椭圆柱形材料中一种特殊电流系统的研究  

RESEARCH ON A SPECIAL CURRENT SYSTEM IN ELLIPTICAL CYLINDRICAL MATERIALS

作　　者：刘世勇 袁晓忠 张小灵 LIU Shiyong;YUAN Xiaozhong;ZHANG Xiaoling(School of Physics and Astronomy,Shanghai Jiao Tong University,Shanghai 200240)

机构地区：[1]上海交通大学物理与天文学院,上海200240

出　　处：《物理与工程》2025年第1期21-24,28,共5页Physics and Engineering

摘　　要：保角变换和电像法是解决电磁学问题非常重要的方法,本文以椭圆柱形材料中两平行电极构成系统的电流分布问题为例,展示这两种方法在实际中的一个应用。利用保角变换中的儒阔夫斯基变换,结合电像法,可将泊松方程问题转化为较简单边界条件的拉普拉斯方程问题,从而得到椭圆柱形材料中两平行电极系统电流和电压的解析解。通过定量计算,本文展示了边界面上电荷以及材料内电势和电流的分布情况。Methods of conformal mapping and electric images are two important methods for solving problems in electromagnetism.In the paper we present an application of these two methods by solving the problem of current distribution in a system of two parallel electrodes within an elliptical cylindrical material.By means of Zhukovsky transform from conformal mapping and electric image method,the Poisson equation problem is trans-formed into a Laplace equation problem with simplified boundary conditions and the ana-lytical solution is obtained.Using quantitative calculations,charge distribution on the boundary surfaces,as well as the potential and current distributions within the material are demonstrated.

关 键 词：儒阔夫斯基变换 泊松方程 拉普拉斯方程 

分 类 号：O441[理学—电磁学] O441.1[理学—物理]