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

By K. J. Binns

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Sample text

If a set is proposed for one region only, it can be verified by consideration of surface charge distribution. A simpler check is possible when the boundaries are equipotential or flux line, for then the boundary conditions are easily seen to be satisfied by the system of images which is symmetrically disposed about all the boundary lines. (1) (2) (3) (4) (5) 37 38 ELECTRIC A N D MAGNETIC FIELD PROBLEMS It is convenient here to consider images under two headings: firstly those due to plane boundaries, and, secondly, those due to circular boundaries.

All problems treated in this book are essentially steady-state ones, but an approximate method, using steady-state results, can be used for certain transient problems involving boundaries carrying eddy-currents induced by the applied field. The effect of the eddy-current is to reduce the quantity of flux crossing the boundary and, if the assumption is made that no flux penetrates (that is the boundary is a flux line), solutions may be obtained by taking the boundary permeability to be zero. The field of a line-current near a semi-infinite block of impermeable material is given by eqn.

4) This is the same field distribution, however, as would result either from a charge —q(e —£i)/(£2+£i) at a distance a behind the boundary line, or, equally, from a charge + q(s2—£i)/(fi2+£i) at a distance a from the boundary in region 1. Hence either of these charges can be used to account for the effect of the boundary. However, only one of them can be used in the representation of the field in each of the two regions. Thus, considering first the field in region 1, it is seen that the second of the charges would cause a change in the total flux entering or leaving any curve enclosing the charge q in region 1 [that is eqn.

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