THE ELECTROSTATIC PROBLEM OF A CONDUCTING CIRCULAR TORUS WITH DIELECTRIC SLEEVE

Integral-equation perturbation theory, which has been described previously, is applied here to the electrostatic problem of a freely-charged conducting circular torus embedded in a dielectric, the outer surface of the dielectric being itself a circular torus with cross-section concentric with that of the conducting torus. The method requires that a perturbation parameter which is the ratio of a cross-sectional radius to a radius of revolution be not too large, and a solution is obtained to the second order in this parameter. From this solution, a formula for the capacity of the conductor is obtained. 1