线电荷与接地开缝平面导体所形成的电场

The Electric Field of a Line Charge and a Grounding Plane Conductor with Straight Gap

线电荷与接地开缝平面导体所形成的电场的研究,可通过复数坐标系Z上的施瓦茨—克利斯多菲变换及其反变换,将ζ平面上宽度为S的开缝平面导体,映射为Z平面上的无开缝平面导体,利用平面镜像法计算线电荷与无开缝平面导体所形成的电场,再通过施瓦茨—克利斯多菲的反变换关系,得到线电荷与开缝平面导体所形成的电场,并根据该电场的复势,利用软件MATLAB绘制出其电场线和等势线图。由线电荷与开缝平面导体所形成电场的电场线与等势线图,可以部分地说明利用金属网罩而无须空腔导体就能够实现静电屏蔽的原理。

This paper is intended to calculate the complex potential of electric field of a line charge and a grounding plane conductor with straight gap. By using the Sch-Chris conversion in the complex coordinate system, a ζ plane conductor with straight gap whose width is S is mapped to a z plane conductor without gap. The electric field of a line charge and a grounding plane conductor without gap can be determined with mirror method and then inverse converted into that of a line charge and a grounding plane conductor with straight gap. With the line maps of electric field and equi-potential plotted by MATLAB, it is demonstrated that electrostatic screening can be realised with metal mesh rather than cavity conductor.