e the same as your answers tob and c? Should they be? Briefly explain.

18-57. Compare and contrast the behavior of the circuits inFigures 18-26 and 18-17.

18-58. Batteries make use of chemical reactions in which onechemical 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-resistanceconductor like a short length of copper wire connectedbetween the terminals of the battery?

18-59. SSM The circuit in Figure 18-27is identical to the circuit in Figure18-16a, except that a second capac-itor identical to the first one has beenconnected between points 1 and 2.a. Compare the brightness of the

bulbs in the two circuits just afterclip B is connected to completethe circuit. Briefly explain.

b. Compare how long the bulbs inthe two circuits glow once clip Bis connected. Briefly explain.

18-60. The circuit in Figure 18-28 has thesame elements as the circuit in Figure18-16a, but they are arranged differently.a. Compare the brightness of the bulbs

in the two circuits just after clip B isconnected to complete the circuit.Briefly explain.

b. Compare how quickly the capacitors in the two circuitscharge once clip B is connected. Briefly explain.

18-61. Draw the simplest schematic circuit diagram you canfor the circuit depicted in Figure 18-29.

18-62. In a series of popular lectures in 1934, British Nobellaureate W. L. Bragg proposed the following analogy: “Nowsuppose I take the spare cash in my pocket and hand it overto you. Ought I to say that a current of riches has passed fromme to you, or that a current of poverty has passed from youto me? Unfortunately . . . it was as if everyone agreed to saythat the current of poverty passed from you to me, before itwas realized that the actual cash . . . went from pocket topocket in the opposite direction” (W. L. Bragg, Electricity, Macmillan,

New York, 1936, p. 57). To what situation in physics was Braggreferring? What in the physics situation is like the cash in thesituation Bragg described? What in the physics situation is likethe “current of poverty” in this situation?

18-63. When a positively charged rod is brought near sometiny shreds of newspaper, the shreds are attracted to the rod.What would happen if the rod were negative instead? Why?

18-64. Suppose you haveonly the bulb, battery, andsingle piece of flexible con-ducting wire that are shown inFigure 18-30. Very carefullysketch a way of arrangingthese circuit elements thatwould make the bulb light. Besure that your sketch showsclearly where the wire is making contact with other objects.

18-65. A simple closed circuit consists of a battery connectedto a bulb by wires. Within the battery, does the conventionalcurrent flow from the negative terminal to the positive terminalor from the positive terminal to the negative terminal? Brieflyexplain.

18-66. In each of two set-ups, a capacitor is charged by con-necting its plates to the two terminals of a battery. The set-ups are identical, except that the wires in set-up B have greaterresistance than the wires in set-up A. Is the charge acquiredby the capacitor in A less than, equal to, or greater than thecharge acquired by the capacitor in B? Briefly explain.

18-67. The leaves of an electroscope (Figure 18-24a) spreadout when a positively charged rod is brought close to but nottouching 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

Figure 18-29 Problems 18-61


A

B1 2 (RB > RA)

+ –

Figure 18-26 Problems 18-55,18-56, and 18-57

1 2

Clip B

+ –

Figure 18-27 Problem18-59

+ –+ –

+ –


Clip B

+ –

Figure 18-28Problem 18-60

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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 ofaluminum foil started out neutral before being attracted to thenegatively charged comb. We can best show that this is actu-ally the case by bringing (a positively charged rod; other neg-atively charged objects; a second, identically treated piece ofaluminum foil) close to it and seeing what happens. Give areason for your choice.

18-69. If you think of your body’s circulatory system as beinganalogous to an electric circuit, a. what in your circulatory sys-tem is analogous to a battery in the electric circuit? b. what in

the circuit is analogous to blood pressure in your circulatorysystem?

18-70. Example 18-2 (Figure 18-5) involved an effective trans-fer of positive charge. Suppose that the conducting sphere ismetallic, so that the charge carriers that are free to move areactually negative electrons. How do the electrons move? Sketchdiagrams showing the stages of the motion.

18-71. A positively charged rod is held a small distance to theleft of a neutral solid conducting sphere. Because the sphereis conducting, there will be excess electrons ____ (within theleft half of the sphere; on the surface of the left half of thesphere; within the right half of the sphere; on the surface of theright half of the sphere).


P ro b l e m s o n We b L i n k s18-72. Suppose you wanted to show that the piece of alu-minum foil involved in the observations in WebLink 18-1started out neutral.a. Could you accomplish this by putting it next to a charged

object to see what happened? If so, tell whether the objectshould be positively or negatively charged. If not, brieflyexplain why not.

b. Could you accomplish this by putting it next to an identi-cal piece of aluminum foil to see what happened? Brieflyexplain.

18-73. Which (one or more) of the following ideas is neces-sary to explain why the aluminum foil is attracted to thecharged 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 replacedby a kind of metal foil that has only one conduction electroncontributed by each atom. Just before the foil actually touchesthe comb, is the number of conduction electrons in the partof foil furthest from the comb less than, equal to, or greaterthan the number of positive ions in that part of the foil?

18-75. In WebLink 18-3, the conduction electrons on the lowerwire surface don’t all get “pumped” to the upper wire surfacebecause as more electrons accumulate on the upper wire ____(the battery runs down; the electrostatic force they exert onother electrons increases; the pressure builds up; the batteryruns out of electrons).

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Electrical Phenomena: Forces, Charges, Currents

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