A.S. Cherepanov - Dr. Sc. (Phys.-Math.), Associate Professor, St. Petersburg State Polytechnical University. E-mail: ascher@radio.rphf.spbstu.ru

The electrostatic problem about ellipsoid containing anisotropic dielectric material, disposed in uniform static electric field, has been solved. Following assumptions have been made: 1. The field out of ellipsoid is a superposition of a constant field and a field, which structure coincides with a field out of isotropic ellipsoid placed in the same uniform field. 2. The field inside anisotropic ellipsoid is homogeneous (as well as in isotropic one, but can differ in a direction). Such fields satisfy to the electrostatics equations. Further it has been shown, that it is possible to satisfy to boundary conditions on a surface of ellipsoid, choosing properly arbitrary constants, which exist in expressions for fields in external and internal areas. Thus, the constructed solution is the unique solution of the given electrostatic problem (on the basis of the theorem about uniqueness of electrostatics problems solution). The formulas have been obtained, allowing to calculate a field inside and out of ellipsoid.