Singular integral equation for an electric dipole taking into account the finite metal conductivity from which it is made

Abstract

A singular integral equation for an electric dipole has been obtained, which makes it possible to take into account the finite conductivity of the metal from which it is made. The derivation of the singular integral equation is based on the application of the Green’s function for free space, written in a cylindrical coordinate system, taking into account the absence of the dependence of the field on the azimuthal coordinate, on a point source located on the surface of an electric dipole. Methods for its solution are proposed. In contrast to the well-known mathematical models of an electric dipole, built in the approximation of an ideal conductor, the use of the singular integral equation obtained in this work makes it possible to take into account heat losses and calculate the efficiency.

Keywords

• electric dipole
• field in the near zone
• ill-posed mathematical problem
• green’s function
• singular integral equations
• self-consistent formulation of the problem
• heat losses
• finite electrical conductivity
• efficiency