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arXiv · 2606.12626

Teaching Maxwell's Equations from 2D to 3D with Bivectors

Steuard Jensen·Edward Markarian
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Abstract

Electromagnetism is one of the few core physics topics without simple two-dimensional examples to start from: the cross product and curl require three dimensions. Previous work described magnetism as a bivector field, visualized with oriented (clockwise/counterclockwise) "tiles" rather than the traditional (pseudo)vector "arrows." Here, we express Maxwell's equations in this bivector language: magnetic flux is understood as a sum along a surface rather than through it, and the magnetic field tiles encircle the boundary of an Amperian loop or ribbon in a natural way. This allows a gentle two-dimensional starting point and makes symmetry arguments natural for magnetism.

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Steuard Jensen, Edward Markarian. 2026-06-10. Teaching Maxwell's Equations from 2D to 3D with Bivectors. https://arxiv.org/abs/2606.12626

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