浅谈电动力学角域静电场问题  

Study of electrostatic field between intersecting planes in electrodynamics

作　　者：石寰宇 苗荣欣 SHI Huan-yu;MIAO Rong-xin(School of Physics and Astronomy,Sun Yat-sen University,Zhuhai,Guangdong 519802,China)

机构地区：[1]中山大学物理与天文学院,广东珠海519082

出　　处：《大学物理》2022年第11期65-71,共7页College Physics

基　　金：国家自然科学基金(11905297);广东省自然科学基金(2020A1515010900)资助。

摘　　要：角域静电场问题指两块半无限大接地导体板通过一夹角相接,给定所夹区域的电荷分布,求空间各处的电场.简单起见,本文研究源电荷为点电荷时的情况.首先利用镜像法分析了一类特殊夹角的电势分布,然后通过分离变量法求解了一般的角域静电场问题,并验证两种方法得到的结果一致.最后本文讨论了满足第二类边界条件和混合边界条件的角域静电场问题,给出电势通解并得到一系列关于第二类勒让德函数的恒等式.It is an interesting problem to investigate the electrostatic field between two intersecting planes with given opening angle and charge distribution.For simplicity,we focus on the case that the source is a point charge.First,the potential distribution of some special opening angles is analyzed by using the method of image.Furthermore,the general case is solved by applying the separation of variables.The equivalence of the two results is verified by mathematical derivations.Finally,the discussion is generalized to Neumann and mixed boundary conditions,where the general solutions of electric potential and a series of identities for the second kind of Legendre function are obtained.

关 键 词：电像法 分离变量法 格林函数 

分 类 号：O442[理学—电磁学]