An alternative integral equation for calculating the surface charge in a parallel disk capacitor

Abstract

The potential from a parallel disk capacitor can be obtained by solving the Love integral equation. Although an expansion of the kernel yields fast convergence of the capacitance, at not too small disk separations, other quantities like the surface charge exhibit a considerably slower convergence. We present an alternative integral equation formulation of the problem that leads to more rapid convergence when computing the surface charge on the disks. The derivation of the kernel is outlined as well as the numerical implementation using a suitable set of expansion functions. Numerical results for the capacitance and the surface charge are presented, for several orders of disk separations.