利用多边形逼近圆环的思想计算有限长均匀带电的偏轴圆筒在空间任一点的电场

Calculation of the electric field of finite uniformly charged cylinder with excavated a small cylinder by using the idea of polygon approximation

根据有限长均匀带电线的电场强度解析公式以及叠加原理,用二重积分求解有限长均匀带电圆柱在空间(真空状态下)任一点的电场,借助计算机数值计算并模拟出有限长均匀带电的偏轴圆筒(即在大圆柱中挖去一个与之平行的非共轴的小圆柱空腔),在空间任一点的电场大小及方向.

According to the formula of the electric field due to finite unifomfly charged line and the superposition of electric field, this article gives a new method to calculate the electric field of finite uniformly charged cylinder with excavated a small cylinder, （in vacuum） which is easier, faster and more definite than the method using elliptical integral. Furthermore, discussion and simulation of the cases that arbitrary number of small cylinders are excavated are presented.