Hidden momentum of a relativistic fluid carrying current in an external electric field

American Journal of Physics

Volumn 65, Issue 1, 1997, Pages 92-94

  Hnizdo, V ^a  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031540496     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18500     Document Type: Article

References (24)

1. W. Shockley and R. P. James, " 'Try simplest cases' discovery of 'hidden momentum' forces on 'magnetic currents,' " Phys. Rev. Lett. 18, 876-879 (1967); H. A. Haus and P. Penfield, "Force on a current loop," Phys. Lett. A 26, 412-413 (1968).
2. W. Shockley and R. P. James, " 'Try simplest cases' discovery of 'hidden momentum' forces on 'magnetic currents,' " Phys. Rev. Lett. 18, 876-879 (1967); H. A. Haus and P. Penfield, "Force on a current loop," Phys. Lett. A 26, 412-413 (1968).
3. W. H. Furry, "Examples of momentum distributions in the electromagnetic field and in matter," Am. J. Phys. 37, 621-636 (1969).
4. Haus and Penfield, Ref. 1.
5. L. Vaidman, "Torque and force on a magnetic dipole," Am. J. Phys. 58, 978-983 (1990).
6. S. Coleman and J. H. Van Vleck, "Origin of 'hidden momentum forces' on magnets," Phys. Rev. 171, 1370-1375 (1968); M. G. Calkin, "Linear momentum of the source of a static electromagnetic field," Am. J. Phys. 39, 513-516 (1971);
7. S. Coleman and J. H. Van Vleck, "Origin of 'hidden momentum forces' on magnets," Phys. Rev. 171, 1370-1375 (1968); M. G. Calkin, "Linear momentum of the source of a static electromagnetic field," Am. J. Phys. 39, 513-516 (1971);
8. Y. Aharanov, P. Pearle, and L. Vaidman, "Comment on 'Proposed Aharanov-Casher effect: Another example of Aharanov-Bohm effect arising from a classical lag,' " Phys. Rev. A 37, 4052-4055 (1988); L. Vaidman, Ref. 4.
9. Y. Aharanov, P. Pearle, and L. Vaidman, "Comment on 'Proposed Aharanov-Casher effect: Another example of Aharanov-Bohm effect arising from a classical lag,' " Phys. Rev. A 37, 4052-4055 (1988); L. Vaidman, Ref. 4.
10. See, for example, M. G. Calkin, Ref. 5.
11. See, for example, L. Vaidman, Ref. 4.
12. Aharanov, Pearle and Vaidman, Ref. 5; L. Vaidman, Ref. 4.
13. Aharanov, Pearle and Vaidman, Ref. 5; L. Vaidman, Ref. 4.
14. This includes the current realized by two counter-rotating oppositely charged solid disks of Shockley and James (Ref. 1), as the essential features of this mechanism can be covered in model (ii) by two counter-circulating oppositely charged liquids.
15. As a result of the net force between the current induced in the conducting body by an external electric field varying slowly with time and the current that is responsible for the body's dipole moment, the net force on the magnetic dipole in a conducting body is the same as if the body contained the hidden momentum of Eq. (1), see V. Hnizdo, "Comment on 'Torque and force on a magnetic dipole,' " Am. J. Phys. 60, 279-280 (1992).
16. An ideal fluid has a negligible thermal conductivity and viscosity; it also does not support any shear stresses.
17. The author is indebted to E. Comay of Tel Aviv University for bringing this point to his attention.
18. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987), 2nd ed., Secs. 133 and 134.
19. L. D. Landau and E. M. Lifshitz, Ref. 13, Sec. 133.
20. i and the fact that ▽·(qh) = h·▽q for a divergenceless h.
21. Except in the short bends of the rectangularly shaped loop; such regions of nonuniform speed can be made negligibly small compared to the straight sections of the tube.
22. L. D. Landau and E. M. Lifshitz, Ref. 13, Sec. 2.
23. C. Møller, The Theory of Relativity (Clarendon, Oxford, 1972), 2nd ed., pp. 191-192.
24. Assuming not only that v′ = 0 but also that ∂v′/∂t′ = 0, which holds in the local rest frame except at the bends of the tube.