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.
Highlights
Closed-form expressions are presented for the magnetic fields generated by four electrical current configurations: rectangular and circular finite-length solenoids and rectangular and circular current loops
The expressions for the magnetic fields of rectangular finitelength solenoids and rectangular current loops are written in terms of elementary functions
Μ0 is the permeability of free space, I is the current in an infinitesimally thin wire that is wound in a rectangular or circular scitation.org/journal/adv shape around the z axis of a Cartesian coordinate system to form either a single-turn current loop or a multi-turn solenoid, and n is the number of wire turns per unit length of a solenoid
Summary
Closed-form expressions are presented for the magnetic fields generated by four electrical current configurations: rectangular and circular finite-length solenoids and rectangular and circular current loops. The expressions for the magnetic fields of circular finite-length solenoids and circular current loops are written in terms of complete elliptic integrals and elementary functions. The closed-form expression presented here for the magnetic field generated by a rectangular finite-length solenoid has not been published previously, to our knowledge. The closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and rectangular and circular current loops are summarized in Sec. II for easy reference. Appendixes B–D provide derivations of the closed-form expressions for the magnetic fields of the rectangular current loop and the circular finite-length solenoid and current loop
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