导体电荷分布的唯一性是静电场中最本质的性质之一，也是电磁学其中一个教学难点，表述为：孤立导体在静电平衡状态下，电荷唯一确定分布在表面.有不少研究者曾经得出很多不同导体表面电荷的分布关系，但是，这些解析结果仅对一些对称性较高的体系有效且仅适用于电荷连续分布情形.本研究中创新性地使用了蒙特卡洛退火算法来搭建计算机模型，尝试验证椭球状导体中达到静电平衡后离散电荷在导体表面的面密度分布，与已有理论结果符合.该方法可拓展应用于任意形状导体中离散电荷的静电平衡分布问题，为静电问题的数值模拟提供了一种新的算法，同时也为电磁学课程实践提供了一种新的教学手段.

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.