球对称静电场求解方法  

Method of solving spherically symmetric electrostatic field

作　　者：吕嫣[1] 崔崧[1] 李慧玲[1] LÜ Yan;CUI Song;LI Huiling(College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China)

机构地区：[1]沈阳师范大学物理科学与技术学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2021年第5期446-449,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11703018)。

摘　　要：静电场由静止电荷激发,满足静电场高斯定理和环路定理,是有源无旋场。静电场是电磁理论的重要组成部分,在普通物理电磁学部分和理论物理的电动力学中都占有一席之地,求解静电场是非常基本而又重要的问题,也是教学中的重点和难点。针对静电场的特点,以同一球对称静电场分布为例,讨论了静电场的求解方法。具体分为2种情况:由场源分布确定电场分布,包含电场叠加法、高斯定理法和等效法;由电势分布确定电场分布,包含电势叠加法和分离变量法。结果表明,对于同一球对称静电场问题,不同的方法所得的结果是完全一致的,但解题的繁复程度却各不相同,所以在求解静电场时,首先要确定各个方法的适用条件,再选择合理有效的方法进行计算。Electrostatic field is excited by static charge,which satisfies Gauss theorem and loop theorem.It is an active and irrotational field.Electrostatic field is an important part of electromagnetic theory,which occupies a certain space in electromagnetic and electrodynamics.Solving electrostatic field is basic and important,and it is also the key and difficult point in the teaching.According to the characteristics of the electrostatic field,taking the distribution of the same spherically symmetric electrostatic field as an example,the solving method of the electrostatic field is discussed.There are two situations.The first one is to determine the electric field distribution by the field source distribution,including the electric field superposition method,Gauss theorem method and equivalent method;the second one is to determine the electric field distribution by the electric potential distribution,including the electric potential superposition method and the variable separation method.The results show that for the same spherically symmetric electrostatic field problem,the results obtained by different methods are completely consistent,but the complexity of solving the problem is different.Therefore,in solving the electrostatic field,we must first determine the applicable conditions of each method,and then select a reasonable and effective method for calculation.

关 键 词：静电场 高斯定理 电势 分离变量法 

分 类 号：O441[理学—电磁学]