Analytical expressions of potential and electric field generated by a triangular surface charge with a high-order charge density distribution

We have derived analytical expressions of the potential and electric field generated by a triangular surface charge that has a second- or third-order charge density distribution on each element. These expressions are applicable to the surface charge method (SCM) for calculating electric field in three-dimensional arrangements. In general, the higher-order charge density expression improves the accuracy of the SCM. Moreover, the SCM with analytical 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 analytical expressions by comparing the calculated results with those by the numerical method. (C) 2002 Wiley Periodicals, Inc.