Spherical image potentials for an N-charged particle system

Abstract

The potential energy interaction between a system of N charged particles and a spherical conducting surface is obtained by means of direct integration of the electrostatic energy density. Making use of the image charge method we show that the full potential can be split into a sum of one-body central potentials and two-body contributions related to particle-particle and particle-sphere interactions. Analytical expressions are provided for all contributions. The spherical surface of radius R can be considered to correspond to a cavity inside a conductor or a metallic ball, with two different electric conditions, namely the grounded and isolated charged cases. By taking the limit R → ∞ of the spherical case, one recovers the image potential for a N -charged particle system interactingwith a planar conductor. While the final results for the potential do not appear as unexpected, the provided analytical expressions should help in diverse physical applications modeled by a number of charged particles interacting close to a spherical surface.