By K. J. Binns
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Additional info for Analysis and Computation of Electric and Magnetic Field Problems
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.
27) where sieo is the permittivity in the field region, and £2^0 is that inside the second region, and where t is the position of the doublet and h is the complex conjugate of t\. The image for the field in the region of permittivity e e can easily be found, but it is not given here. The images of a doublet near a circular boundary can be found similarly, though rather more care is required. The case of the doublet exterior to the boundary and the solution for the region containing the doublet is examined.
18) In the iron, r can be zero so that, as the potential at the origin must be finite, d must be zero. This region does not contain a current or pole, so there are no additional terms. 19) and it remains to determine d and c from the continuity of the two functions ip and xpj on the cylinder surface. 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.