{"paper":{"title":"Time dependent electromagnetic fields and 4-dimensional Stokes' theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Douglas Singleton, Ryan Andosca","submitted_at":"2016-08-24T00:47:12Z","abstract_excerpt":"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 ({\\it e.g.} $\\oint {\\bf A} \\cdot d{\\bf x}$) and purely spatial area integrals ({\\it e.g.} $\\int (\\nabla \\times {\\bf A}) \\cdot d{\\bf a} = \\int {\\bf B} \\cdot d{\\bf a}$). Here we address this gap by giving some explicit examples of how Stokes' theorem plays out with time-depende"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08865","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}