VI. The scattering of plane electric waves by spheres

Abstract

The problem which gives its title to the present paper has been handled by various writers, notably by Lord Rayleigh, Sir J. J. Thomson, and Prof. Love. In most cases the solutions have been expressed in a Cartesian form; but it appears to me that a marked simplification is introduced by using spherical polar co-ordinates. The preliminary analysis becomes shorter, and the conclusions are easier to interpret; in fact, the analysis is nearly as simple as in the analogous problem of electrostatics, when an electric field is disturbed by the presence of a dielectric sphere. To obtain the requisite solutions a new general solution of the electromagnetic equations in Cartesian form is given in § 1, and is then transformed to the spherical polar form; 2, 3 contain a summary of certain analytical results required in the sequel.