Publicação: Time dependent electromagnetic fields and 4-dimensional Stokes' theorem
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Stokes' theorem is central to many aspects of physics-electromagnetism, the Aharonov-Bohm effect, and Wilson loops to name a few. However, the pedagogical examples and research work almost exclusively focus on situations where the fields are time-independent so that one need only deal with purely spatial line integrals (e.g. ∫ A dx) and purely Ð spatial area integrals (e.g. ∫(▿× Ada =∫ B da). Here, we address this gap by giving some explicit examples of how Stokes' theorem plays out with time-dependent fields in a full 4-dimensional spacetime context. We also discuss some unusual features of Stokes' theorem with time-dependent fields related to gauge transformations and non-simply connected topology.
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American Journal of Physics, v. 84, n. 11, p. 848-857, 2016.
