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

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.