{
  "annotation_id": "192c7540-c935-4733-bb65-8383dbf95d43",
  "date_created": "2026-03-02T18:00:32.933000Z",
  "date_modified": "2026-03-02T18:00:32.933000Z",
  "file_hash": "a555583fd82f29ff7989c49fdea674e0ece97adc745cc39f6fc8a6c58868ddc1",
  "private": false,
  "record": {
    "abstract": "The Biot-Savart law is a well-known and powerful theoretical tool used to\ncalculate magnetic fields due to currents in magnetostatics. We extend the\nrange of applicability and the formal structure of the Biot-Savart law to\nelectrostatics by deriving a Biot-Savart-like law suitable for calculating\nelectric fields. We show that, under certain circumstances, the traditional\nDirichlet problem can be mapped onto a much simpler Biot-Savart-like problem.\nWe find an integral expression for the electric field due to an arbitrarily\nshaped, planar region kept at a fixed electric potential, in an otherwise\ngrounded plane. As a by-product we present a very simple formula to compute the\nfield produced in the plane defined by such a region. We illustrate the\nusefulness of our approach by calculating the electric field produced by planar\nregions of a few nontrivial shapes.",
    "arxiv_id": "physics/0011015",
    "authors": [
      "Mario H. Oliveira",
      "Jose A. Miranda"
    ],
    "categories": [
      "physics.class-ph",
      "physics.gen-ph"
    ],
    "doi": "10.1088/0143-0807/22/1/304",
    "title": "Biot-Savart-like law in electrostatics",
    "url": "https://arxiv.org/abs/physics/0011015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bfaae1e7-6a6b-4f85-9d4f-de6901c96bbc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}