Solution of inverse problem for a charge combined with a point-like dipole

Inverse problems in electrodynamics are not sufficiently advanced though they are of certain theoretical interest and practical implementation. Here we propose a particular inverse problem of electrostatics. It is well known that the field induced by electric charge arbitrarily distributed within a finite area is, in the far-field approximation, equal to the field of a point-like charge and dipole moment. Calculation of the field produced by a given charge or dipole moment is referred to as a direct problem