Closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and current loops

2020/06/01 by S. Hampton, Ryan A. Lane, R. M. Hedlof +2 · 1 voice
Engineering · Physics and Astronomy · #Magnetic confinement fusion research #Particle accelerators and beam dynamics #Scientific Research and Discoveries

paper · pdf · doi:10.1063/5.0010982

openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

A summary of closed-form expressions for the magnetic fields produced by rectangular- and circular-shaped finite-length solenoids and current loops is provided altogether for easy reference. Each expression provides the magnetic field in all space, except locations where a current of infinitesimal thickness is considered to exist. The closed-form expression for the magnetic field of a rectangular-shaped finite-length solenoid is derived using the Biot–Savart law. Closed-form expressions for the magnetic fields of solenoids and current loops can be used to avoid approximations in analytical models and may reduce computation time in computer simulations.

Discussions

• The surface field usually refers to the magnetic field at the intersection of the surface and the central axis, which is at coordinates $(0,0,\pm L_z/2)$ for a cuboid magnet of length $L_z$ centered a [stackexchange, 1 points]

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