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# chapt06 - CHAPTER 6 EXPERIMENTAL MAPPING METHODS We have...

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CHAPTER 6 EXPERIMENTAL MAPPING METHODS We have seen in the last few chapters that the potential is the gateway to any information we desire about the electrostatic field at a point. The path is straight, and travel on it is easy in whichever direction we wish to go. The electric field intensity may be found from the potential by the gradient operation, which is a differentiation, and the electric field intensity may then be used to find the electric flux density by multiplying by the permittivity. The divergence of the flux density, again a differentiation, gives the volume charge density; and the surface charge density on any conductors in the field is quickly found by eval- uating the flux density at the surface. Our boundary conditions show that it must be normal to such a surface. Integration is still required if we need more information than the value of a field or charge density at a point . Finding the total charge on a conductor, the total energy stored in an electrostatic field, or a capacitance or resistance value are examples of such problems, each requiring an integration. These integrations cannot generally be avoided, no matter how extensive our knowledge of field theory becomes, and indeed, we should find that the greater this knowledge becomes, the more integrals we should wish to evaluate. Potential can do one important thing for us, and that is to quickly and easily furnish us with the quantity we must integrate. Our goal, then, is to find the potential first. This cannot be done in terms of a charge configuration in a practical problem, because no one is kind enough to 169

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tell us exactly how the charges are distributed. Instead, we are usually given several conducting objects or conducting boundaries and the potential difference between them. Unless we happen to recognize the boundary surfaces as belong- ing to a simple problem we have already disposed of, we can do little now and must wait until Laplace's equation is discussed in the following chapter. Although we thus postpone the mathematical solution to this important type of practical problem, we may acquaint ourselves with several experimental methods of finding the potential field. Some of these methods involve special equipment such as an electrolytic trough, a fluid-flow device, resistance paper and the associated bridge equipment, or rubber sheets; others use only pencil, paper, and a good supply of erasers. The exact potential can never be deter- mined, but sufficient accuracy for engineering purposes can usually be attained. One other method, called the iteration method, does allow us to achieve any desired accuracy for the potential, but the number of calculations required increases very rapidly as the desired accuracy increases.
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