数值计算在求解带电体电势教学中的应用

The Application of Numerical Calculation Method in Teaching for Solving the Potential of Uniformly Charged Object

连续带电体产生的电势通常利用点电荷产生的电势及电势叠加原理进行求解。但在实际计算过程中,一些电势积分计算过于复杂,无法求其解析解。对此,需要引入数值计算获得高精度的数值解。首先将均匀带电圆环内任意一点电势解析解与数值解进行比较分析,引入此类问题数值解法,并将此方法扩展到一般的非规则带电体在空间任意点产生的电势。最后在此基础上研究开孔平行板孔径大小对电极间电势分布的影响,为开孔电极板在实际的应用提供理论指导。

The potential generated by a uniformly charged body can usually be solved by using the potential generated by point charges and the principle of superposition of potential,but in the actual calculation process,some electric potential integral calculation is too complicated to get the analytical solution.Therefore,numerical calculation is needed to obtain a more accurate numerical solution.In this paper,the analytical and numerical solutions of the electric potential generated by a uniformly charged ring at any point in the ring are compared,and the numerical solution of this kind of problem is introduced,and the method is extended to more general electric potential generated by irregular charged bodies at any point in space.On this basis,the influence of aperture size of open-hole parallel plate on the potential distribution between electrodes is studied,which provides theoretical guidance for the application of open-hole electrode plate in practice.