By K. J. Binns
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Additional info for Analysis and Computation of Electric and Magnetic Field Problems
3. Intersecting plane boundaries Solutions have been obtained, in the first instance by Lodge, for a number of problems involving intersecting boundaries. The range of these solutions is, however, limited: a maximum of four boundaries can be handled, and the angles of intersection in the field region must in all cases be submultiples of it. ) The discussion is to be restricted to the magnet(1) 43 IMAGES ic field since the analogy with the electric field is now obvious and since flux-line boundaries occur only in the magnetic case.
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.
These are reasonably simple to apply and give solutions for most fields of practical interest. For general reading on the calculation of force the authors recommend the recent papers by Carpenter and the books by Moullin, Stratton, and Carter, and Maxwell. The calculation of force distribution is briefly mentioned in Maxwell and reference (3), but the application to practical problems is not discussed, except by Carter and Hammond . 4 is given a simple method applicable to equipotential boundaries.