{"paper":{"title":"Evaluation of the Biot-Savart integral in electrostatic problems with non-uniform Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Camilo Bayona, J. S. Sol\\'is Chaves, Robert Salazar","submitted_at":"2019-07-02T23:38:27Z","abstract_excerpt":"We present an analytical strategy to solve the electric field generated by a planar region $\\mathcal{A}$ enclosed by a contour $c$ which is kept with a fixed but non-uniform electric potential. The approach can be used in certain situations where the electric potential on the space requires to solve the Laplace equation with non-uniform Dirichlet boundary conditions. We show that the electric field is due to a contribution depending on the circulation on the contour in a Biot-Savart way plus another one taking into account the angular variations of the potential in $\\mathcal{A}$ valid for any "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02066","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"}