大学物理 ›› 2021, Vol. 40 ›› Issue (9): 21-.doi: 10.16854 / j.cnki.1000- 0712.200546

• 教学讨论 • 上一篇    下一篇

半球面上的电荷量有多大?

邱为钢   

  1. 湖州师范学院公共教研部,浙江湖州 313000
  • 收稿日期:2020-12-23 修回日期:2021-02-23 出版日期:2021-09-20 发布日期:2021-09-24
  • 作者简介:邱为钢(1975 —),男,江苏张家港人,湖州师范学院副教授,博士,主要从事大学物理教学和数学物理研究工作.

How much charges on a hemisphere?

QIU Wei-gang   

  1. Public Teaching Department, Huzhou Teacher’s College, Huzhou. Zhejiang 313000, China
  • Received:2020-12-23 Revised:2021-02-23 Online:2021-09-20 Published:2021-09-24

摘要: 在球坐标下,带电上下半球面保持固定相反电势,所产生的全空间电势表达式是含有勒让德函数的无穷求和. 给出了半球面上的电荷密度并计算了半球面上的电荷量.计算发现,这个电荷量是无穷大.

关键词: 半球面, 勒让德函数, 电荷密度

Abstract: The electric potential produced by two hemispheres with constant and opposite potential

is expressed as infinite sums of Legendre functions in spherical coordinate. The electric charge density and total charges on the

hemisphere are derived. Calculation shows that the charge is infinite.

Key words: hemisphere, Legendre function, charge density