大学物理 ›› 2021, Vol. 40 ›› Issue (2): 21-22.doi: 10.16854 /j.cnki.1000-0712.200300

• 教学讨论 • 上一篇    下一篇

介质存在时利用镜像法求解电势的讨论

付春娥   

  1. 西安交通大学物理学院应用物理系,陕西西安710049
  • 收稿日期:2020-07-13 修回日期:2020-08-31 出版日期:2021-02-20 发布日期:2021-02-22
  • 作者简介:付春娥( 1985—) ,女,山东济宁人,西安交通大学理学院副教授,博士,主要从事广义相对论,额外维及膜世界方面的研究.
  • 基金资助:
    国家自然科学基金( 11405121) ; 西安交通大学基本科研业务费( xzy012019061) 资助

Discussion on image method within dielectic

FU Chun-e   

  1. School of Physics,Xi’an Jiaotong University,Xi’an,Shaanxi 710049,China
  • Received:2020-07-13 Revised:2020-08-31 Online:2021-02-20 Published:2021-02-22

摘要:

镜像法是解析求解静电定解问题时一种比较简单的方法,即在所求解的空间之外引入镜像电荷,并使得由镜像电荷与源电荷激发的场的叠加形成的总场满足边界条件及边值关系即可.当将这种方法应用于介质存在的情形时,本文发现可以选择两种不同的镜像电荷,最终求得空间中同样的电势解.这也符合静电问题的唯一性定理,因为无论哪种镜像电荷,均没有改变原空间中的源分布,亦没有改变边界条件与边值关系.而由总场即可求出束缚电荷的电量,此时将进一步发现只有一种镜像电荷与束缚电荷的电量相等.

关键词: 镜像法, 镜像电荷, 唯一性定理

Abstract:

The method of images is a mathematical tool to solve the electrostatic differential problem,i.e.,introducing

image charge outside the solved space,and making the total field formed by the image charge and the

source charge satisfy the boundary. When this method is applied to the presence of adielectic,it will be found that

the choice of image charge is not unique. This also accords with the uniqueness theorem of the electrostatic problem,

because no matter what kind of image chargeis,the total field is the same. From the total field,the amount of

bound charge can be obtained. At this time,it will be further found that the reisonly one kind of image charge equal

to the amount of bound charge.

Key words:  , method of images, image charge, uniqueness theorem