Electrostatic image theory for the dielectric prolate spheroid

Electrostatic image theory for a point charge at the axis of revolution of a dielectric prolate spheroid is introduced. Applying Neumann's integral id entity, the image is represented as a line charge between the two focal poi nts of the spheroid in terms of Legendre series. Because the series converg es only for source points located beyond a certain critical distance depend ing on the dimensions of the spheroid, another representation for sources c loser to the spheroid is given by extracting a point source and a line sour ce from the focal-line image. Because the image expression contains those o f the conducting spheroid and the dielectric sphere as special cases, the p resent theory appears as a generalization of both Kelvin's theory for the c onducting sphere and Neumann's theory for the dielectric sphere.