2005/01/28 by Alexander Kholmetskii, Alexander L. Kholmetskii, Kholmetskii, Alexander L.
Physics and Astronomy · #Classical Physics (physics.class-ph) #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #physics.class-ph #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0501148
32 pages, 7 figures; changed content of section 4
openalex publication_date 2005/01/28 · arxiv created 2005/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.