Fractal characterization of the dipole moments of dielectric particle chains

A simple self-similar fractal model is presented for obtaining the dipole moments of dielectric particle chains subjected to uniform electric field. The chains are replaced by equivalent spheres, and the effective radii of these spheres are determined from a fractal generating process. The dipole moments are determined in terms of the effective radii and are expressed as simple functions of the fractal dimension and the number of the particles in chain. The computed results for the longitudinal dipole moments are consistent with the previous calculations of the linear multipole expansion. The many-sphere nature of the moments of chains is well understood.