Approximation of the electric field of conductors by screened point charges and multipoles

Abstract

Efficiency of application of the mathematical screened multipole apparatus for a variational solution of the problem on screened conductor capacitance is demonstrated.The concepts of point multipoles in a plane were analyzed in detail in [1] where it was also demonstrated that based on the variational Gauss principle, the electric field of a circular parallel wire system can be approximated by fields of point multipoles of isolated wires with any arbitrary degree of accuracy. The complex electric potentials and energy relations for the screened point charges and screened point multipoles of arbitrary orders were found in [2]. Kazantsev et al. [2] demonstrated that both the complex electric potentials of screened point multipoles and the energy of their interaction could be expressed through derivatives of the complex Green's function. Examples of application of the mathematical screened multipole apparatus for a variational solution of the problem on screened conductor capacitance are considered in the present paper.