Reaction Concept in Electromagnetic Theory

Abstract

A physical observable called the reaction is defined to simplify the formulation of boundary value problems in electromagnetic theory. To illustrate its value it is used to obtain formulas for scattering coefficients, transmission coefficients, and aperture impedances. An approximate solution to problems of this type is obtained by replacing the correct source (of the scattered field for example) with an approximate source which is adjusted so that its reaction with certain "test" sources is correct. This insures that the approximate source "looks" the same as the correct source according to the physical tests which are inherent in the problem. The formulas so obtained have a stationary character (for the cases considered) and thus the results could also be obtained from a variational approach. However the physical approach has two important advantages. It is general whereas the variational technique has to be worked out for each problem. It is conceptually simple and leads directly to results which might not be uncovered by the variational approach because of the complexity of the mathematical formulation. The problem of scattering by a dielectric body is used to illustrate this latter point.