knight ch 20 electric force and fields OCR.pdf

20.1 Charges and Forces 697 20.1 Charges and Forces You can receive a mildly unpleasant shock and produce a little spark if you touch a metal doorknob after scuffing your shoes across a carpet. A plastic comb that you've run through your hair will pick up bits of paper and other small objects. I...

20.1 Charges and Forces 697 20.1 Charges and Forces You can receive a mildly unpleasant shock and produce a little spark if you touch a metal doorknob after scuffing your shoes across a carpet. A plastic comb that you've run through your hair will pick up bits of paper and other small objects. In both of these cases, two objects are rubbed together. Why should rubbing an object cause forces and sparks? What kind of forces are these? These are the questions with which we begin our study of electricity. Our first goal is to develop a model for understanding electric phenomena in terms of charges and forces. We will later use our contemporary knowledge of atoms to understand electricity on a microscopic level, but the basic concepts of electricity make no reference to atoms or electrons. The theory of electricity was well established long before the electron was discovered. Experimenting with Charges Let's imagine working in a laboratory where we can make observations of electric phenomena. This is a modest lab, much like one you would have found in the year 1800. The major tools are: ■ ■ ■ A number of plastic and glass rods, each several inches long. These can be held in your hand or suspended by threads from a support. Pieces of wool and silk. Small metal spheres, an inch or two in diameter, on wood stands. We will manipulate and use these tools with the goal of developing a theory to explain the phenomena we see. The experiments and observations described below are very much like those of early investigators of electric phenomena. The ancient Greeks first noted the electrical nature of matter by observing amber, a form of fossilized tree resin. When rubbed with fur, amber buttons would attract bits of feather, hair, or straw. The Greek word for amber, elektron, is the source of our words "electric;' "electricity;' and-of course" electron:' Discovering electricity I Experiment 2 Experiment 1 Rods that haven't been rubbed Plastic Plastic rubbed Glass rubbed ~ Plastic Take a plastic rod that has been undisturbed for a long period of ti me and hang it by a thread. Pick up another undisturbed plastic rod and bring it close to the hanging rod. Nothing happens to either rod. Vigorously rub both the hanging plastic rod and the handheld plastic rod with wool. Now the hanging rod moves a111ay from the handheld rod when you bring the two close together. Rubbing two glass rods with silk produces the same result: The two rods repel each other. Interpretation: There are no special electrical properties to these undisturbed rods. We say that they are neutral. Interpretation: Rubbing a rod somehow changes its properties so that forces now act between two such rods. We call this process of rubbing charging and say that the rubbed rod is charged, or that it has acquired a charge. Experiment 2 shows that there is a long-range repulsive force (i.e., a force requiring no contact) between two identical objects that have been charged in the same way, such as two plastic rods both rubbed with wool or two glass rods rubbed with silk. The force between charged objects is called the electric force. We have seen a long-range force before, gravity, but the gravitational force is always attractive. This is the first time we've observed a repulsive long-range force. However, the electric force is not always repulsive, as the next experiment shows. 698 CHAPTER 20 Electric Fields and Forces Discovering electricity II Experiment 3 Experiment 4 Glass rubbed ~ Increased distance Plastic rubbed with wool r,- /( ~ &:; Bring a glass rod that has been rubbed with silk close to a hanging plastic rod that has been rubbed with wool. These two rods auract each other. • If the two rods are held farther from each other, the force between them decreases. Interpretation: We can explain this experiment as well as Experiment 2 by assuming that there are two d/ffere111kinds of charge that a mate1ial can acquire. We define the kind of charge acquired by a glass rod as positive charge, and that acquired by a plastic rod as negative charge. Then these two experiments can be summarized as like charges (positive/positive or negative/negative) exert repulsive forces on each other, while opposite charges (positive/negative) exert attractive forces on each other. • The strength of the force is greater for rods that have been rubbed more vigorously. Interpretation: Like the gravitational force, the electric force decreases with the distance between the charged objects. And, the greater the charge on the two objects, the greater the force between them. Although we showed experimental results for only plastic rods rubbed with wool and glass rods rubbed with silk, further experiments show that there are only two kinds of charge, positive and negative. For instance, when you rub a balloon on your hair, the balloon becomes negatively charged, while nylon rubbed with a polyester cloth becomes positively charged. Visualizing FIGURE 20.1 Visualizing charge. Negalive charge is represented by Positive charge / is represented by ·~~ We represent eqLial·amounts of positive and negative charge by drawing the same number of+ and - signs. More charge is represented by more + or -,..signs. ~/ ~ Charge Diagrams are going to be an important tool for understanding and explainjng charges and the forces between charged objects. FIGURE20.1shows how to draw a charge cliagram, which gives a schematic picture of the distribution of charge on an object. It's important to realize that the + and - signs drawn in Figure 20.1 do not represent "individual" charges. At this point, we are thinking of charge only as something that can be acquired by an object by rubbing, so in charge diagrams the + and - signs represent where the charge is only in a general way. In Section 20.2 we'll look at an atomic view of charging and learn about the single microscopic charges of protons and electrons. We can gain an important insight into the nature of charge by investigating what happens when we bring together a plastic rod and the wool used to charge it, as the following experiment shows. Discovering electricity Ill Experiment 5 Start with a neutral, uncharged hanging plastic rod and a piece of wool. Rub the plastic rod with the wool, then hold the wool close to the rod. The rod is auracted to the wool. Charged plastic rod Interpretation: From Experiment 3 we know that the plastic rod has a negative charge. Because the wool attracts the rod, the wool must have a positive charge. Wool used to rub plastic 20.1 Experiment 5 shows that when a plastic rod is rubbed by wool, not only does the plastic rod acquire a negative charge, but the wool used to rub it acquires a positive charge. This observation can be explained if we postulate that a neutral object is not one that has no charge at all; rather, a neutral object contains equal amounts of positive and negative charge. Just as in ordinary addition, where 2 + ( -2) = 0, equal amounts of opposite charge "cancel," leaving no overall or net charge. In this model, an object becomes positively charged if the amount of positive charge on it exceeds the amount of negative charge; the mathematical analogy of this is 2 + ( -1 ) = +I. Similarly, an object is negatively charged when the amount of negative charge on it is greater than the amount of positive charge, analogous to 2 + ( - 3) = - l. As FIGURE 20.2 shows, the rubbing process works by tram:ferring charge from one object to the other. When the two are rubbed together, negative charge is transferred from the wool to the rod. This clearly leaves the rod with an excess of negative charge. But the wool, having lost some of its negative charge to the rod, now has an excess of positive charge, leaving it positively charged. (We'll see in Section 20.2 why it is usually negative charge that moves.) FIGURE 20.2 How a plastic rod and wool acquire charge during the rubbing Charges and Forces 699 llll llil A video to support a section's topic is embedded in the eText. Video Charges and Forces: Demonstrations process. Wool ~ ~ I. The rod and wool are initially neutral. 