General relation for the vector magnetic field of a circular current loop: A closer look
General relation for the vector magnetic field of a circular current loop: A closer look
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DOI：
10.1109/tmag.2003.808597
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发表时间：
2003-03-01
影响因子：
2.1
通讯作者：
Schill, RA
中科院分区：
文献类型：
--
作者：
Schill, RA
本文提出了一种计算圆形电流环磁场的一般理论，并与已有的理论进行了比较。矢量磁场的现有的、一般的、封闭的解可以用许多看似不同但等价的形式来表示。这些关系提供了替代的封闭形式的解决方案，可以找到各种应用，包括亥姆霍兹线圈的表征。本文提供了球坐标系和柱坐标系中的替代闭合形式。它采用高斯的磁性定律表明，替代封闭形式是自洽的和正确的，也表明与众所周知的解决方案的协议。最后，它开发了一个新的（或不容易找到的）列表数学恒等式。
This paper presents a general theory for the fields generated by a circular current loop and compares it with existing theories. The existing, general, closed solution for the vector magnetic field may be expressed in a number of seemingly different but equivalent forms. These relations offer alternative closed-form solutions that may find various applications, including the characterization of Helmholtz coils. The paper provides alternative closed forms in both spherical and cylindrical coordinate systems. It employs Gauss's magnetic law to show that the alternative closed form is self-consistent and correct and also shows agreement with well-known solutions. Finally, it develops a new (or not readily found) tabulated mathematical identity.