Electrostatic Image Theory for the Dielectric Prolate Spheroid

Abstract

Electrostatic image theory for a point charge at the axis of revolution of a dielectric prolate spheroid is introduced. Applying Neumann's integral identity, the image is represented as a line charge between the two focal points of the spheroid in terms of Legendre series. Because the series converges only for source points located beyond a certain critical distance depending on the dimensions of the spheroid, another representation for sources closer to the spheroid is given by extracting a point source and a line source from the focal-line image. Because the image expression contains those of the conducting spheroid and the dielectric sphere as special cases, the present theory appears as a generalization of both Kelvin's theory for the conducting sphere and Neumann's theory for the dielectric sphere.