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Electric Charge and Electric Field

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Electric Charge and Electric Field CHAPTER 17 By the end of this chapter, you will be able to: 1. Sketch the distribution of charges for both Electric Charge conducting and insulating objects in various arrangements. and Electric Field 2. Calculate the number of fundamental units of charge in a particular quantity of charge. 3. Determine both the magnitude and direction of the force one charge exerts on another using Coulomb’s law. 4. Determine the net force acting on a charge due to an array of point charges. 5. Relate both the magnitude and direction of the electric field at a point to the force felt by a charge placed at that point. 6. Determine the net electric field at a point due to both an array of point charges and a symmetric charge distribution. In a thundercloud, it is believed that collisions between ice and slush particles 7. Determine the electric flux through a surface. give the ice particles a slight positive 8. Relate the net electric flux through a closed charge. Although the details of this process surface to the amount of charge enclosed by are not understood, the resulting charge the surface. separation can produce enormous electric fields that result in a lightning bolt. hen you scuff your shoes across a carpet, you can In this chapter, we’ll study how electric charges that are at get zapped by an annoying spark of static electricity. rest in our frame of reference influence each other; we call these WThat same spark could, in principle, totally destroy an electrostatic interactions. We’ll find that charge has interest- integrated circuit chip in your computer. Fortunately, most mod- ing properties. It is quantized: The total electric charge in a sys- ern electronic devices are designed to prevent such a catastrophe. tem must be an integer multiple of the charge of a single electron. Lightning, the same phenomenon on a vastly larger scale, can Electric charge also obeys a conservation law: Charge can be destroy a lot more than computer chips. All these phenomena in- neither created nor destroyed. However, most of the chapter will volve electric charges and the interactions between such charges. be devoted to the forces that charges produce on other charges. 525 M17_YOUN2788_10_SE_C17_525-561.indd 525 9/23/14 4:59 PM 526 CHAPTER 17 Electric Charge and Electric Field These electrostatic forces are governed by Coulomb’s law and are mediated by electric fields. Electrostatic forces hold atoms, molecules, and our bodies together, but they also are constantly trying to tear apart the nuclei of atoms. We’ll explore all these concepts in this chapter. 17.1 Electric Charge The ancient Greeks discovered as early as 600 B.C. that when they rubbed amber with wool, the amber could attract other objects. Today we say that the amber has acquired a net electric charge, or has become charged. The word electric is derived from the Greek word elektron, meaning “amber.” When you scuff your shoes across a nylon carpet, you become electrically charged, and you can charge a comb by passing it through dry hair. Plastic rods and fur (real or fake) are particularly good for demonstrating electric-charge interactions. In Figure 17.1a, we charge two plastic rods by rubbing them on a piece of fur. We find that the rods repel each other. When we rub glass rods with silk (Figure 17.1b), the glass rods also become charged and repel each other. But a charged plastic rod attracts a charged glass rod (Figure 17.1c, top). Furthermore, the plastic rod and the fur attract each other, and the glass rod and the silk attract each other (Figure 17.1c, bottom). These experiments and many others like them have shown that there are exactly two ▲ Application (no more) kinds of electric charge: the kind on the plastic rod rubbed with fur and the kind Run! on the glass rod rubbed with silk. Benjamin Franklin (1706–1790) suggested calling these The person in this vacation snapshot, taken two kinds of charge negative and positive, respectively, and these names are still used. at a scenic overlook in Sequoia National Park, was amused to find her hair standing on end. Luckily, she and her companion left the Like and unlike charges overlook after taking the photo—and before Two positive charges or two negative charges repel each other; a positive and a it was hit by lightning. Just before lightning negative charge attract each other. strikes, strong charges build up in the ground and in the clouds overhead. If you’re standing on charged ground, the charge will spread In Figure 17.1, the plastic rod and the silk have negative charge; the