Image dipole method for the dipole moments of conducting particle clusters

Often it is difficult to calculate the dipole moments of clusters of conducting particles imposed to uniform electric fields, because of the difficulty in handling the mutual coupling between the particles. Such mutual coupling generally causes the polarization of the particles to be dependent upon the structures and the sizes of the clusters. In this paper, an image dipole method is employed for the analysis of this effect. First, a pair of two identical conducting spheres with arbitrary separation immersed in a longitudinal or transverse field is considered, and the image dipoles and image charges, and their distribution induced in each sphere are determined. Then, the dipole moments for the clusters with 4 and 8 spheres arranged on the vertexes of a square or a cube are estimated, and closed-form expressions are given. Comparison with previous calculations is made, and good agreement has been obtained.