2. "Neutral" actually means that they each have equal amounts of positive and negative charge. 3. Now we rub the plastic and wool together. As we do so, negative charge moves from the wool to the rod. 4. This leaves the rod with extra negativecharge. The wool is left with more positive charge than negative. 5. In a charge diagram, we draw only the excess charge.This shows how the rod and wool acquire their charge. There is another crucial fact about charge implicit in Figure 20.2: Nowhere in the rubbing process was charge either created or destroyed. Charge was merely transferred from one place to another. It turns out that this fact is a fundamental law of nature, the law of conservation of charge. If a certain amount of positive charge appears somewhere, an equal amount of negative charge must appear elsewhere so that the net charge doesn't change. The results of our experiments, and our interpretation of them in terms of positive and negative charge, can be summarized in the following charge model. Charge model, part I The basic postulates of our model are: ■ Frictional forces, such as rubbing, add something called charge to an object or remove it from the object. The process itself is called charging. More vigorous rubbing produces a larger quantity of charge. ■ There are two kinds of charge, positive and negative. ■ Two objects with like charge (positive/positive or negative/negative) exert repulsive forces on each other. Two objects with opposite charge (positive/ negative) exert attractive forces on each other. We call these electric forces. ■ The force between two charged objects is a long-range force. The magnitude of the force increases as the quantity of charge increases and decreases as the distance between the charges increases. ■ Neutral objects have an equal mixture of positive and negative charge. ■ The rubbing process charges the objects by transferring charge from one to the other. The objects acquire equal but opposite charges. ■ Charge is conserved: It cannot be created or destroyed. Dust in the wind When sand and dust grains collide as they blow across a sandy surface, the contact separates charges. The grains develop a charge; so does the surface. In some cases, a repulsive force between the charged sUJface and the charged particles can cause a dramatic increase in the number of particles leaving the surface. When you see images of an intense sandstorm, know that it nlight be more than the wind that's lifting up the grains~it could also be the electric forces between them. 700 CHAPTER 20 Electric Fields and Forces Insulators and Conductors Experiments 2, 3, and 5 involved a transfer of charge from one object to another. Let's do some more expe1iments with charge to look at how charge moves on different materials. Discovering electricity IV Experiment 6 Experiment 7 The metal sphere acquires charge. This sphere remains neutral. Experiment 8 This sphere acquires charge. Both spheres acquire charge. ··-..~ Metal~-··/ Metal rod Charge a plastic rod by rubbing it with wool. Touch a neutral metal sphere with the rubbed area of the rod. The metal sphere then repels a charged, hanging plastic rod. The metal sphere appears to have acquired a charge of the same sign as the plastic rod. Place two metal spheres close together with a plastic rod connecting them. Charge a second plastic rod, by rubbing, and touch it to one of the metal spheres. Afterward, the metal sphere that was touched repels a charged, hanging plastic rod. The other metal sphere does not. Repeat Experiment 7 with a metal rod connecting the two metal spheres. Touch one metal sphere with a charged plastic rod. Afterward, both metal spheres repel a charged, hanging plastic rod. Our final set of experiments has shown that charge can be transferred from one object to another only when the objects touch. Contact is required. Removing charge from an object, which you can do by touching it, is called discharging. In Experiments 7 and 8, charge is transferred from the charged rod to the metal sphere as the two are touched together. In Experiment 7, the other sphere remains neutral, indicating that no charge moved along the plastic rod connecting the two spheres. In Experiment 8, by contrast, the other sphere is found to be charged; evidently charge has moved along the metal rod that connects the spheres, transferring some charge from the first sphere to the second. We define conductors as those materials tlu·ough or along which charge easily moves, and insulators as those materials on or in which charges remain immobile. Glass and plastic are insulators; metal is a conductor. This new information allows us to add more postulates to our charge model: Charge model, part II ■ There are two types of materials. Conductors are materials through or along wllich charge easily moves. lnsulators are materials on or in which charges remain fixed in place. ■ Charge can be transferred from one object to another by contact. lmID ► Both insulators and conductors can be charged. They differ in the ability of charge to move. ◄ ◄ A dry day, a plastic slide, and a child with clothes of the right fabric lead to a lovely demonstration of electric charges and forces. The rubbing of the child's clothes on the slide has made her build up charge. The body is a good conductor, so the charges spread across her body and her hair. The resulting repulsion produces a dramatic result! 