Causality in electrodynamics is a subject of some confusion, especially regarding the application of Faraday's law and the Ampère-Maxwell law.1–3 This has led to the suggestion that we should not teach students that electric and magnetic fields can cause each other,1 but rather focus on charges and currents as the causal agents.3 In this paper I argue that fields have equal status as casual agents, and that we should teach this. Following a discussion of causality in classical physics, I will use a numerical solution of Maxwell's equations to inform a field-based causal explanation in electrodynamics.
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To avoid the complication of modelingthe establishment of an electric field to drive the current, we assume that the charges are self-propelled rather than accelerated by an applied electric field. One might think, for example, of charged nano-machines that are programmed to simultaneously start moving along the z direction. Although impractical, there is nothing that fundamentally forbids such a scenario.
Equations (4) and (5) were solved using a pseudo-spectral method with an adaptive Runge-Kutta time step and 1024 spatial lattice points.
