By K. J. Binns
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Additional info for Analysis and Computation of Electric and Magnetic Field Problems
Engrs. 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.
Hence, substituting for R and S in eqn. 2) gives a particular solution of the original equation as (g cos md + h sin md). 8) This function is known as a circular harmonic of order m. 8) capable of satisfying eqn. 1). Since a linear combination of these particular solutions also satisfies eqn. 1) (see, for example, Churchill, p. 9) where m takes all integral values between 1 and oo. For any fixed value of r in the range 0 r =s= oo, the right-hand side of this equation is a Fourier series in 9 (which can be used to represent any single-valued and periodic function, such as ip) and, therefore, it is capable of describing the field due to any physically realizable boundary influences.
Analysis and Computation of Electric and Magnetic Field Problems by K. J. Binns