dorsal/arxiv
View SchemaOn the interaction between a current density and a vector potential: Amp\`{e}re force, Helmholtz tension and Larmor torque
| Authors | Germain Rousseaux |
|---|---|
| Categories | |
| ArXiv ID | physics/0503108 |
| URL | https://arxiv.org/abs/physics/0503108 |
Abstract
Several mathematical formulae are used nowadays in order to compute a magnetic torque. We demonstrate that its more general expression is the vectorial product of the current density with the vector potential. We associate this Larmor's torque with Amp\`{e}re's force and more specifically with Helmholtz mechanical tension, which is at the origin of the longitudinal stresses in "open" circuits carrying current. We show that Amp\`{e}re's force enters into the realm of Newtonian Electrodynamics and we explain the absence of contradiction with special relativity. Hence, we provide for the first time a theoretical basis for the numerous experiments, which claimed to have demonstrated the existence of the longitudinal mechanical tension starting with the historical Amp\`{e}re's hairpin demonstration and the more modern ones of the Graneaus and of Saumont.
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"abstract": "Several mathematical formulae are used nowadays in order to compute a\nmagnetic torque. We demonstrate that its more general expression is the\nvectorial product of the current density with the vector potential. We\nassociate this Larmor\u0027s torque with Amp\\`{e}re\u0027s force and more specifically\nwith Helmholtz mechanical tension, which is at the origin of the longitudinal\nstresses in \"open\" circuits carrying current. We show that Amp\\`{e}re\u0027s force\nenters into the realm of Newtonian Electrodynamics and we explain the absence\nof contradiction with special relativity. Hence, we provide for the first time\na theoretical basis for the numerous experiments, which claimed to have\ndemonstrated the existence of the longitudinal mechanical tension starting with\nthe historical Amp\\`{e}re\u0027s hairpin demonstration and the more modern ones of\nthe Graneaus and of Saumont.",
"arxiv_id": "physics/0503108",
"authors": [
"Germain Rousseaux"
],
"categories": [
"physics.class-ph",
"physics.hist-ph"
],
"title": "On the interaction between a current density and a vector potential: Amp\\`{e}re force, Helmholtz tension and Larmor torque",
"url": "https://arxiv.org/abs/physics/0503108"
},
"schema_id": "dorsal/arxiv",
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