环状电极诱导的静电场电位分布研究

Study of Electric Potential of Electrostatic Field Induced by Annular Electrode

有限差分法是电磁场数值计算中应用最早的一种方法,它以简单、直观的特点而广泛应用于电磁场工程问题中。文中针对在真空罐中用环状电极诱导的静电场分布的实际工程问题,基于有限差分法离散柱坐标系下的拉普拉斯方程,将三维对称静电场问题转化为二维静电场问题,运用EXCEL软件计算空间内各离散点上的电位值,采用MATLAB软件绘制三维对称静电场中的电位分布,为实际工程问题的分析和设计提供了理论依据和技术支持。

The finite differential method is one of the earliest methods applied in the numerical calculation of electromagnetic fields.It is still widely used in electromagnetic engineering due to simple and intuitive features.In this paper,electrostatic potential distribution induced by annular electrode in a vacuum tank is analyzed for practical engineering problems.Discrete Laplace equation from the finite differential method under cylindrical coordinate system is firstly obtained.Then,the three-dimensional symmetrical electrostatic field problem is transformed into a two-dimensional electrostatic field problem.At the same time,the potential values of all the discrete points in space are calculated using EXCEL software,and the potential distribution map of three dimensional symmetric electrostatic field is plotted by MATLAB software,which provides theoretical basis and technical support for the analysis and design of the actual engineering problems.