Electrostatic image theory for the conducting prolate spheroid

Abstract

Electrostatic image theory is developed for a point charge at theaxis of revolution of a perfectly conducting prolate spheroid. A previoustheory, introduced in 1995, presenting the image as a line charge between thefocal points, was seen to be numerically stable only when the charge is farenough from the spheroid and when the eccentricity of the spheroid is largeenough. The theory is improved by extracting a point charge from the lineimage, whence the remaining line charge becomes numerically better behaved, asdemonstrated by some examples. Because the extracted point image theoryreduces analytically to the classical Kelvin image in the case when thespheroid reduces to a sphere, and the line image simultaneously vanishes, thepresent theory can be seen as a generalization of the Kelvin image theory.