glass rod and the fur onto your body. Because like charges repel, have positive charge. all your hairs tend to get as far from each When we rub a plastic rod with fur (or a glass rod with silk), both objects acquire net other as they can. But the key thing is for you to get as far from that spot as you can! charges, and the net charges of the two objects are always equal in magnitude and opposite in sign. These experiments show that in the charging process we are not creating electric Plain plastic rods neither Plain glass rods neither The fur-rubbed plastic attract nor repel each attract nor repel each rod and the silk- other... other... rubbed glass rod attract each other... ––––– Fur Plastic +++ + + Silk Glass ... but after being ... but after being ... and the fur and silk rubbed with fur, rubbed with silk, each attracts the rod it the rods repel the rods repel rubbed. each other. each other. +++ + + ––––– – +++ + + – + – + – + + + – + + + + + + ++ (a) Interaction between plastic rods rubbed (b) Interaction between glass rods rubbed (c) Interaction between objects with opposite on fur on silk charges ▲ FIGURE 17.1 Experiments illustrating the nature of electric charge. M17_YOUN2788_10_SE_C17_525-561.indd 526 9/23/14 4:59 PM 17.1 Electric Charge 527 charge, but transferring it from one object to another. We now know that the plastic rod ac- quires extra electrons, which have negative charge. These electrons are taken from the fur, which is left with a deficiency of electrons (that is, fewer electrons than positively charged protons) and thus a net positive charge. The total electric charge on both objects does not change. This is an example of conservation of charge; we’ll come back to this important principle later. CONCEPTUAL ANALYSIS 17.1 The sign of the charge SOLUTION Since balls 1 and 2 repel, they must be of the same sign, Three balls made of different materials are rubbed against different either both positive or both negative. Since balls 2 and 3 repel each types of fabric—silk, polyester, and others. It is found that balls 1 and 2 other, they also must be of the same sign. This means that 1 and 3 both repel each other and that balls 2 and 3 repel each other. From this result, have the same sign as 2, so all three balls have the same sign. The cor- we can conclude that rect answer is C. A. balls 1 and 3 carry charges of opposite sign. B. balls 1 and 3 carry charges of the same sign; ball 2 carries a charge of the opposite sign. C. all three balls carry charges of the same sign. The physical basis of electric charge Atom When all is said and done, we can’t say what electric charge is; we can only describe its properties and its behavior. However, we can say with certainty that electric charge is one Most of the of the fundamental attributes of the particles of which matter is made. The interactions atom’s volume ~10 -10 m is occupied responsible for the structure and properties of atoms and molecules—and, indeed, of all or- sparsely by dinary matter—are primarily electrical interactions between electrically charged particles. electrons. The structure of ordinary matter can be described in terms of three particles: the nega- tively charged electron, the positively charged proton, and the uncharged neutron. The protons and neutrons in an atom make up a small, very dense core called the nucleus, with -15 Tiny compared with the a diameter on the order of 10 m (Figure 17.2). Surrounding the nucleus are the elec- rest of the atom, the 10 Nucleus trons, which orbit the nucleus out to distances on the order of 10- m. If an atom were a nucleus contains over few miles across, its nucleus would be the size of a tennis ball. 99.9% of the atom’s mass. The masses of the individual particles, to the precision that they are currently known, ~10 -15 m are as follows: Proton: Positive charge -31 27 Mass of electron = me = 9.10938291 40 * 10 kg, Mass = 1.673 * 10 - kg Mass of proton m 1.672621777 74 10-27 kg, = p = 1 2 * Neutron: No charge Mass of neutron m 1.674927351 74 10-27 kg. Mass = 1.675 * 10 -27 kg = n = 1 2 * The numbers in parentheses are the uncertainties in the last two digits. Note that the masses Electron: Negative charge 1 2 -31 of the proton and neutron are nearly equal (within about 0.1%) and that the mass of the Mass = 9.109 * 10 kg proton is roughly 2000 times that of the electron. Over 99.9% of the mass of any atom is The charges of the electron and concentrated in its nucleus. proton are equal in magnitude. The negative charge of the electron has (within experimental error) exactly the same ▲ FIGURE 17.2 Schematic depiction of the magnitude as the positive charge of the proton.
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