Document Type

Article - Open Access

Publication Title

European Journal of Physics

Publication Date

9-2023

Abstract/ Summary

This work reports on the uses of the magnetic vector potential A for understanding, visualizing and teaching electromagnetic phenomena. The teaching benefits of this work include examples of numerical modeling that facilitate understanding, and complementary visualization approaches. To facilitate discussion of A we first include a brief section looking at Φ in a system comprised of two hollow, positively charged spheres, demonstrating that the work required to bring the two spheres close together QΦ is equal to change in the total integrated electric field energy density. We then introduce a system comprised of a hollow, positively charged sphere interacting with two parallel, current-carrying wires, for which Awires is determined as a function of position. Two calculations of the field momentum of the system are compared and shown to be equal: the first is QAwires, the second is the integration over all space of the interaction momentum density ∈0E × B. We conclude by analyzing the trajectory of Q near the wires, establishing a visual connection between particle motion and the magnetic vector potentials sourced by the wires, including a discussion of relativistic implications.

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