Static Equilibrium Configurations of Charged Metallic Bodies

Abstract

When charged particles are placed on an uncharged metallic body, the charged particles redistribute themselves along the surface of the body until they reach a point or a configuration that no net tangential force is experienced on each particle. That point is referred to as electrostatic equilibrium configuration or simply as static equilibrium configuration. One of the properties which a metallic body possesses at static equilibrium configuration is among others that the distribution of charges is such that the potential energy is minimized. In this paper we developed a simple numerical scheme to determine the static equilibrium configuration of charged metallic bodies by minimizing the potential energy function. The method developed has some advantages; it combines the general theory and the physical meanings nested in the mathematical model and this has a positive implication on the computational aspect. For numerical simulations we considered the case of ellipsoids. Numerical solutions were produced, presented and discussed.