Dr John Proctor J.E.Proctor@salford.ac.uk
Associate Professor/Reader
Derivation of the Field Due to a Magnetic Dipole Without Use of the Vector Potential
Proctor, John E.; Gould, Harvey Thomas
Authors
Harvey Thomas Gould
Abstract
The mathematical form of the magnetic field due to a current loop, and the fact that it is identical to the electric field due to an electric dipole in the far field, are fundamental to our understanding of electromagnetism. While undergraduate level electromagnetism textbooks usually derive the electric field from an electric dipole, few derive the magnetic field from a current loop. Most simply state it without proof, or perform the derivation for simpler cases such as the on-axis field. Those that perform the derivation use the magnetic vector potential, a relatively advanced concept that most undergraduate students would not encounter until their final year of study, if at all. Here, a simple derivation to obtain the magnetic field due to a current loop in the far-field approximation is presented. The derivation begins from the Biot–Savart law and does not require the vector potential. The problem is set up so that only a single integration is necessary (from angle α = 0 to α = 2π around the current loop), and the result is compared with that for the electric field surrounding an electric dipole.
Citation
Proctor, J. E., & Gould, H. T. (2023). Derivation of the Field Due to a Magnetic Dipole Without Use of the Vector Potential. Physics Teacher, 61(1), 40-42. https://doi.org/10.1119/5.0077127
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 1, 2022 |
Online Publication Date | Dec 28, 2022 |
Publication Date | Jan 1, 2023 |
Deposit Date | Jan 5, 2023 |
Publicly Available Date | Jan 5, 2023 |
Journal | The Physics Teacher |
Print ISSN | 0031-921X |
Electronic ISSN | 1943-4928 |
Publisher | AIP Publishing |
Volume | 61 |
Issue | 1 |
Pages | 40-42 |
DOI | https://doi.org/10.1119/5.0077127 |
Keywords | General Physics and Astronomy, Education |
Publisher URL | https://doi.org/10.1119/5.0077127 |
Additional Information | Additional Information : This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in John E. Proctor and Harvey Thomas Gould , "Derivation of the Field Due to a Magnetic Dipole Without Use of the Vector Potential", The Physics Teacher 61, 40-42 (2023) https://doi.org/10.1119/5.0077127 and may be found at https://aapt.scitation.org/doi/10.1119/5.0077127 |
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