20.1 CONCEPTUAL EXAMPLE 20.1 ■ and Forces Transferring charge In Experiment 8. touching a metal sphere wiLh a charged plastic rod caused a econd metal sphere. connected by a metal rod to the first. to become charged wilh the same type of charge as Lhe rod. Use the postulates of Lhecharge model to construct a charge diagram for the process. REASON Charges We need Lhefollowing ideas from Lhecharge model: Charge is transferred upon contact. The plastic rod was charged by rubbing wiLh wool, giving it a negative charge. The charge doesn't move around on Lhe rod. an insulator. but ome of Lhe charge is transferred to the metal upon contact ■ Metal is a conductor. Once in Lhe metal. which is a conductor. Lhecharges are free to move around. ■ Like charges repel. Because like charges repel. these negative charges quickly move a far apart a Lhey po sibly can. Some move through Lhe connecting metal rod to the second sphere. Consequently. the second sphere acquires a net negative charge. The repulsive forces drive Lhe negative charges as far apart as they can possibly get. causing them to end up on the swfaces of the conductors. The charge diagram in AGURE 20.3 illustrates these three steps. FIGURE 20.3 A charge diagram for Experiment 8. Charged insulating~ Charge is transferred The charge on the rod away from the contact point stays fixed. ~;:::Ph='rf ::;;;' ::.,";;':,;;,'=> =={IM••l~l The repulsive forces cause the charge to spread out over the surfaces of the conductors. £~1remely fast In Conceptual Example 20.1, once the charge is placed on the conductor it rapidly distributes itself over the conductor's surface. This movement of charge is extremely fast. Other than this very brief interval during which the charges are adjusting, the charges on an isolated conductor are in static equiljbrium with the charges at rest. This condition is called electrostatic equilibrium. CONCEPTUAL EXAMPLE 20.2 Drawing a charge diagram for an electroscope Many electricity demonstrations are carried out wiLh Lhe belp of an electroscope like the one shown in FlGURE 20.4. Touching the sphere at the top of an electroscope with a charged plastic rod causes the leaves to fly apart and remain hanging at an angle. Use charge diagrams to explain why. We will use the charge model and our understanding of insulators and conductors to make a series of charge diagrams in FIGURE 20.5 that show the charging of Lheelectroscope. FIGURE 20.4 A charged electroscope. Glass box to REASON The charges move around. but. because charge is conserved, the total number of negative charges doesn't change from picture to picture. ASSESS Verythin --1----✓/ gold leaves Charging the electroscope causes the gold leavesto repel ..-···each other. ....•······· FIGURE 20.5 Charging an electroscope. ~ Very fast Electroscope- Gold leaves -I. Negativecharges are transferred from the rod to the metal sphere upon contact. 2. Metal is a conductor.Therefore charge spreads {veryrapidly) throughout the entire electroscope. The leaves become negative!} charged. 3. Like charges repel. The negativelycharged Iea,es exen repulsiveforces on each other, causing them to spread apart. 701 702 CHAPTER 20 Electric Fields and Forces Polarization Picking up pollen @!iJ Rubbing a rod with a cloth gives the rod an electric charge. In a similar fashion, the rapid motion of a bee's wings through the air gives the bee a small positive electric charge. As small pieces of paper are attracted to a charged rod, so are tiny grains of pollen attracted to the charged bee, making the bee a much more effective pollinator. At the beginning of this chapter we showed a picture of a small feather being picked up by a piece of amber that had been rubbed with fur. The amber was charged by rubbing, but the feather had not been rubbed-it was neutral. How can our charge model explain the attraction of a neutral object toward a charged one? Although a feather is an insulator, it's easiest to understand this phenomenon by first considering how a neutral conductor is attracted to a charged object. FIGURE 20.6 shows how this works. Because the charged rod doesn't touch the sphere, no charge is added to or removed from the sphere. Instead, the rod attracts some of the sphere's negative charge to the side of the sphere near the rod. This leaves a deficit of negative charge on the opposite side of the sphere, so that side is now positively charged. This slight separation of the positive and negative charge in a neutral object when a charged object is brought near is called charge polarization. Figure 20.6 also shows that, because the negative charges at the top of the sphere are more strongly attracted to the rod than the more distant positive charges on the sphere are repelled, there is a net attractive force between the rod and the sphere. This polarization force arises because the charges in the metal are slightly separated, not because the rod and metal are oppositely charged. Had the rod been negatively charged, positive charge would move to the upper side of the sphere and negative charge to the bottom. This would again lead to an attractive force between the rod and the sphere. The polarization force between a charged object and a neutral one is always attractive. FIGURE 20.6 Why a neutral The neutral sphere contains equal amounts of positive and negar\e charge. ···u metal object is attracted Negative charge is attracted to the positive rod. This leaves behind positive charge on the other side of t~~- ~Ai o·.// .... +++ •••• The rod doesn't touch the sphere. II Video What the Physics? Franklin's Bells Video Charged Rod and Aluminum Can to a charged object. The negative charge on the sphere is close to the rod, so it is s~·tronglyatt~_actedto the rod. \f.,e1 r-.. : The 11e1force is .toward the rod. The positive charge on the sphere is far from the rod. so it is weakly repelled by lhe rod. Polarization explains why forces arise between a charged object and a metal object along which charge can freely move. But the feathers attracted to amber are insulators, and charge can't move tlu·ough an insulator. Nevertheless, the attractive force between a charged object and an insulator is also a polarization force. As we' 11 learn in the next section, the charge in each atom that makes up an insulator can be slightly polarized. Although the charge separation in one atom is exceedingly small, the net effect over all the countless atoms in an insulator is to shift a perceptible amount of charge from one side of the insulator to the other. This is just what's needed to aUow a polarization force to arise. STOP TO THINK 20. 1 An electroscope is charged by touching it with a pos1ttve glass rod. The electroscope leaves spread apart and the glass rod is removed. Then a negatively charged plastic rod is brought close to the top of the electroscope, but it doesn't touch. What happens to the leaves? A. The leaves move closer together. B. The leaves spread farther apart. C. The leaves do not change their position. 20.2 703 Charges, Atoms, and Molecules 20.2 Charges, Atoms, and Molecules We have been spealcing about giving objects positive or negative charge without explaining what is happening at an atomic level. You already know that the basic constituents of atoms-the nucleus and the electrons surrounding it-are charged. fn this section we will connect our observations of the previous section with our understanding of the atomic nature of matter. Our current model of the atom is that it is made up of a very small and dense positively charged nucleus that contains positively charged protons as well as neutral particles called neutrons. The nucleus is surrounded by much-less-massive negatively charged electrons that form an electron cloud, as illustrated in FIGURE 20.1. The atom is held together by the attractive electric force between the positive nucleus and the negative electrons. Experiments show that charge, like mass, is an inherent property of electrons and protons. It's no more possible to have an electron without charge than it is to have an electron without mass. FIGURE 20. 