An electrostatic image solution for the conducting prolate spheroid

Electrostatic image theory for a point charge on the axis of a perfectly conducting prolate spheroid is formulated. The exact image expression is found using the Havelock identity, according to which the external harmonics of the potential solution emanate from a system of continuous image sources distributed along the focal line. An approximate image is derived in the case of a slightly prolate sphere, which in the spherical limit resembles the image solution due to Lord Kelvin. An expression for the image polarization density function is derived for the axial dipolar source.