带电厚椭球壳空腔内的电场

Electric field in the cavity of a charged thick ellipsoidal shell

确定一个均匀带电的厚椭球壳空腔内的电场,该厚椭球壳是由非导体构成的,其内表面和外表面分别是二个共轴的、等偏心率的椭球面.方法是把厚椭球壳分割成无限多个共轴的、等偏心率的薄椭球壳,先求出薄椭球壳上的电荷分布,经过与带电导体椭球表面上的电荷分布对比,得到薄椭球壳内的电场强度,最后用场强迭加原理求得厚椭球壳空腔内的电场强度,结果为零.

The electric field inside the cavity of a uniformly charged thick ellipsoidal shell is calculated.This shell is composed of non-conductor.Its inner and outer surfaces are two coaxial ellipsoidal surfaces with the same eccentricity ratios.The method is used to divide this thick ellipsoidal shell to infinite thin ones.Firstly,the charge distribution of the thin ellipsoidal shell is calculated.In comparsion with the charge distribution of the charged conducting ellipsoidal surface,the electric field in the thin ellipsoidal shell is found.Finally,with the help of the superposition principle of electric field,the electric field in the cavity of thick ellipsoidal shell equals zero is found.