dorsal/arxiv
View SchemaOn momentum and energy of a non-radiating electromagnetic field
| Authors | Alexander L. Kholmetskii |
|---|---|
| Categories | |
| ArXiv ID | physics/0501148 |
| URL | https://arxiv.org/abs/physics/0501148 |
Abstract
This paper inspects more closely the problem of the momentum and energy of a bound (non-radiating) electromagnetic (EM) field. It has been shown that for an isolated system of non-relativistic mechanically free charged particles a transformation of mechanical to EM momentum and vice versa occurs in accordance with the requirement PG=const, where PG is the canonical momentum. If such a system contains bound charges, fixed on insulators then, according to the assumption of a number of authors, a so-called "hidden" momentum can contribute into the total momentum of the system. The problem of "hidden momentum" (pro and contra) is also examined in the paper, as well as the law of conservation of total energy for different static configurations of the system "magnetic dipole plus charged particle". Analyzing two expressions for electromagnetic momentum of a bound EM field, qA and the Poynting expression, we emphasize that they coincide with each other for quasi-static configurations, but give a discrepancy for rapid dynamical processes. We conclude that neither the first, nor the second expressions provide a continuous implementation of the momentum conservation law. Finally, we consider the energy flux in a bound EM field, using the Umov vector. It has been shown that Umov vector can be directly derived from Maxwell equations. A new form of the momentum-energy tensor, which explicitly unites the mechanical and EM masses, has been proposed.
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"abstract": "This paper inspects more closely the problem of the momentum and energy of a\nbound (non-radiating) electromagnetic (EM) field. It has been shown that for an\nisolated system of non-relativistic mechanically free charged particles a\ntransformation of mechanical to EM momentum and vice versa occurs in accordance\nwith the requirement PG=const, where PG is the canonical momentum. If such a\nsystem contains bound charges, fixed on insulators then, according to the\nassumption of a number of authors, a so-called \"hidden\" momentum can contribute\ninto the total momentum of the system. The problem of \"hidden momentum\" (pro\nand contra) is also examined in the paper, as well as the law of conservation\nof total energy for different static configurations of the system \"magnetic\ndipole plus charged particle\". Analyzing two expressions for electromagnetic\nmomentum of a bound EM field, qA and the Poynting expression, we emphasize that\nthey coincide with each other for quasi-static configurations, but give a\ndiscrepancy for rapid dynamical processes. We conclude that neither the first,\nnor the second expressions provide a continuous implementation of the momentum\nconservation law. Finally, we consider the energy flux in a bound EM field,\nusing the Umov vector. It has been shown that Umov vector can be directly\nderived from Maxwell equations. A new form of the momentum-energy tensor, which\nexplicitly unites the mechanical and EM masses, has been proposed.",
"arxiv_id": "physics/0501148",
"authors": [
"Alexander L. Kholmetskii"
],
"categories": [
"physics.class-ph",
"physics.gen-ph"
],
"title": "On momentum and energy of a non-radiating electromagnetic field",
"url": "https://arxiv.org/abs/physics/0501148"
},
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