dorsal/arxiv
View SchemaComparing a current-carrying circular wire with polygons of equal perimeter; Magnetic field versus magnetic flux
| Authors | J. P. Silva, A. J. Silvestre |
|---|---|
| Categories | |
| ArXiv ID | physics/0605210 |
| URL | https://arxiv.org/abs/physics/0605210 |
| DOI | 10.1088/0143-0807/26/5/010 |
| Journal | Eur. J. Phys. 26 (2005) 783 |
Abstract
We compare the magnetic field at the center of and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of the wires, we compare the self-fluxes utilizing several regularization procedures. The calculation is best performed utilizing the vector potential, thus highlighting its usefulness in practical applications. Our analysis answers some of the intuition challenges students face when they encounter a related simple textbook example. These results can be applied directly to the determination of mutual inductances in a variety of situations.
{
"annotation_id": "caefcea3-bdd4-407c-980c-55907c4f7982",
"date_created": "2026-03-02T18:01:07.894000Z",
"date_modified": "2026-03-02T18:01:07.894000Z",
"file_hash": "88cde70d3b748b5a1b8435c661195f3d6846c43060ad1deb439a572e35410c7a",
"private": false,
"record": {
"abstract": "We compare the magnetic field at the center of and the self-magnetic flux\nthrough a current-carrying circular loop, with those obtained for\ncurrent-carrying polygons with the same perimeter. As the magnetic field\ndiverges at the position of the wires, we compare the self-fluxes utilizing\nseveral regularization procedures. The calculation is best performed utilizing\nthe vector potential, thus highlighting its usefulness in practical\napplications. Our analysis answers some of the intuition challenges students\nface when they encounter a related simple textbook example. These results can\nbe applied directly to the determination of mutual inductances in a variety of\nsituations.",
"arxiv_id": "physics/0605210",
"authors": [
"J. P. Silva",
"A. J. Silvestre"
],
"categories": [
"physics.ed-ph"
],
"doi": "10.1088/0143-0807/26/5/010",
"journal_ref": "Eur. J. Phys. 26 (2005) 783",
"title": "Comparing a current-carrying circular wire with polygons of equal perimeter; Magnetic field versus magnetic flux",
"url": "https://arxiv.org/abs/physics/0605210"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "79b22d84-15a0-40e0-bfef-7d302392fb62",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}