Electrostatic image theory for the conducting prolate spheroid

Electrostatic image theory is developed for a point charge at the axis of revolution of a perfectly conducting prolate spheroid. A previous theory, introduced in 1995, presenting the image as a line charge between the focal points, was seen to be numerically stable only when the charge is far enough from the spheroid and when the eccentricity of the spheroid is large enough. The theory is improved by extracting a point charge from the line image, whence the remaining line charge becomes numerically better behaved, as demonstrated by some examples. Because the extracted point image theory reduces analytically to the classical Kelvin image in the case when the spheroid reduces to a sphere, and the line image simultaneously vanishes, the present theory can be seen as a generalization of the Kelvin image theory.