Ch0204_2 - Chapter 4 Conductors and the Electric Field 4...

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Chapter 4 Conductors and the Electric Field 24 4 Conductors and the Electric Field An ideal conductor is chock full of charged particles that are perfectly free to move around within the conductor. Like all macroscopic samples of material, an ideal conductor consists of a huge amount of positive charge, and, when neutral, the same amount of negative charge. When not neutral, there is a tiny fractional imbalance one way or the other. In an ideal conductor, some appreciable fraction of the charge is completely free to move around within the conducting material. The ideal (perfect) conductor is well-approximated by some materials familiar to you, in particular, metals. In some materials, it is positive charge that is free to move about, in some, it is negative, and in others, it is both. For our purposes, the observable effects of positive charge moving in one direction are so close to being indistinguishable from negative charge moving in the opposite direction that, we will typically treat the charge carriers as being positive without concern for what the actual charge carriers are 1 . Here, we make one point about conductors by means of an analogy. The analogy involves a lake full of fish. Let the lake represent the conductor and the fish the charge carriers. The fish are free to move around anywhere within the lake, but, and this is the point, they can’t, under ordinary circumstances, escape the lake. They can go to every boundary of the body of water, you might even see some on the surface, but, they cannot leave the water. This is similar to the charge carriers in a conductor surrounded by vacuum or an insulating medium such as air. The charges can go everywhere in and on the conductor, but, they cannot leave the conductor. The facts we have presented on the nature of charge, electric fields, and conductors allow one to draw some definite conclusions about the electric field and unbalanced charge within the material of, and at or on the surface of, an ideal conductor. Please try to reason out the answers to the following questions: 1) Suppose you put a neutral ideal conducting solid sphere in a region of space in which there is, initially, a uniform electric field. Describe (as specifically as possible) the electric field inside the conductor and the electric field at the surface of the conductor. Describe the distribution of charge in and on the conductor. 2) Repeat question 1 for the case of a non-uniform field. 3) Suppose you put some charge on an initially-neutral, solid, perfectly-conducting sphere (where the sphere is not in a pre-existing electric field). Describe the electric field inside the conductor, at the surface of the conductor, and outside the conductor as a result of the unbalanced charge. Describe the distribution of the charge in and on the conductor. 4) Repeat questions 1-3 for the case of a hollow perfectly-conducting spherical shell (with the
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Ch0204_2 - Chapter 4 Conductors and the Electric Field 4...

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