{
  "annotation_id": "074c7752-9829-4f4b-b6af-63d6e1885385",
  "date_created": "2026-03-02T18:00:53.736000Z",
  "date_modified": "2026-03-02T18:00:53.736000Z",
  "file_hash": "6da272fb3ad0b99c7907760ce244c2054823fe08026d70946f7cd920c7fd36a8",
  "private": false,
  "record": {
    "abstract": "A scalar field method to obtain transverse solutions of the vector Laplace\nand Helmholtz equations in spherical coordinates for boundary-value problems\nwith azimuthal symmetry is described. Neither scalar nor vector potentials are\nused. Solutions are obtained by use of separation of variables instead of\ndyadic Green\u0027s functions expanded in terms of vector spherical harmonics.\nApplications to the calculations of magnetic fields from steady and oscillating\nlocalized current distributions are presented.",
    "arxiv_id": "physics/0412127",
    "authors": [
      "Ernesto A. Matute"
    ],
    "categories": [
      "physics.class-ph",
      "physics.ed-ph"
    ],
    "title": "Transverse Solutions of the Vector Laplace and Helmholtz Equations for   Spherical Coordinates and Boundary Conditions with Azimuthal Symmetry",
    "url": "https://arxiv.org/abs/physics/0412127"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "12d5b1ed-0840-4e66-abe8-e05931662beb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}