Solution procedure for the Laplace equation in bispherical coordinates for two spheres in a uniform external field: Perpendicular orientation

Abstract

A solution procedure is developed for the Laplace equation in bispherical coordinates for two spheres which are embedded in an infinite medium and which are aligned perpendicular to an external field which is uniform at infinity. The boundary conditions, continuity of the potential and continuity of the normal component of the flux density at the surfaces of the two spheres, are often encountered in several branches of the macroscopic field theory of linear media: electrostatics, magnetostatics, steady-state diffusion, electric current, and flow of heat.