Abstract: The uniqueness of the charge distribution of a conductor is one of the most essential properties in electrostatic fields and is challenging part for the teaching of electromagnetics course, which states that an isolated conductor has a uniquely determined distribution of charges on its surface in the state of electrostatic equilibrium. Many researchers have obtained different distributions of surface charges on conductors, but these analytical results are only valid for systems with high symmetry and only apply to cases where the charge distribution is continuous. In this study, we innovatively use the Monte Carlo annealing algorithm to build a computer model to try to verify the distribution of surface density of discrete charges on the surface of an ellipsoidal conductor after reaching electrostatic equilibrium, which is consistent with existing theoretical results. This method can be extended to the electrostatic equilibrium distribution of discrete charges in conductors of arbitrary shape, providing a new algorithm for numerical simulation of electrostatic problems and enriching toolbox for the teaching of electromagnetics. 

Key words: electrostatic equilibrium, Monte Carlo methods, annealing algorithms, charge distribution