导体椭球的面电荷密度和曲率的关系

The relationship between the surface charge density and curvature for an ellipsoidal conductor

通过求解拉普拉斯方程,得到导体椭球的电势分布情况,进一步分析了导体表面的面电荷密度和曲率的关系,得到面电荷密度不是和曲率成正比,而是和曲率的1/3次方成正比的.

Using the Laplace＇ s equation, the potential distribution and the relationship of surface charge density to the curvature of an ellipsoidal conductor are obtained. It turns out that the surface charge density is not proportional to the curvature but to the cube root of the curvature.