7 Our modern view of the atom. The nucleus, exaggerated in size for "" ,,,. '"r: P•"'""'· ""'''~ w 'Y++\ /,=The electron cloud is negatively charged. An Atomic View of Charging Electrons and protons are the basic charges in ordinary matter. There are no other sources of charge. Consequently, the observations we made in Section 20.1 need to be explained in terms of electrons and protons. Experimentally, electrons and protons are found to have charges of opposite sign but exactly equal magnitude. Thus, because charge is due to electrons and protons, an object is charged if it has an unequal number of electrons and protons. An object with a negative charge has more electrons than protons; an object with a positive charge has more protons than electrons. Most macroscopic objects have an equal number of protons and electrons. Such an object has no net charge; we say it is electrically neutral. In practice, objects acquire a positive charge not by gaining protons but by losing electrons. Protons are extremely tightly bound within the nucleus and cannot be added to or removed from atoms. Electrons, however, are bound much more loosely than the protons and can be removed with Littleeffort. The process of removing an electron from the electron cloud of an atom is called ionization. An atom that is missing an electron is called a positive ion. Some atoms can accommodate an extra electron and thus become a negative ion. FIGURE 20.8 shows positive and negative ions. The charging processes we observed in Section 20. l involved rubbing and friction. The forces of friction often cause molecular bonds at the surface to break as two materials slide past each other. Molecules are electrically neutral, but FIGURE 20.9 shows that molecular ions can be created when one of the bonds in a large molecule is broken. If the positive molecular ions remain on one material and the negative ions on the other, one of the objects being rubbed ends up with a net positive charge and the other with a net negative charge. This is how a plastic rod is charged by rubbing with wool or a comb is charged by passing through your hair. FIGURE 20.8 Positive and negative Positive ion - ions. Negative ion ~) ..\ The atom has lost one electron, giving it a nc1positive charge. The atom has gained one electron, giving it a net negative charge. FIGURE 20.9 Charging result from molecular bonds are broken. by friction may ions produced as Electrically neutral molecule Atoms Bond 0Fric1ion Charge Conservation Charge is represented by the symbol q (or sometimes Q). The SI unit of charge is the coulomb (C), named for French scientist Charles Coulomb, one of many scientists investigating electricity in the late 18th century. Protons and electrons have the same amount of charge, but of opposite signs. We use the symbol e for the fundamental charge, the magnitude of the charge of an electron or a proton. The fundamental charge e has been measured to have the value e = 1.60 X 10- 19 C These bonds were broken by friction. i /@ Positive molecular ion '~"-••"!'~/ion ~ ~\r Negative moleculm· ,,,,) This half of Lhe_.: ·•••This half of the molecule lost an molecule gained an electron as 1he extra cleclron as the bond broke. bond broke. 704 20 CHAPTER Electric Fields and Forces TABLE 20.1 Protons and electrons Particle Mass (kg) Proton 1.67 X I0- Electron 9.IJXIQ- Charge TABLE20.1 (C) lists the masses and charges of protons and electrons. lmlEI 27 +e = 1.60 X 10- 19 31 -e=-l.60XI0- 19 ► The amount of charge produced by rubbing plastic or glass rods is typically in the range l nC ( 10- 9 C) to 100 nC ( l 0- 7 C). This corresponds to an excess or deficit of I 0 10 to 10 12 electrons. But, because of the enormous number of atoms in a macroscopic object, this represents an excess or deficit of only perhaps I electron in 10 13. ◄ That charge is associated with electrons and protons explains why charge is conserved. Because electrons and protons are neither created nor destroyed in ordinary processes, their associated charge is conserved as well. Insulators and Conductors FIGURE 20.10 A microscopic insulator and a conductor. FIGURE20.10 looks inside an insulator and a metallic conductor. The electrons in the insulator are all tightly bound to the positive nuclei and so are not free to move around. Charging an insulator by friction leaves patches of molecular ions on the surface, but these patches are immobile. In metals, the outer atomic electrons (called the valence electrons in chemistry) are only weakly bound to the nuclei. As the atoms come together to form a solid, these outer electrons become detached from their parent nuclei and are free to wander about through the entire solid. The solid as a whole remains electrically neutral, because we have not added or removed any electrons, but the electrons are now rather like a negatively charged gas or liquid-what physicists Like to call a sea of electrons-permeating an atTay of positively charged ion cores. However, although the electrons are highly mobile within the metal, they a.re still weakly bound to the ion cores and will not leave the metal. look at an Insulator Nucleus Core electrons Valence electrons Valence electrons are tightly bound. Metal Positive ion cores • • Electric Dipoles Valence electrons are free to move throughout the metal. FIGURE 20.11 An induced electric dipole. The external positive charge attracts the atom's nega1ivelycharged electrons, ,,.:::'.,"' 1hcrro" do"d sh;~;awmd ~rge ··•- Fexternal on i\l<lcmnl on 0 ;, ""i.,j\'C - ~!~"'• .. Fne1.... The atom's 'negativelycharged electron cloud is closer lo the external charge than its positively charged nucleus, so the atom is a11rt1cted toward the external charge. In the last section we noted that an insulator, such as a feather, becomes polarized when brought near a charged object. We can use an atomic description of matter to see why. Consider what happens if we bring a positive charge near a neutral atom. As FIGURE 20.11 shows, the charge polarizes the atom by attracting the electron cloud while repelling the nucleus. The polarization of just one atom is a very small effect, but there are an enormous number of atoms in an insulator. Added together, their net polarization-and the resulting polarization force-can be quite significant. This is how the rubbed amber picks up a feather, exerting an upward polarization force on it larger than the downward force of gravity. Two equal but opposite charges with a separation between them are called an electric dipole. In this case, where the polarization is caused by the external charge, the atom has become an induced electric dipole. Because the negative end of the dipole is slightly closer to the positive charge, the attractive force on the negative end slightly exceeds the repulsive force on the positive end, and there is a net force toward the external charge. If the charge on a piece of amber causes the atoms in a feather to become induced electric dipoles, the net attractive force can be enough to lift the feather. Hydrogen Bonding Some molecules have an asymmetry in their charge distribution that makes them permanent electric dipoles. An important example is the water molecule. Bonding between the hydrogen and oxygen atoms results in an unequal sharing of charge that, as shown in FIGURE20.12, leaves the hydrogen atoms with a small positive charge and the oxygen atom with a small negative charge. When two water molecules are close, the attractive electric force between the positive hydrogen atom of one molecule and the negative oxygen atom of the second molecule can form a weak bond, called a hydrogen bond, as illustrated in FIGURE20.13. These weak bonds result in a certain "stickiness" between water molecules that is 20.3 FIGURE 20.12 A water molecule permanent electric is a FIGURE 20.13 Hydrogen water molecules. dipole. ........ The electrons .,,,... spend more time with oxygen than hydrogen, so the oxygen end is slightly negative. The slightly negative oxygen is attracted to the slightly positive, Coulomb's Law 705 bonds between 't"'(} \.J,) This water molecule forms hydrogen bonds with neighboring :::~~5-0,.~"'..'.'.'"'" ...••The hydrogen end ~................ is slightly positive. 0 responsible for many of water's special properties, including its expansion on freezing, the wide range of temperatures over which it is liquid, and its high heat of vaporization. Hydrogen bonds are extremely important in biological systems. As you know, the DNA molecule has the structure of a double helix. Information in DNA is coded in the nucleotides, the four molecules guanine, thymine, adenine, and cytosine. The nucleotides on one strand of the DNA helix form hydrogen bonds with the nucleotides on the opposite strand. The nucleotides bond only in certain pairs: Cytosine always forms a bond with guanine, adenine with thymine. This preferential bonding is crucial to DNA replication. When the two strands of DNA are taken apart, each separate strand of the DNA forms a template on which another complementary strand can form, creating two identical copies of the 01;ginal DNA molecule. The preferential bonding of nucleotide base pairs in DNA is explained by hydrogen bonding. In each of the nucleotides, the hydrogen atoms have a small positive charge, oxygen and nitrogen a small negative charge. The positive hydrogen atoms on one nucleotide attract the negative oxygen or nitrogen atoms on another. As the detail in FIGURE 20.14 shows, the geometry of the nucleotides allows cytosine to form a hydrogen bond only with guanine, adenine only with thymine. FIGURE 20.14 • DNA base pairs. Hydrogen bonds in /DNA double helix ,,,,. Guanine ..•....The base pairs of the two strands can join only in certain combinations. 1ydrogcn bonds join these bases. Two hydrogen bonds join these bases. •···········•••••••• Rank in order, from most positive to most negative, the of these five systems. STOP TO THINK 20.2 charges q A to qE Glass ball missing 3 Proton Electron 1,000,000 protons 1,000,000 electrons electrons • 17 protons 19 electrons • A B C D E 0 20.3 Coulomb's Law The last two sections established a model of charges and electric forces. This model is very good at explaining electric phenomena and providing a general understanding of electricity. Now we need to become quantitative. Expe1iment 4 in Section 20.1 found that the electric force increases for objects with more charge and decreases as charged objects are moved farther apart. The force law that describes this behavior is known as Coulomb's law. In the mathematical formulation of Coulomb's law, we will use the magnitude of the charge only, not the sign. We show this by using the absolute value notation we used earlier in the text. therefore represents the magnitude of the charge. It is always a positive number, whether the charge is positive or negative. lql Atoms comprising the bases @ 'N' @ fa\ ~ \,;;,,I 706 c HAP TE R 20 Electric Fields and Forces Ill Video Charges and Forces:Warm-Ups Coulomb's law Magnitude: If two charged particles that have charges q 1 and q 2 are a distance r apai1. the pai1icles exert forces on each otber of magnitude F I\ (20.1) p.191, ~ INVERSESQUARE where the charges are in coulombs (C). and K = 8.99 X 109 N • m2/C 2 is called the electrostatic constant. The e forces are an action/reaction pair. equal in magnitude and opposite in direction. It is customary to round K to 9.0 X !0 9 N • m2/C 2 for all but extremely precise calculations. and we will do so. Direction: The forces are directed along the line joining the two pai1icles. The forces are repulsive for two like charges and at1rac1ivefor two opposite charges. FIGURE 20.15 Attractive and repulsive forces between charged particles. Two positive charges F2on /::> ,. C/2 1{+) ~ Two negative charges Opposite charges <.±.}" We sometimes speak of the "force between charge q 1 and charge q2 ," but keep in mind that we are really dealing with charged objects that also have a mass, a size, and other properties. Charge is not some disembodied entity that exists apart from matter. Coulomb's law describes the force between charged particles. 1miiJ ► Coulomb's law applies only to point charges. A point charge is an idealized material object with charge and mass but with no size or extension. For practical purposes, two charged objects can be modeled as point charges if they are much smaller than the separation between them. ◄ Coulomb's law looks much like Newton's law of gravity, which you studied in .c SECTION 6.5, but there is a key difference: The charge q can be either positive or negative, so the forces can be attractive or repulsive. Consequently, the absolute value signs in Equation 20.1 are especialJy important. The first part of Coulomb's law gives only the magnitude of the force, which is always positive. The direction must be determined from the second part of the law. FIGURE 20.15 shows the forces between different combinations of positive and negative charges. Using Coulomb's Law Coulomb's law is a force law, and forces are vectors. Electric forces, like other forces, can be superimposed. If multiple charges 1, 2, 3, ... are present, the net electric force on charge j due to all other charges is therefore the sum of all the individual forces due to each chai·ge; that is, = F1onj + F'2onj + F'3onj + • • • F'i1e1 where each of the forces F;onj is given by Equation 20.1. ◄ Separating the girls from the boys 4iJ Sperm cells can be sorted according to whether they contain an X or a Y chromosome. The cells are put into solution, and the solution is forced 1hrough a nozzle, which breaks the solulion into droplets. Suppose a droplet contains a sperm cell. An optical test measures which type of chromosome, X or Y, the cell has. The droplet is then given a positive charge if it has an X sperm cell, negative if it contains a Y. The droplets fall between two oppositely charged plates where they are pushed left or right depending on their charge-separating the X from the Y. (20.2) 20.3 Coulomb's Law 707 PROBLEM-soLviNG Electric forces and Coulomb's law APPROACH 20.1 We can use Coulomb's law to find the electric force on a charged particle due to one or more other charged particles. STRATEGIZE Identify point charges or objects that can be modeled as point charges. Think about the forces involved. their likely directions and magnitudes. Think about what you are trying to find and the likely details of the result. Create a visual overview in which you establish a coordinate system. show the positions of the charges, show the force vectors on the charges, and define distances and angles. PREPARE SOLVE The magnitude of the force between point charges is given by Coulomb's Jaw: Use your visual overview as a guide to the use of this law: ■ ■ ■ ■ Show the directions of the forces-repulsive for like charges, attractive for opposite charges-on the visual overview. Draw the lengths of your force vectors according to Coulomb's law: A paiticle with a greater charge, or one that is closer, will lead to a longer force vector. When possible, do graphical vector addition on the