计及边缘效应的平行板电容器单位长度电容的计算  

The Calculation of Capacitance Per Unit Length of a Parallel Plate Capacitor with Edge Effect

作　　者：李文 赵威 王福谦 LI Wen;ZHAO Wei;WANG Fu-qian(Basic Department,Hope College of Southwest Jiaotong University,Chengdu 610400,China;Chengdu Transportation+Tourism Big Data Application Technology Research Base,Chengdu 610400,China)

机构地区：[1]西南交通大学希望学院基础部,四川成都610400 [2]成都市交通+旅游大数据应用技术研究基地,四川成都610400

出　　处：《数学的实践与认识》2023年第10期136-141,共6页Mathematics in Practice and Theory

摘　　要：将保角变换法与格林函数法相结合,研究计及边缘效应的平行板电容器的电场,得到其电势和场强分布,利用软件MATLAB对场分布进行数值模拟,给出其单位长度电容量的计算公式,并与忽略边缘效应的电容量的计算公式进行比较,得到两计算公式产生的相对误差随其宽与板间距之比变化的函数关系。By combining the conformal transformation method and Green's function method,the electric field of parallel plate capacitor with edge effect is studied,and the distribution of its electric potential and field strength is obtained.The numerical simulation of field distribution is carried out by using MATLAB software,and the calculation formula of the capacitance per unit length is given,and compared with the calculation formula of the capacitance with edge effect,the relative of the two calculation formulas is obtained The relationship between the error and the ratio of the width to the distance between plates.

关 键 词：平行板电容器 边缘效应 保角变换法 格林函数法 电势分布 场强分布 数值模拟 电容量 

分 类 号：TM53[电气工程—电器]