AN ELECTROSTATIC IMAGE SOLUTION FOR THE CONDUCTING PROLATE SPHEROID

Electrostatic image theory for a point charge on the axis of a perfect ly conducting prolate spheroid is formulated. The exact image expressi on is found using the Havelock identity, according to which the extern al harmonics of the potential solution emanate from a system of contin uous image sources distributed along the focal line. An approximate im age is derived in the case of a slightly prolate sphere, which in the spherical limit resembles the image solution due to Lord Kelvin. An ex pression for the image polarization density function is derived for th e axial dipolar source.