The electrical interaction of a system containing multiple, charged, rigid spherical particles of arbitrary orientation and size is analyzed theoretically. The equation governing the spatial variation of electrical potential is solved by a boundary integral method, and the electrical free energy of the system under consideration is evaluated. Several approximate analytical expressions fdr the electrical free energy are presented. We show that pairwise addition will, in general, overestimate the electrical free energy, except that when the electrical double layer around a particle is thin, it is approximately correct. Since the electrolyte concentration at which coagulation occurs is usually high, the classic analysis based on the interaction between two particles is representative of a system containing multiple particles and leads to reasonable results.