导体表面的场强与等位面曲率的关系

The relation between the field magnitude on a conductor surface and the curvature of the equipotential surface

文中按照近一百年前J.J.汤姆逊的方法和引用平行曲面来近似相邻等位面的方法得到了在静电场中沿力线相邻两点场强量值的两个算式,它们都显含等位面的曲率。并指出了所得的结果与已知的孤立带电导体上的电场量值的算式不同,且两者不能互相转化。最后对用旋转抛物面作为等位面的近似所具有的普遍意义做了初步的讨论。

According to the method suggested by J.J.Thomson one hundred years ago,we approxi-mate neighboring equipotential surfaces by parallel surfaces to obtain formulas for calculatingfield magnitudes of two neighboring points along a flux line in electrostatics.We point out thatthe results obtained are different from the known expressions and that the latter and the for- mer cannot be transformed into each other.Finally,the approximation by a paraboloid of rev-olution which has a general meaning for equipotential surfaces is discussed.