General Relation for the Vector Magnetic Field of a Circular Current Loop: A Closer Look

Document Type

Article

Publication Date

4-2-2003

Publication Title

IEEE Transactions on Magnetics

Volume

39

First page number:

961

Last page number:

967

Abstract

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.

Keywords

Coils; Magnetic fields

Disciplines

Computer Engineering | Electrical and Computer Engineering | Engineering

Language

English

Permissions

Use Find in Your Library, contact the author, or interlibrary loan to garner a copy of the item. Publisher policy does not allow archiving the final published version. If a post-print (author's peer-reviewed manuscript) is allowed and available, or publisher policy changes, the item will be deposited.

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