The magnetic field of current-carrying polygons: An application of vector field rotations

We calculate the magnetic field around a current loop consisting of a regul ar N-sided polygon by successively rotating the field obtained from a strai ght, finite, current-carrying wire. This involves developing and applying a vector field rotation operator, which transforms vector fields the way a r otation matrix transforms scalar fields. Using this result, we explore the various magnetic field components about the current loop and notice an inte resting structure that results from the geometry of the polygons. The magne tic field on the axis of the current loop as well as the field at all point s around a circular loop are considered as limiting cases. (C) 2000 America n Association of Physics Teachers.