Teaching Magnetism with Bivectors

Abstract

The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in rotational physics, we present an alternative pedagogical approach that describes magnetic fields using bivectors. These objects can be visualized as oriented tiles whose components form an antisymmetric matrix. Historically, bivectors have been mostly used in specialized contexts like spacetime classification or geometric algebra, but they are not necessarily more complicated to understand than cross products. Teaching magnetism in this language addresses common student difficulties, generalizes directly to relativity (and extra dimensions), and brings fresh insight to familiar ideas.