文献类型：期刊文献

中文题名：Three-dimensional electric potential induced by a point singularity in a multilayered dielectric medium

英文题名：Three-dimensional electric potential induced by a point singularity in a multilayered dielectric medium

作者：Xu WANG[1];P. SCHIAVONE[2]

机构：[1]School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China;[2]Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering Edmonton, Alberta T6G 1H9, Canada

年份：2019

卷号：40

期号：9

起止页码：1327

中文期刊名：Applied Mathematics and Mechanics(English Edition)

外文期刊名：应用数学和力学（英文版）

收录：Scopus;CSCD:【CSCD2019_2020】；

基金：Project supported by the National Natural Science Foundation of China(No.11272121);the Natural Sciences and Engineering Research Council of Canada(No.RGPIN-2017-c3716115112)

语种：英文

中文关键词：multilayered;dielectric;medium;point;charge;point;electric;dipole;linear;recurrence;relation;analytical;solution

外文关键词：multilayered dielectric medium;point charge;point electric dipole;linear recurrence relation;analytical solution

摘要：A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N-phase dielectric medium composed of N-2 intermediate dielectric layers of equal thickness encased in two semi-infinite dielectric media. The point singularity can include a point charge or a point electric dipole. The original boundary value problem for the N-phase medium is reduced to the determination of a single unknown three-dimensional harmonic function through satisfaction of the continuity conditions across all of the N-1 perfect planar interfaces. The single harmonic function can be completely determined after analytically solving the resulting linear recurrence relations, which are independent of the type and the specific location of the singularity. When the singularity is a point charge, we obtain the self-energy of the point charge expressed in terms of a single function and the Coulomb force on the point charge expressed in terms of the negative derivative of this function.
A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N-phase dielectric medium composed of N-2 intermediate dielectric layers of equal thickness encased in two semi-infinite dielectric media. The point singularity can include a point charge or a point electric dipole. The original boundary value problem for the N-phase medium is reduced to the determination of a single unknown three-dimensional harmonic function through satisfaction of the continuity conditions across all of the N-1 perfect planar interfaces. The single harmonic function can be completely determined after analytically solving the resulting linear recurrence relations, which are independent of the type and the specific location of the singularity. When the singularity is a point charge, we obtain the self-energy of the point charge expressed in terms of a single function and the Coulomb force on the point charge expressed in terms of the negative derivative of this function.