静电场能量之两种表述及等价性探讨  

Discussion on Two Expressions and Equivalence of Electrostatic Field Energy

作　　者：陈三[1] 朱光平[1] 杨远贵[1] CHEN San;ZHU Guangping;YANG Yuangui(School of Physics and Electronic Information,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学物理与电子信息学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2024年第1期82-86,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省教育厅教学研究项目(2022szsfkc084,2020kcszyjxm215);淮北师范大学教学研究项目(2020xyjxyj012)。

摘　　要：为给出静电场能量电荷体密度积分形式成立的条件和澄清把体密度积分形式直接改写为面密度积分形式的不恰当,从静电场能量的定义式出发,采用麦克斯韦方程和静电势公式推导出静电场能量的另一表达式,并对该静电场能量表达式作一般性推广,用于处理电荷分布不连续的任意无限空间或有限空间区域内的静电场能量问题,具有普适性。举例说明2种能量表述形式的等价性。澄清面电荷积分形式1/2∬σϕdS来自于积分-1/2∳ϕD∙dS,而非来自积分1/2∭ϕρdV。To provide the conditions for the integral form of electrostatic field energy by charge bulk density and clarify the inappropriate rewriting of the integral form of bulk density to the integral form of surface density,another expression of electrostatic field energy is derived using Maxwell′s equation and electrostatic potential formula,and a general extension of the expression of electrostatic field energy is made.It can be used to handle the energy problem of electrostatic fields in any infinite or finite space region with discontinuous charge distribution and has universality.Some examples are given to illustrate the equivalence of two energy expression.The integral form of surface charge 1/2∬σϕdS comes from integral-1/2∳ϕD∙dS instead of from integral 1/2∭ϕρdV which is clarified.

关 键 词：静电场能量 电荷密度 自能和互能 

分 类 号：O441[理学—电磁学] O442[理学—物理]