Analysis and Computation of Electric and Magnetic Field by K. J. Binns

By K. J. Binns

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Extra info for Analysis and Computation of Electric and Magnetic Field Problems: Pergamon International Library of Science, Technology, Engineering and Social Studies

Sample text

107 C, 238 (1960). 13. J. F. H . DOUGLAS, Reactance of end-connections, Trans. Am. Inst. Elect. Engrs. 5 6 , 2 5 7 (1937). 14. P. J. LAWRENSON, The magnetic field of the end-windings of turbo-generators, Proc. Instn. Elect. Engrs. 108 A , 538 (1961). Additional Reference MACK, C , The field due to an infinite dielectric cylinder between two parallel conducting plates, Br. J. Appl. Phys. 6 , 59 (1955). 1. Introduction The method of images, because of its simplicity, is of considerable value, but for many problems involving multiple boundaries or specified distributions of potential or potential gradient, it is more convenient to solve the field equations directly.

5. P . HAMMOND, Forces in electric and magnetic fields, Bull. Elect. Engng. Educ. 2 5 , 1 7 ( 1 9 6 0 ) . 1. Introduction The method of images can be used to give solutions to some important problems involving straight-line or circular boundaries and in a particularly simple manner; for it offers certain ready-made solutions which eliminate the need for formal solutions of Laplace's and Poisson's equations. The idea of images for field problems is due to Lord Kelvin, but Maxwell, Lodge, and Searle extended the scope of the method.

The boundary conditions there, eqns. 21) where p is the relative permeability of the iron. Substituting in \p for a from eqn. 12), A THE SOLUTION OF LAPLACE'S EQUATION 65 then differentiating w and w and substituting in eqns. 25) The radial and tangential components of field strength are given by — (dip/dr) and — (dip/r dd) respectively. In forming them, a is expressed in terms of 0 as described in the previous section. The equivalence of the solution obtained by the method of images to that obtained above may be shown by summing the potential functions of the source and image currents, and by representing them in series form using eqns.

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