大学物理 ›› 2022, Vol. 41 ›› Issue (9): 9-.doi: 10.16854/j.cnki.1000-0712.220059

• 教学讨论 • 上一篇    下一篇

有限长螺线管的磁场——对一种计算方法的评述与修正

林琼桂   

  1. 中山大学物理学院,广东 广州510275
  • 收稿日期:2022-02-12 修回日期:2022-04-01 出版日期:2022-09-20 发布日期:2022-09-30
  • 作者简介:林琼桂(1963—),男,广东潮阳人,中山大学物理学院教授,博士生导师,从事理论物理学的教学和研究工作.
  • 基金资助:
    中山大学教务部2022年度教学质量工程项目(中山大学教务[2022]20号,74130-12220011) 资助

Magnetic field of a finite solenoid—Comments on an approach and corrections to its results

LIN Qiong-gui   

  1. School of Physics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
  • Received:2022-02-12 Revised:2022-04-01 Online:2022-09-20 Published:2022-09-30

摘要: 对于有限长螺线管的磁场,本刊曾经发表过一种计算方法,它给出了级数形式的结果.然而作者对级数的收敛性未作分析,因而没有发现其存在发散问题.本文分析发现,该文的级数结果在圆柱面(包括螺线管圆柱面及其延长部分) 外处处收敛,而在圆柱面内则不然.重新计算了圆柱面内的结果,并验证了圆柱面两侧的边界条件.

关键词: 螺线管, 磁场, 磁感应强度, 无穷级数, 边界条件

Abstract:  One approach to the magnetic field of a finite solenoid was published in this journal, which give the results in terms of infinite series. However, the convergence of the series was not examined, thus some divergence issues was overlooked. We reexamine the series and find that it is convergent everywhere outside the cylinder surface (the cylinder surface of the solenoid extended to infinity) but not inside it. The results inside the cylinder surface are recalculated, and the boundary conditions on the cylinder surface are verified.

Key words:  solenoid, magnetic field, magnetic induction, infinite series, boundary condition