Dipole moments of a pair of two touching unequal metallic spheres in an uniform electric field

The induced charge distributions on two touching metallic spheres, immersed in uniform electric field, are influenced by the mutual interactions between the spheres. This influence depends in a complicated way on their radical and the orientation of the external field. In this paper, the image method is applied to this electrostatic problem. The image charges are determined exactly. The longitudinal and transverse dipole moments of the pair are derived. Because the total induced charge of the pair is required to be zero, this results have the generality compared with previous discussions.