Analytic Expressions of Potential and Electric Field Generated by a Triangular Surface Charge with a High-order Charge Density Distribution

Abstract

We have derived analytic expressions of the potential and electric field generated by a triangular surface charge that has a second-order or third-order charge density distribution on each element. These, expressions are applicable to the surface charge method (SCM) for electric field calculations in three-dimensional arrangements. In general, the higher-order charge density expression improves the accuracy of the SCM. Moreover, the SCM with analytic expressions needs no troublesome treatment of singular points inevitably involved in the SCM using numerical integration. We have also confirmed the validity of these derived analytic expressions by comparing the calculated results with those by the numerical method.