均匀带电半球体轴线上的场强分布求解探讨

Discussion on the solution of electric field strength s distribution on theaxis of a uniformly charged hemispheroid

对于均匀带电半球体,因电荷分布不具有高度对称性不能利用高斯定理求其轴线上的电场分布,采用场强叠加原理和电势梯度两类多种方法经严格地推导求出了其轴线上任一点电场强度分布的解析解,结果表明均匀带电半球体内外轴线上各个区域电场强度分布的解析解不同,虽然采用的方法不同,但是得到的结论是一致的.对于均匀对称分布的带电体,选取合适的电荷元,利用场强叠加原理求解场强分布比较简捷,而电荷非均匀对称分布利用叠加原理求解较困难时,可采用电势梯度求解.

For uniformly charged hemispheroid,the distribution of the electric field strength on its axis cannot be calculated by the Gauss law because the charge distribution is not highly geometrical symmetry.Based on the superposition principle of electric field strength and the method of electric potential gradient,the analytical solutions of electric field strength s distribution on its axis is derived strictly,the results show that the analytical solutions of the electric field strength s distribution in each region of the axis of the uniformly charged hemispheroid are different,the same conclusions are obtained by various methods.For the charged body with uniform and symmetrical distribution,it is easier to select the appropriate charge element and use the superposition principle of field strength to solve the field strength distribution,while the potential gradient can be used to solve the non-uniform and symmetrical distribution when it is difficult to solve by the superposition principle.