visual overview. While not exact, it tells you the type of answer you should expect. Write each force vector in terms of its x- and y-components, then add the components to find the net force. Use the visual overview to determine which components ai·e positive and which are negative. Check that your result has the c01Tectunits, is reasonable, and answers the question. ASSESS Exercise 15 ~ EXAMPLE 20.3 Adding electric forces in one dimension Two + 10 nC charged particles are 2.0 cm apart on the x-axis. What is the net force on a + 1.0 nC charge midway between them? What is the net force if the charged particle on the right is replaced by a - IO nC charge? STRATEGIZE We will proceed using the steps of Problem-Solving Approach 20.1. We will model the charged particles as point charges. PREPARE The visual overview of FIGURE 20.16 establishes a coordinate system and shows the forces F1 onJ and F'2onJ· Figure 20.16a shows a + IO nC charge on the tight; Figure 20.16b shows a -10 nC charge. FIGURE 20.16 Electric forces are vectors, and the net force on q3 is the sum Fnei = F' 1on3 + f'2on3· Charges q 1 and each exert a repulsive force on q 3 , but these forces are equal in magnitude and opposite in direction. Consequently, Fne, = 0.The situation changes if q2 is negative, as in Figure 20.16b. ln this case, the two forces are equal in magnitude but in the direction, so F'ne, = 2F 1on 3 . The magnitude of the force is given by Coulomb's law. The force due to q 1 is SOLVE Fector q 2 same F1on3= KICJ1~ICJ3I rj3 A visual overview of the forces for the two cases. (9.0 X 109 N • nhC 0 =9.0X '{, 0 10 X 10- 9 C)( 1.0 X 10--9C) 10-4 N There is an equal force due to q2 , so the net force on the 1.0 nC charge is Fnel = ( 1.8 X l 0- 3 N, to the right). I This example illustrates the important idea that electric forces are An important part of assessing our answer is to see if it is ·'reasonable." In the second case. the net force on the charge is approximately I mN. Generally, charges of a few nC separated by a few cm experience forces in the range from a fraction of a mN to several mN. With this guideline. the answer appears to be reasonable. ASSESS (b) vectors. 0 tf_, 0 2 )( (0.010 m) 2 (a) .2., 708 c HAP TE R 20 Electric Fields and Forces Adding electric forces in two dimensions EXAMPLE 20.4 Three charged panicles with q 1 = -50 nC. q2 = +50 nC, and q3 = + 30 nC are placed as shown in AGURE 20.11. What is the ne1 force on charge q3 due to I.beother two charges? FIGURE 20.11 _ Klq 1Ilq3 1 F r2 1on J - 2)(50X 10-9C)(30X 10-9C) ·m 2/C___:_..:._ ___ _c:....;__ ____ _:_ (9.0X 109 = _:__ ______ (0.0707 m)2 The arrangement of the charges. q 1 =-50nC 5.0cm ~-------- 5.0cm 0 = 2.7 q2=+50nC 0 q3=+30nC X I0- 3 The magnitudes of the charges and the distance are the same for F2on3• SO 5.0cm 0 The components of these forces are illustrated in AGURE20.19a. We will solve for the net force using the steps of Problem-Solving Approach 20. I. STRATEGIZE We stan wilh the visual overview shown in FIG• We have defined a coordinate system. with charge q3 at the origin. We have drawn the forces on charge q3 , with directions determined by the signs of the charges. We can see from the geometry that the forces Fion 3 and F2 on 3 are at the angles noted in I.be figure. The vector addition in FIGURE 20.18b shows the anticipated direction of the net force: this will be a good check on our final result. The distance between charges q 1 and q 3 is the same as that between charges q 2 and q3 : I.bis clistance is r = V(5.0 cm)2 + (5.0 cm)2 = 7.07 cm. Because the magnitudes of q 1 and q 2 are equal and they are equidistant from q 3. we expect the magnitudes of the forces they exert to be equal. as we have drawn in Figure 20.18. PREPARE URE 20.18a. FIGURE 20.18 A visual overview jy (cm) 0 r : .! 5.0 .:-F1onJ r, "i\ + 1-----.r q3 No110scale Computing values for the components. we find = -(2.7 (F1onJ)y = (2.7 X 10-3 N) sin 45° = 1.9 X I0- 3 N (F2onJ)., = -(2.7 X I0- 3 N) cos 45° = -1.9 X I0- 3 N (F2onJ)y = -(2.7 X 10-3 N) sin 45° = -1.9 X I0- 3 N X I0- 3 N) cos 45° = - l.9 X 10- 3 N (Fi onJ)x Next, we add components of the net force: ,,, F1, = (F1onJ)x x (cm) ·1---~- -5.0 )' X )' ,e The net force 0 (b) q2 (b) q, so 1heforceis attractive. q, The net force on q3 is to the left. (a) A closeupof the forces of the charges and forces. q 1 is nega1i,eandq 3 positive, (a) FIGURE 20.19 5.0 •····· •q2 andq3 are positive,so the forceis repulsive. / -~ - F1 vectorsum showsthe anticipateddirectionof the net force. A We are interested in the net force on charge q3 . Let's stan by using Coulomb's law LOcompute the magnitudes of the two forces on charge q3 : + (F2onJ)., = - 1.9 X I0- 3 N - 1.9 X 10-3 N = -3.8 = (Fi on3)y + (F2onJ)y X I0- 3 F3y = + 1.9 X I0- 3 N - 1.9 X 10-3 N = 0 Thus the net force. as shown in AGURE 20.19b, is F3 = (3.8 X I0- 3 N. -x-direction) SOLVE The net force is directed to the left, as we anticipated. The magnitudeof the net force, a few mN, seems reasonable as well. ASSESS You've had a lot of expe1ience with the weight force, the friction force, and other forces that we've talked about, but you likely haven't had much experience with the electric force. How large are electric forces in practical situations? How does the magnitude of this force compare to other forces? We'll look at a couple of examples to give us a sense of scale, starting with an example involving small objects that have been deliberately charged by rubbing or some other means so that they acquire charges of ± 10 nC, a reasonable value for small objects that have been charged this way. How does the magnitude of the electric force compare to that of the weight force in such circumstances? 20.3 EXAMPLE Coulomb's Law 709 Comparing electric and gravitational forces 20.5 A small plastic sphere is charged to - IO nC. It is held 1.0 cm above a small glass bead at rest on a table. The bead has a mass of 15 mg and a charge of+ 10 nC. Will the glass bead "leap up" to the plastic sphere? STRATEGIZE We'll model the bead and the sphere as point charges, and measure distances from their centers. There is an attractive electric force from the bead that wi!J tend to pull the sphere upward. If this force is greater than the downward weight force, then the bead will leap upward. PREPARE We can start with a visual overview of the situation. AGURE 20.20 establishes a y-axis. identifies the plastic sphere as q 1 and the glass bead as q2 . and shows a free-body diagram. The glass bead wi!J tise if F1 on 2 > II': if F1 on 2 < ir. the bead wilJ remain at rest on the table, which then exerts a normal force ii on the bead. FIGURE 20.20 A visual SOLVE Using the values provided, we have overview showing the charges and forces. = 9 0 10-3 N Flon2 = Klqillq~I , .X r111= m2g = 1.5 X 10- 4 N /.Ocm F1 011 2 exceeds the bead ·s weight by a factor of 60, so the glass bead will leap upward. The values used in this example are realistic for spheres = 2 mm in diameter. These are small spheres that have been charged purposefully, given charges in the nC range. In such cases. for small separations, the electric force is considerable-much larger than the weight force. ASSESS iii- Sorne objects are deliberately charged, but others acquire charges as a matter of course; these charges tend to have smalJer magnitudes. For example, bees develop an electric charge as they fly through the air. This causes the