POTENTIAL OF A CHARGED CYLINDER

A method, based on complex variable theory, is presented for solving potential problems involving conducting solids of revolution. Attention is paid exclusively to the right circular cylinder, both because this problem possesses a high degree of symmetry which brings about certain simplifications, and because comparison can be made with previous results. The generalization from the cylinder to other axially symmetric geometries should become obvious. This method depends on the establishment of an intergral representation for the potential function which leads to the formulation of the problem in terms of a pair of coupled Fredholm integral equations of the first kind. As an illustrative example, these equations are solved numerically in the lowest approximation and the capacitance of the cylinder is calculated.