Solution of the electrostatic problem for a non-confocal core-mantle spheroid

We consider two-layered spheroidal particles when the layer surfaces are not confocal. By an analog of the separation of variables method using two spheroidal coordinate systems we find the exact solution to the electrostatic problem. Assuming that the field inside the particle core is uniform, we get the explicit approximation which coincides with the well-known Rayleigh approximation for spheroids with the confocal layers.