Surface Charge Density of a Conducting Ellipsoid in a Coaxial Electric Field

An effective method was proposed for determining the surface charge density of an ellipsoidal conductor placed in an axisymmetric external electric field. The method is based on solving a one-dimensional Fredholm integral equation of the first kind by applying the Galerkin method. Numerical experiments with test problems show that the numerical errors of the proposed method are significantly smaller than previously obtained ones.