Erratum: “Energy change in deflecting plates’’ [Am. J. Phys. <b>47</b>, 555 (1979)]

Coombes, Charles A.

doi:10.1119/1.11987

Cited by 1 publication

(5 citation statements)

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“…The expression − µ · B is commonly dubbed in elementary textbooks "magnetic potential energy"; for this reason some authors [27,38,81] have interpreted this term as meaning that the potential energy contributes to the particle's mass. We argue (in agreement with the analysis in [82][83][84][85]), that the term − µ · B is actually internal (not potential) energy of the test particle; in fact, we shall see (Sec. VI A 3) that, for a quasi-rigid body, it is essentially rotational kinetic energy, associated with the rotation of the body around its center of mass.…”

Section: E Mass Of the Spinning Particlesupporting

confidence: 88%

“…There is no potential energy involved (cf. [82][83][84][85]), which is consistent with the fact that the static field does no work on the magnetic dipole: (77). A case of interest in the context of this work is the one depicted in Fig.…”

Section: Conserved Quantities Proper Mass and Work Done By The Fieldssupporting

confidence: 83%

“…[27,38,81]). This establishes, in a relativistic covariant formulation, and in the context of Dixon's multipole approach, the claims in [82][83][84][85]. The second terms in the right members of Eqs.…”

Section: Torque On Spherical Charged Bodysupporting

confidence: 64%

“…The analysis above generalizes and reformulates, in a relativistic covariant framework, the arguments in [82][83][84][85], and supports the claim in [28] that the solution of the apparent paradox lies on the variation of m. It is also useful, to make these points more clear, to compare with the cases of a monopole charged particle, and of an electric dipole subject to an electromagnetic field: there is also a force on the particle, which is set into motion gaining kinetic energy; but, in these cases, the electric field is doing work , there is a potential energy involved, and the gain in translational kinetic energy is not canceled out by a variation of the particle's proper mass (m is constant for a monopole particle, and also for an electric dipole if one assumes that the dipole 11 That this is a solution of the equations of motion supplemented with Mathisson-Pirani condition can be seen by arguments analogous to the ones given in Appendix C 1 for the gravitational counterpart.…”

Section: Electromagnetismmentioning

confidence: 71%

“…Sec. VI A 3 and [82][83][84][85]). Hence what the field does is to interconvert translational kinetic energy into rotational or other forms of internal energy.…”

Section: Conserved Quantities Proper Mass and Work Done By The Fieldsmentioning

confidence: 96%

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Spacetime dynamics of spinning particles: Exact electromagnetic analogies

2016

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We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers", a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.

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