American Journal of Physics
We calculate the magnetic field around a current loop consisting of a regular N-sided polygon by successively rotating the field obtained from a straight, finite, current-carrying wire. This involves developing and applying a vector field rotation operator, which transforms vector fields the way a rotation matrix transforms scalar fields. Using this result, we explore the various magnetic field components about the current loop and notice an interesting structure that results from the geometry of the polygons. The magnetic field on the axis of the current loop as well as the field at all points around a circular loop are considered as limiting cases.
Grivich, Matthew I., and David P. Jackson. "The Magnetic Field of Current-Carrying Polygons: An Application of Vector Field Rotations." American Journal of Physics 68, no. 5 (2000): 469–474. https://aapt.scitation.org/doi/abs/10.1119/1.19461