Exact solution of the problem of spatial potential theory for two spheres

Abstract

The problem of theory of potentials for two spherical conductors of the same radius is considered. Using the transformation formulas of harmonic functions for origin of spherical coordinates transfer, an infinite system of algebraic equations is obtained to determine the unknown constants. An approach to study of properties of solutions is proposed. This approach can be applied to the investigation of infinite systems for solving problems of potential theory for several spheres.