Capacitance of a cylindrical system

Abstract

A wide class of electromagnetic problems can be expressed as a system of dual integral equations. These kinds of integral equations occur in boundary value problems wherein there is an integral equation for a certain region and another for the rest of the region. In this paper it is shown that the integral equation for the charge density on a hollow metallic cylinder of finite length enclosed in another cylinder of infinite length can be put into «a standard form» of dual integral equations, which can be transformed into a numerically well-posed system of linear equation by means of a Neumann series. A general method to compute the coefficients of the linear system is discussed and some plots of the charge density distributions, and of the capacitance as a function of the ratioh/r1 (half-length/radius of the cylinder) are given. The range of validity of the classical asymptotic expansion is finally discussed.