Title: Approximate evaluation of capacitances by means of Green’s reciprocal theorem
Abstract: The application of Green’s reciprocal theorem to a system of two conductors forming a capacitor leads to an analytical expression for the capacitance that involves the equilibrium charge density on the surface of one conductor. This unknown density can be approximated on the basis of physical arguments (in the simplest case, with a constant) or with the aid of Thomson’s theorem. The method is applied to the evaluation of the capacitance of the sphere-plane system and the parallel disk capacitor, and is shown to yield fairly accurate results. For the latter capacitor, the constant density approximation yields a maximum deviation of about 7% from recently published numerical values; an improved density is also proposed that yields agreement within 1.5%.