Integral-equation Perturbation Theory for Electrostatic Torus Problems with Applied Fields

A perturbation method has been given for solving the Fredholmintegral equations of electrostatics as applied to tori of revolution,but under the restriction that there be in no case an appliedfield other than perhaps one that is uniform and parallel tothe axis of the torus. In the present paper this restrictionis removed, both for the conductor situation (Robin's equation)and the dielectric one (Durand's equation), and the generalizedmethod is illustrated by three applications. Two of these areto new problems which prove to be of considerable interest inthemselves, and one of the two leads to an example of significantfailure of the perturbation method.