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Register a new userOn the question of the electromagnetic momentum of a charged body
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Authors
V. B. Morozov
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The incorporation of a relativistic momentum of a nonelectromagnetic nature into macroscopic problems of electrodynamics obviates the lack of correspondence between the electromagnetic mass and the electromagnetic momentum of macroscopic bodies, allowing, in particular, the resolution of the well-known 4/3 paradox.
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We consider the Einstein equation, where the common electromagnetic energy momentum tensor is replaced by its generalized equivalent as suggested in our earlier paper (A.L. Kholmetskii et al. Phys. Scr. 83, 055406 (2011)). Now we show that with this new electromagnetic energy-momentum tensor, the scalar curvature at the location of charges is significantly altered in comparison with the common result, and it even may change its sign. Some implications of the obtained results are discussed.
A decomposition of the angular momentum of the classical electromagnetic field into orbital and spin components that is manifestly gauge invariant and general has been obtained. This is done by decomposing the electric field into its longitudinal and transverse parts by means of the Helmholtz theorem. The orbital and spin components of the angular momentum of any specified electromagnetic field can be found from this prescription.
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Robert N. C. Pfeifer
, Timo A. Nieminen
, Norman R. Heckenberg andn Halina Rubinsztein-Dunlop
2009
Almost a hundred years ago, two different expressions were proposed for the energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowskis tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abrahams tensor predicted its decrease. Theoretical arguments were advanced in favour of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy--momentum tensor is complete on its own. When the appropriate accompanying energy--momentum tensor for the material medium is also considered, experimental predictions of all the various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.
Three objections to the canonical analytical treatment of covariant electromagnetic theory are presented: (i) only half of Maxwells equations are present upon variation of the fundamental Lagrangian; (ii) the trace of the canonical energy-momentum tensor is not equivalent to the trace of the observed energy-momentum tensor; (iii) the Belinfante symmetrization procedure exists separate from the analytical approach in order to obtain the known observed result. It is shown that the analytical construction from Noethers theorem is based on manipulations that were developed to obtain the compact forms of the theory presented by Minkowski and Einstein; presentations which were developed before the existence of Noethers theorem. By reformulating the fundamental Lagrangian, all of the objections are simultaneously relieved. Variation of the proposed Lagrangian yields the complete set of Maxwells equations in the Euler-Lagrange equation of motion, and the observed energy-momentum tensor directly follows from Noethers theorem. Previously unavailable symmetries and identities that follow naturally from this procedure are also discussed.
An analysis of the influences of a high frequency (30 kHz) alternating current on the uniformity of the magnetic field (B) in an electromagnetic casting (EMC) mould is investigated by means of parametric numerical simulations where the induction current (Js) varies in the range of [1 to 10000 A]. The results show that values of the magnetic flux density along the casting direction (Bz) near the square mould corners are small, compared to those at the other locations where Js < 10000 A, and that the magnitude of Bz increases with an increased induction current (Js). However, it is shown that, for the EMC mould structure investigated in this paper, the variations of Js have no significant influences on the uniformity of the magnetic field, especially for the regions near molten steel level. Moreover, the effective acting region (Rbz) for the critical magnetic field (Bzc) is first introduced in this paper, which opens an interesting topic for future research.
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