Shielded point charges and multipoles

Complex electric potentials and energy relations for shielded point charges and point multipoles of any arbitrary orders are derived. It is demonstrated that both the complex electric potentials of shielded point multipoles and their interaction energies can be expressed through derivatives of the Green’s complex function. As an example, relations for the complex potentials of point multipoles of all orders in a half-plane are presented. It is indicated that the mathematical apparatus of shielded point multipoles can be used, in particular, for successive refinement of estimates of the shielded conductor capacitance. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 81–87, December, 2007.