Electrostatic Interaction of a Charged Dielectric Sphere with a Flat Charged Interface between Homogeneous Dielectrics - Filippov, A. V. (Journal of experimental and theoretical physics, 2022)
The interaction of two charged dielectric spheres, the radius of one of which is much larger than the radius of the other sphere, is considered for small distances between their surfaces. Analytic solutions are obtained for the expansion coefficients of the potential for large multipole moments. Exact analytic expressions are derived for the interaction force in the method of expansion of the potential in the bispherical coordinate system in the case when the permittivity of one of the spheres coincides with the permittivity of the medium in which the spheres are located. A transition is made to the case of an infinitely large radius of the sphere with the permittivity differing from that of the medium. It is shown that these solutions coincide with the familiar solution to problems of interaction of a point charge with a dielectric sphere and with a flat charged interface between the dielectrics. A transition is made to an infinitely large radius of one of the spheres in the case when the permittivities of both spheres differ from that of the medium, and analytic solution is obtained to the problem of interaction of a charged dielectric sphere with a flat charged interface between homogeneous dielectrics.