Magnetic Fields and Asymptotic Limits of Current Loops

Nadiya Rodriguez

doi:10.20944/preprints202310.1699.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 25 October 2023 / Approved: 26 October 2023 / Online: 26 October 2023 (11:08:36 CEST)
Version 2 : Received: 25 January 2024 / Approved: 25 January 2024 / Online: 26 January 2024 (07:03:35 CET)

This article theoretically derives the magnetic field and vector potential produced by a steady current I flowing in an arbitrary plane loop at an arbitrary point r. Numerical examples are presented to demonstrate the behavior of the magnetic field produced by loops of various shapes such as polygons, circles, ellipses, and p-norm balls. Taking the limit as the loop shrinks to a point and the current I grows to infinity so that the magnetic dipole moment m of the loop (defined as the current I times the vector area of the loop) is kept constant, the magnetic field and vector potential are theoretically shown to converge to those of an ideal point magnetic dipole m.

magnetic dipole; current loop; vector potential; electromagnetic field

Physical Sciences, Theoretical Physics

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Magnetic Fields and Asymptotic Limits of Current Loops

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