Commonalities in the electrostatic characterization of several thin conducting cylinders using the singularity expansion method

Abstract

In this paper the Singularity Expansion Method (SEM) is used to describe the electrostatic charge distribution on a conducting body placed in a uniform electric field. Using the SEM, the step plane wave induced transient current on the body is expanded in terms of its singularities (poles) in the Laplace transform or complex frequency plane. Transient charge is derived from the induced current expression using the continuity equation and the final value theorem applied to obtain the electrostatic charge distribution. The SEM factorization is examined for a thin-wire “star” geometry (subsequently referred to as the tetra-arm structure) composed of four equal-length thin cylindrical conductors connected at a common junction. This element is observed to contain the essential electrostatic response modes of the planar symmetric cross, planar tri-arm, and linear elements. Electric polarizability is derived in terms of the SEM electrostatic charge description and is computed, as a function of arm bend angle, for the nonplanar tetra-arm element.