静电场中电场量值沿力线变化的微分方程及其解

Solutions of the differential equation of the variation of field magnitude along a flux line in an electrostatic field

本文对静电场中电场量值沿力线变化的微分方程的解分为三种情况进行了必要的证明和讨论:(1)等位面的平均曲率为一常数;2)等位面是平行曲面的近似;(3)等位面与正交曲线系的坐标曲面相合.还用一个普通的非弧立带电导体的例子说明三种情况下解的相对精确程度.最后。

Necessary proofs and discussions of the variation of field magnitude along a flux linein an electristatic field have been given for three cases: (1) The average curvature of anequipotential surface is a constant; (2) Equipotential surfaces are approximated by paral-lel surfaces; (3) The equipotential surface coincides with one of the coordinate surfaces incurvilinear coordinate systems. A typical example of nonisolated conductor is cited to illus-trate to what extent the results can be used in approximations. Finally, simple commentsare made on the equation and its solution.