A dipole approximation for a dielectric mixture based on the equal field energy method

In this paper, a dipole-energy approximation for calculating the electric field distribution and saturation charge of spheres in an infinitely large dielectric mixture has been carried out. The approximation rests on the assumption that the field energy of mixture calculated using two different methods have the same value. One way is considering that the mixture in a uniform field E₀ as a uniform object of effective permittivity ?_eff from a macroscopic point of view, where ?_eff is seen as the average characteristic parameter of the object. The other way is assuming that the spheres in mixture are in the equivalent external field E₀′, and E₀′ related to the dielectric mismatch and the ratio of the sphere radius to the average distance between neighboring spheres has been obtained. Based on dipole-energy model, the approximate formulas for calculating the maximum field strength and saturation charge of spheres are derived separately.