By K. J. Binns
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Additional resources for Analysis and Computation of Electric and Magnetic Field Problems
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 essence of the method consists in replacing the effects of a boundary on an applied field by simple distributions of currents or charges behind the boundary line (called images), the desired field being given by the sum of the applied and the image fields.
5. F. CHORLTON, Circle and sphere theorems in potential theory and the determination of image systems, Birm. Coll. Adv. Tech. Technical Report, N o . 7 (1965). 6. C. J. CARPENTER, The application of the method of images to machine end-winding fields, Proc. Instn. Elect. Engrs. 107 A , 487 (1960). 7. J. K U N Z and P. L . BAYLEY, Some applications of the method of images, Phys. Rev. 17,147-56 (1921). 8. G . B . WALKER, Electric field of a single grid radio valve, Proc. Instn. Elect. , Part III, 98,57 (1951).
For any field in which the effect of currents is ignored, the potential at (r, 0') is the same as that at (r, d'+2nn\ where n is an integer, so that the solution sought for must be periodic in 6. 7) where c, d, g, and h are constants. 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.
Analysis and Computation of Electric and Magnetic Field Problems by K. J. Binns