Dipole images in conducting-particle chains

When a chain of conducting spheres is exposed to a uniform electric field, the spheres are polarized and a dipole moment is induced in each of them. Due to the mutual interaction of the spheres, the dipole moment depends on the configuration and size of the chain. Here the image charge method is employed, and the effects of such mutual interaction are considered by analyzing the higher-order image dipoles and image charges induced in the spheres. Closed-form expressions for chains containing 2 and 3 spheres are derived. The results are compared with previous calculations of a fractal model. Good agreement is obtained.