Insulators and Conductors

Suppose you rub one end of an amber rod with fur. being careful not to touch the other end. The result is that the rubbed portion becomes charged, whereas the other end remains neutral. In particular, the negative charge transferred to the rubbed end stays put; it does not move about from one end of the rod to the other. Materials like amber, in which charges are not free to move, are referred to as insulators. Most in­sulators are nonmetallic substances, and most are also good thermal insulators.

In contrast, most metals are good conductors of electricity, in the sense that they allow charges to move about more or less freely. For example, suppose an un­charged metal sphere is placed on an insulating base. If a charged rod is brought into contact with the sphere, as in Figure 19-6 (a), some charge will be transferred to the sphere at the point of contact. The charge does not stay put, however. Since the metal is a good conductor of electricity, the charges are free to move about the sphere, which they do because of their mutual repulsion. The result is a uniform distribu­tion of charge over the surface of the sphere, as shown in Figure 19-6 (b). Note that the insulating base prevents charge from flowing a way from the sphere into the ground.

On a microscopic level, the difference between conductors and insulators is that the atoms in conductors allow one or more of their outermost electrons to become detached. These detached electrons, often referred to as "conduction electrons" can move freely throughout the conductor. In a sense, the conduction electrons be­have almost like gas molecules moving about within a container. Insulators, in contrast, have very few, if any, free electrons; the electrons are bound to their atoms and cannot move from place to place within the material.

Some materials have properties that are intermediate between those of a good conductor and a good insulator. These materials, referred to as semiconductors, can be fine-tuned to display almost any desired degree of conductivity by con­trolling the concentration of the various components from which they are made. The great versatility of semiconductors is one reason they have found such wide areas of application in electronics and computers.

Exposure to light can sometimes determine whether a given material is an in­sulator or a conductor. An example of such a photoconductive material is sele­nium, which conducts electricity when Light shines on it but is an insulator when in the dark. Because of this special property, selenium plays a key role in the production of photocopies. To see how, we first note that at the heart of every photocopier is a selenium-coated aluminum drum, Initially, the selenium is given a positive charge and kept in the dark—which causes it to retain its charge. When flash lamps illuminate a document to be copied, an image of the document falls on the drum. Where the document is light, the selenium is illuminated and be­comes a conductor, and the positive chaise flows away into the aluminum drum, leaving the selenium uncharged. Where the document is dark, the selenium is not illuminated, meaning that it is an insulator, and its charge remains in place. At this point, a negatively charged "toner" powder is wiped across the drum, where it sticks to those positively charged portions of the drum that were not illuminated. Next, the drum, is brought into contact with paper, transferring the toner to it. Finally the toner is fused into the paper fibers with heat, the drum is cleaned of excess toner, and the cycle repeats. Thus, a slight variation in electrical properties due to illumination is the basis of an entire technology.

The operation of a laser printer is basically the same as that of a photocopier, with the difference that in the laser printer the selenium-coated drum is illumi­nated with a computer-controlled laser beam. As the laser sweeps across the sele­nium, the computer turns the beam on and off to produce areas that will print light or dark, respectively.

19-3 Coulomb's Law

We have already discussed the fact that electric charges exert forces on one another. The precise law describing these forces was first determined by Coulomb in the late I780s. His result is remarkably simple. Suppose, for example, that an idealized point charge q1 is separated by a distance r from another point charge q2. Both charges are at rest; that is, the system is electrostatic. According to Coulomb's law, the magnitude of the electrostatic force between these charges is proportional to the product of the magnitude of the charges, |q1||q2|, and inversely proportional to the square of the distance, r2, between them:

Coulomb's Law for the Magnitude of the Electrostatic Force Between Point Charges

F=k*|q1||q2|/ r2

SI unit: newton, N

In this expression, the proportionality constant k has the value k = 8.89*10^9 N* m2/ C2

Note that the units of k are simply those required for the force F to have the units of newtons.

The direction of the force in Coulomb's law is along the line connecting the two charges. In addition, we know from the observations described in Section 19—1 that like charges repel and opposite charges attract. These properties are illustrated in Figure 19-7, where force vectors are shown for charges of various signs. Thus, when applying Coulomb's law; we first calculate the magnitude of the force using Equation 19-5, and then determine its direction with the "likes repel opposites attract" rule.

Finally note how Newton's third law applies to each of the cases shown in figure 19-7. For example, the force exerted on charge 1 by charge 2, F12, is always equal in magnitude and opposite in direction to the force exerted on charge 2 by charge I, F21; that is, F21 = — F12.

WHERE DO THEY COLLIDE?

An electron and a proton, initially separated by a distance R are released from rest simultaneously. The two particles are free to move. When they collide, are they (a) at the midpoint of their initial separation, (b) closer to the initial position of the proton, or (c) closer to the initial position of the electron?

REASONING AND DISCUSSION

Because of Newton's third law, the forces exerted on the electron and proton are equal in magnitude and opposite in direction. For this reason, it might seem that the particles meet at the midpoint. The masses of the particles, however, are quite different. In fact, as mentioned in Section 19-1, the mass of the proton is about 2000 times greater than the mass of the electron; therefore, the proton's acceleration (a - F/in) is about 2000 times less than the electron's acceleration. As a result, the particles collide near the initial position of the proton. More specifically they collide at the location of the center of mass of the system, which remains at rest throughout the process.

ANSWER

(b) The particles collide near the initial position of the proton.

It is interesting to note the similarities and differences between Coulomb's law, F=k*|q1||q2|/ r2, and Newton's law of gravity, F=Gm1m2/r2. In each case, the force decreases as the square of the distance between the two objects. In addition, both forces depend on a product of intrinsic quantities: in the case of the electric force the intrinsic quantity is the charge; in the сase of gravity it is the mass.

Equally significant, however, are the differences. In particular, the force of gravity is always attractive; whereas the electric force can be attractive or repulsive. As a result, the net electric force between neutral objects, such as the Earth and the Moon, is essentially zero because attractive and repulsive forces cancel one another. Since gravity is always attractive, however, the net gravitational force between the Earth and the Moon is nonzero. Thus, in astronomy gravity rules and electric forces play hardly any role.

Just the opposite is true in atomic systems. To see this, let's compare the electric and gravitational forces between a proton and an electron in a hydrogen atom. Taking the distance between the two particles to be the radius of hydrogen, r =5.29 x 10^-11 m, we find that the gravitational force has a magnitude 3.63*10^-47 N. Similarly, the magnitude of the electric force between the electron and the proton is 8.22X 10 -8N. Taking the ratio, we find that the electric force is greater than the gravitational force by a factor of 2.26 x 10^39.

This huge factor explains why a small piece of charged amber can lift bits of paper off the ground, even though the entire mass of the Earth is pulling downward on the paper.

Clearly, then, the force of gravity plays essentially no role in atomic systems. The reason gravity dominates in astronomy is that, even though the force is incredibly weak, it always attracts, giving a larger net force the larger the astronomical body. The electric force, on the other hand, is very strong but cancels for neutral objects.

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