The Potential Due to Two Point Charges Each at the Centre of a Spherical Cavity and Embedded in a Dielectric Medium

Abstract

A method is found for determining the electrostatic potential due to two separated spherical cavities each containing a point charge with the whole system embedded in a continuous dielectric medium. The potential is obtained as a sum involving Legendre polynomials and it is shown that the coefficients of this series can be expanded as a convergent power series in the reciprocal of the distance between the centres of the cavities. This solution is suitable for numerical calculations because there is a simple relationship between successive terms in the series and because this series is convergent even at contact separation.