bee to pick up pollen (as we've seen) and can enhance the bee's electric sense (which we'll discuss later), but does this charge cause the bee itself to experience electric forces? EXAMPLE 20.6 What is the force between the bees? 4fil!J The magnitude of the force is Two 0.10 g honeybees each acquire a charge of +23 pC ( 1 pC = 1 X 10- 12 C) as they fly back to their hive. As they approach the hive entrance, they are 1.0 cm apart. Approximate the magnitude of the repulsive force between the two bees. How does this force compare with their weight? SOLVE The bees clearly aren't point charges, but modeling them as point charges will give us an approximate value for the electric force they will feel. We'll compute the repulsive force using Coulomb's Jaw and then compare this to the weight force. You've certainly seen bees close together and they don't seem to experience a repulsive force, so we expect the weight force to be nmch greater than the electric force. This is clearly a smalJ force, but to put the size in perspective, we compare this force to the magnitude of the weight force acting on one bee: STRATEGIZE PREPARE The visual overview in FIGURE 20.21 is straightforwardtwo point charges separated by a distance r = 1.0 cm. The magn.itudes of the forces on the bees are equal, so we compute only F 1 011 2 . FIGURE 20.21 A visual overview showing a simplified model of the situation. ,. F2on I : ◄•1---,(j) I f', on 2 0---111► F Kjq, - ---- 1 on 2 - =4.8 111=mg= 11 q2 I ,.2 X (9.0 x 109 N • m2 /C 2 )(23 x 10- 12 c)2 - ----------,------(0.010111)2 10- 8 N (0.10 X 10- 3 kg)(9.8 m/s2 ) = 9.8 X I0- 4 N The weight force is greater Lban the electric force by a factor of 20,000, so the elecuic force is not likely to be noticeable to the bees. For objects that pick up charges naturally, the charges are much smaller-for the bees, in the pC range, not the nC range of the bead and sphere-so the forces are smaller as well. We don't expect to see significant forces between the bees. But the charge of the bee is large enough to attract a much lighter pollen grain from a much smalJer distance. And, as we'll see, bees are very sensitive to nearby electric charges; it's likely that the charge on one bee, although not enough to push a nearby bee away, is large enough for a nearby bee to sense. ASSESS 71 0 c HAP TE A 20 Electric Fields and Forces For the charged bead and sphere, the electric force was larger than the weight force; for the two bees, much less. On our macroscopic scale, electric forces dominate for small objects and deliberately charged objects. For much smaller charges, as on the bee, the electric force is much smaller as well. At an atomic level, the situation is more extreme. The opposite charges on water molecules create the attractive force of a hydrogen bond. The electric force on the molecules in this case is more than 1014 times larger than the weight force. At the atomic scale, the weight force is negligible; there's only one force that matters: the electric force between charged particles. Charges l and 2 exert repulsive STOP TO THINK 20.3 forces on each other. q 1 = 4q 2 . Which statement is true? > F2 on I B · Fi on 2 = F2 on I C. Fi on2 < F2on I 2 A. F1 on 2 20.4 The Concept of the Electric Field FIGURE 20.22 Visualizing the electric field. II Video Figure 20.22 FIGURE 20.23 The force and field models for the interaction between two charges. @ ~ A 0 " 8 In the force model, A exerts a force directly on B. In the field model, A alters the space around it. (The wavy lines are poetic license. We'll soon learn a better representation.) Coulomb's law is the basic law of electrostatics. We can use Coulomb's law to calculate the force a positive charge exerts on a nearby negative charge. But there is an unanswered question: How does the negative charge "know" that the positive charge is there? Coulomb's law tells us how to calculate the magnitude and direction of the force, but it doesn't tell us how the force is transmitted through empty space from one charge to the other. To answer this question, we will introduce the field model, first suggested in the early 19th century by Michael Faraday, a British investigator of electricity and magnetism. FIGURE20.22 shows a photograph of the surface of a shallow pan of oil with tiny grass seeds floating on it. When charged wires, one positive and one negative, touch the surface of the oil, the grass seeds line up to form a regular pattern. The pattern suggests that some kind of electric influence from the charges fills the space around the charges. Perhaps the grass seeds are reacting to this influence, creating the pattern that we see. This alteration of the space around the charges could be the mechanism by which the long-range Coulomb's law force is exerted. This is the essence of the field model. Consider the attractive force between a positive charge A and a negative charge B. FIGURE20.23 shows the difference between the force model, which we have been using, and the field model. In the field model, it is the alteration of space around charge A that is the agent that exerts a force on charge B. This alteration of space is what we call a field. The charge makes an alteration eve,ywhere in space. Other charges then respond to the alteration at their position. The field model applies to many branches of physics. The space around a charge is altered to create the electric field. The alteration of the space around a mass is called the gravitational field. The alteration of the space around a magnet is called the magnetic field, which we will consider in Chapter 24. The Electric Field Is Real • Fneld on B Panicle B then responds to Jhe altered space. The altered space is the agent that exerts the force on B. The field model might seem arbitrary and abstract. We can already calculate forces between charges; why introduce another way of looking at things? We will find that the field model is a very useful tool for visualizing and calculating forces for complex arrangements of charges. It is also a very useful tool for understanding certain aspects of the natural world. 20.4 But the electric field is real; it's not just an abstraction. As we' II see, when your heart beats, a charge separation develops; the same is true of other muscles. This charge separation creates an electric field. You literally affect the space around you in a way that can be detected at a distance. The platypus has an unusual bill that it uses to forage on the bottom of the creeks and ponds that it inhabits. The bill is very sensitive to vibrations produced by crustaceans and other prey, but it is also sensitive to the electric fields created by their heartbeats and muscle action. The platypus closes its eyes and ears as it forages, relying on its vibration sense and its electric sense to find its dinner. When a bee visits a flower, it transfers charge; this affects the electric field in the vicinity of the flower. The electric sense of a second bee allows it to determine, from a distance, that this flower was recently visited. A few mammals, some insects, and many fish have such an electric sense. To these creatures, the electric field is certainly not an abstraction; they actively sense the electric fields in their vicinity and use them to navigate, locate prey, and determine the best flowers to visit. Of course, you use electric fields as well. Toward the end of this section, we'll