4D Integration and Evaluation of Electrostatic Force between Two Charged Parallel Plates

Abstract

Evaluation of electrostatic force between two arbitrary shaped charged objects encounters a six-fold integration. Analytic evaluation of the integral is not conducive and its numeric evaluation is CPU intensive. For two planar objects, the required integration reduces to a four-fold integration; however, it suffers the same two symptoms. In this article, utilizing a discrete method, we evaluate the much needed integration in a fraction of a second. For a special case, we show the output of our approach agrees with its analytic equivalent formulation.