dorsal/arxiv
View SchemaOn the electrodynamics of moving bodies at low velocities
| Authors | Marc De Montigny, Germain Rousseaux |
|---|---|
| Categories | |
| ArXiv ID | physics/0512200 |
| URL | https://arxiv.org/abs/physics/0512200 |
| DOI | 10.1088/0143-0807/27/4/007 |
| Journal | Eur.J.Phys.27:755-768,2006 |
Abstract
We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism.
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"abstract": "We discuss the seminal article in which Le Bellac and Levy-Leblond have\nidentified two Galilean limits of electromagnetism, and its modern\nimplications. We use their results to point out some confusion in the\nliterature and in the teaching of special relativity and electromagnetism. For\ninstance, it is not widely recognized that there exist two well defined\nnon-relativistic limits, so that researchers and teachers are likely to utilize\nan incoherent mixture of both. Recent works have shed a new light on the choice\nof gauge conditions in classical electromagnetism. We retrieve Le\nBellac-Levy-Leblond\u0027s results by examining orders of magnitudes, and then with\na Lorentz-like manifestly covariant approach to Galilean covariance based on a\n5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach\nbased on the vector and scalar potentials as opposed to the Heaviside-Hertz\nformulation in terms of electromagnetic fields. We discuss various applications\nand experiments, such as in magnetohydrodynamics and electrohydrodynamics,\nquantum mechanics, superconductivity, continuous media, etc. Much of the\ncurrent technology where waves are not taken into account, is actually based on\nGalilean electromagnetism.",
"arxiv_id": "physics/0512200",
"authors": [
"Marc De Montigny",
"Germain Rousseaux"
],
"categories": [
"physics.class-ph",
"physics.hist-ph"
],
"doi": "10.1088/0143-0807/27/4/007",
"journal_ref": "Eur.J.Phys.27:755-768,2006",
"title": "On the electrodynamics of moving bodies at low velocities",
"url": "https://arxiv.org/abs/physics/0512200"
},
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