explore electromagnetic waves, waves of electric and magnetic fields that carry energy and information through space. If you are reading this text on a device that has a wireless connection, these very words were transmitted to your device by the use of electric fields. Fields may seem abstract, but they are very, very real. The Concept of the Electric Field 711 A platypus forages in the gravel at the bottom of a creek. The Field Model We begin our investigation of electric fields by postulating a field model that describes how charges interact: II Video Electric Field 1. A group of charges, which we call the source charges, alter the space around them by creating an electric field E. 2. If another charge is then placed in this electric field, it experiences a force F exerted by the field. Suppose charge q experiences an electric force F011 q due to other charges. The strength and direction of this force vary as q is moved from point to point in space. This suggests that "something" is present at each point in space to cause the force that charge q experiences. We define the electric field Eat the point (x, y, z) as _ £ at Fonq (x, •Y.:) = ----- at (.r. y. :) q (20.3) Electric field at a point defined by the force on charge q TABLE 20.2 Typical electric field strengths Field We're defining the electric field as a force-to-charge ratio; hence the units of the electric field are newtons per coulomb, or N/C. The magnitude E of the electric field is called the electric field strength. Typical electric field strengths are given in TABLE 20.2. As the table shows, a very small field in a wire will keep charges in motion. For fields in air-the main situation we' II consider-typical electric fields are much larger than this. The electric field outdoors near the ground is usually about JOON/C. You've never noticed this field before; it doesn't cause observable consequences except in special circumstances. A field of 1,000,000 N/C can cause a spark to jump; if the field around you approaches this value, you'll certainly notice it! The electric field inside the cell membrane is larger than this by a factor of I 0, so the electrical nature of nerve and muscle cells is clearly quite important. And the electric field Field strength (N/C) Inside a currentcarrying wire Earth's field, near the earth's surface Near objects charged by rubbing 103 to J0 6 Needed to cause a spark in air Inside a cell membrane 107 Inside an atom to'' 712 20 CHAPTER FIGURE 20.24 Electric Fields and Forces Charge q is a probe of the electric field. Charge q is placed at two different points in space. The force on the charge tells us that there's an electric field al these points. (a) f 00 'I ~······-;:_{ f Point I :,, ~ 1. The electric field, a vector, exists at every point in space. Electric field dia- Point 2 (b) ..•·This is the electric / .•...- field vector al point I. ( •.•. '.·.: This is the ele.ctric field vector a( point 2. The dots are the ./ ......... ~ points at which .•,.. the field is known. £, / 2~ inside an atom is 10,000 times larger still. At the atom.ic scale, electric forces are the only game in town. You can think of using charge q as a probe to determine whether an electric field is present at a point in space. If charge q experiences an electric force at a point in space, as FIGURE 20.24a shows, then there is an electric field at that point causing the force. Further, we define the electric field at that point to be the vector given by Equation 20.3. FIGURE 20.24b shows the electric field at two points, but you can imagine "mapping out" the electric field by moving the charge q throughout all space. The basic idea of the field model is that the field is the agent that exerts an electric force on a particle with charge q. Notice three important things about the field: grams show a sample of the vectors, but there is an electric field vector at every point whether one is shown or not. 2. If the probe charge q is positive, the electric field vector points in the same direction as the force on the charge; if negative, the electric field vector points opposite the force. 3. Because q appears in Equation 20.3, you might think that the electric field depends on the magnitude of the charge used to probe the field. It doesn't. We know from Coulomb's law that the force F0 n q is proportional to q. Thus the electric field defined in Equation 20.3 is independent of the charge q that probes the field. The electric field depends on only the source charges that create the field. The Electric Field of a Point Charge FIGURE 20.25 Charge q' is used to probe the electric field of point charge q. (a) What is the electric field of q at this poi!.:.t? :,, • shows a point source charge q that creates an electiic field at all points in space. We can use a second charge, shown as q' i11FIGURE 20.2sb, as a probe of the electric field created by charge q. For the moment, assume both charges are positive. The force on q', which is repulsive and points directly away from q, is given by Coulomb's law: FIGURE 20.2sa ➔ F0 n q' (±)....--Point f {b) I. Place q' at the point ,, , 011 q• E➔ = (Kq ,. q' ? , away from q) \, 2. Measure the force on q'. y q E= (Kl;I, [away ,.~ from~ if q > towru·d q if q < 0 O]) 3. The electric field is £=F00 q-/q' It is a vector in the direction of (20.5) The electric field is shown in FIGURE 20.2sc. If q is negative, the magnitude of the force on the probe chru·ge is the same as in Equation 20.5, but the direction is toward q, so the general expression for the field is /....~ 0 (20.4) Equation 20.3 defines the electric field in terms of the force on the probe charge as E= F011 </q', so for a positive charge q, to probe the fiel.ct.:_.,,;'~ (c) , away from q ) charge q , = (Kqq' ? Electric field of point charge q at a distance r from the charge E (20.6) ~1' INVERSE· SQUARE F'on q'· lmiil ► The expression for the electric field is similru· to Coulomb's law. To distinguish the two, remember that Coulomb's law has the product of two charges in the numerator. It describes the force between two charges. The electric field has a single charge in the numerator. It is the field of a single charge. ◄ 20.5 EXAMPLE 20. 7 The Electric Field of Multiple Charges 713 Finding the electric field of a proton The electron in a hydrogen atom orbics the proton at a radius of 0.053 nm. What is the electric field due to the proton at the position of the electron? SOLVE The proton·s charge is q = e. At the distance of the electron. the magnitude of the field is Ke (9.0 X JOY • m!,c!)( 1.60 x E= - = -------------r1 (5.3 X 10- 11 m)1 10-IY C) = 5.1 X 1011 N/C Because the proton is positive. the electric field is directed away from the proton: £ = (5.1 X 10 11 FIGURE 20.2s The electric field near a point charge. N/C, outward from the proton) This is a large field, but Table 20.2 shows that this is the correct magnitude for the field within an atom. ASSESS By drawing electric field vectors at a number of points around a positive point charge, we can construct an electric field diagram such as the one shown in FIGURE20.2sa. Notice that the field vectors all point straight away from charge q. We can draw a field diagram for a negative point charge in a similar fashion, as in FIGURE20.2Gb. In this case, the field vectors point toward the charge, as this would be the direction of the force on a positive probe charge. In the coming secti