格林互易定理在静电学和检验数学恒等式中的应用  

Application of Green’s reciprocation theorem in electrostatics and verification of mathematical identities

作　　者：宋雨霏 梁兆新 SONG Yu-fei;LIANG Zhao-xin(Department of Physics,Zhejiang Normal University,Jinhua,Zhejiang 321004,China)

机构地区：[1]浙江师范大学物理学系,浙江金华321004

出　　处：《大学物理》2022年第12期75-80,共6页College Physics

基　　金：浙江省自然科学基金重点项目(LZ21A040001);国家自然科学基金(12074344)资助。

摘　　要：格林互易定理描述在静电平衡下任意两组导体电势在不同电荷分布下存在的数学关系,该关系在任意导体形状下、任意的其他导体分布情况下均成立.本文讨论了格林互易定理在静电学以及在先验式检验数学恒等式中的应用.通过与镜像法和本征函数展开法比较,本文展示了格林互易定理在处理一些静电学问题时的优势.另外,本文列举了常用方法基本不能求解,格林互易可以轻松求解的无限平行板电容器问题.特别是本文采用先验式的逻辑思路,基于格林互易定理设计了一个检验拉马努金著名无限求和公式以及其他一些数学恒等式的理想物理实验方案.Green’s reciprocation theorem is refereed as to a mathematical relationship between the potentials of any two groups of conductors with electrostatic balance under different charge distributions.Such a relationship stands under any conductor shapes and any other conductor distributions.In this work,we discuss the application of Green’s reciprocation theorem in electrostatics and checking priori mathematical identities.By comparing with the method of images and the method of eigenfunction expansion,we show the advantages of Green’s reciprocation theorem in dealing with some electrostatic problems.In addition,this work lists the infinite parallel plate capacitor problems which can be easily solved by Green’s reciprocation theorem,but hardly be solved by the traditional methods.In particular,this work designs an ideal experimental protocol to test the famous Ramanujan mathematical formula and some other mathematical identities based on Green’s reciprocation theorem.

关 键 词：格林互易定理 静电学 电势 拉马努金无限求和公式 

分 类 号：O4-1[理学—物理]