教学讨论

毕奥-萨伐尔定律的柱坐标表示及其应用

展开
  • 1. 中国矿业大学(北京) 理学院,北京100083;2. 北京交通大学附属中学,北京100081
李子良(1988—),男,河南确山人,中国矿业大学(北京)教师,博士,主要从事大学物理教学和强场物理研究工作.
李子良,E-mail: zlli@cumtb.edu.cn

收稿日期: 2025-05-26

  修回日期: 2025-06-14

  网络出版日期: 2026-03-19

基金资助

中国矿业大学(北京)教改项目(J250703)和大创项目(202407008)资助

Cylindrical coordinate representation of the Biot-Savart #br# law and its applications

Expand
  • 1. School of Science, China University of Mining and Technology-Beijing, Beijing 100083, China;
    2. The High School Attached to Beijing Jiaotong University, Beijing 100081, China

Received date: 2025-05-26

  Revised date: 2025-06-14

  Online published: 2026-03-19

摘要

利用直角坐标系和柱坐标系之间的转换关系给出了毕奥-萨伐尔定律的柱坐标表示形式,并利用该形式计算了无限长载流螺线管和无限长载流圆柱体在空间中产生的磁场分布.结果表明,毕奥-萨伐尔定律的柱坐标形式在计算具有轴对称性的载流导线产生的磁场时会更加简便.另外,还计算了载流椭圆线圈在中心轴线上的磁场分布,特别指出部分文献中提出的用坐标缩放法计算载流椭圆线圈在空间任一点的磁场分布的方法是不可行的.


本文引用格式

李子良, 陆丁, 王伟懿 . 毕奥-萨伐尔定律的柱坐标表示及其应用[J]. 大学物理, 2025 , 44(12) : 16 . DOI: 10.16854/j.cnki.1000-0712.250286

Abstract

The cylindrical coordinate formulation of the Biot-Savart law is derived by coordinate transformation between Cartesian and cylindrical systems. The derived formulation is applied to calculate the magnetic field distributions generated by infinitely long current-carrying solenoids and cylindrical conductors. The results demonstrate that the cylindrical coordinate representation of the Biot-Savart law significantly simplifies magnetic field calculations for current-carrying conductors with axial symmetry. Furthermore, the magnetic field distribution along the central axis of a current-carrying elliptic coil is also calculated. It is specifically noted that the coordinate scaling method proposed in some literature for calculating the magnetic field at arbitrary spatial points around such coils is unfeasible.


文章导航

/