Applying covariant versus contravariant electromagnetic tensors to rotating media

American Journal of Physics

Volumn 67, Issue 5, 1999, Pages 414-421

  Ridgely, Charles T ^a  

^a NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033448066     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19277     Document Type: Article

References (22)

1. C. T. Ridgely, "Applying relativistic electrodynamics to a rotating material medium," Am. J. Phys. 66, 114-121 (1998).
2. L. Landau and E. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1984), 2nd ed., pp. 260-263.
3. H. Weyl, Space-Time-Matter (Dover, New York, 1952), 4th ed., pp. 193-196.
4. W. Pauli, Theory of Relativity (Pergamon, New York, 1958; reprinted. Dover, New York, 1981), pp. 99-113.
5. R. Becker, Electromagnetic Fields and Interactions (Blaisdell, New York, 1964; reprinted, Dover, New York, 1982), Vol. 1, pp. 299-304; 374-376.
6. G. N. Pellegrini and A. R. Swift, "Maxwell's equations in a rotating medium: Is there a problem?" Am. J. Phys. 63, 694-705 (1995).
7. W. Crater, "General covariance, Lorentz covariance, the Lorentz force, and the Maxwell equations," Am. J. Phys. 62, 923-931 (1994).
8. See, for example, B. F. Schutz, A First Course in General Relativity (Cambridge, New York, 1990), pp. 62-78.
9. See, for example, Ohanian and Ruffini, Gravitation and Spacetime (Norton, New York, 1994), 2nd ed., p. 103.
10. Other names for a one-form are covector, covariant vector, or dual vector. See, for example, B. F. Schutz, Ref. 8.
11. E. G. Cullwick, Electromagnetism and Relativity (Longmans, London, 1959), 2nd ed., pp. 161-174.
12. 1). See. for example, W. Pauli, Ref. 4; G. N. Pellegrini and A. R. Swift, Ref. 6; and E. G. Cullwick, Ref. 11.
13. J. Ise and J. Uretsky, "Vacuum electrodynamics on a merry-go-round," Am. J. Phys. 26, 431-435 (1958).
14. Ø. Grøn, "Relativistic description of a rotating disk," Am. J. Phys. 43, 869-876 (1975).
15. D. L. Webster, "Schiff's charges and currents in rotating matter," Am. J. Phys. 31, 590-597 (1963).
16. L. Landau and E. Lifshitz, The Classical Theory of Fields (Addison-Wesley, Reading, MA, 1951), pp. 60-62; 281-282.
17. αβ but composed of the components of the electric and magnetic fields in the presence of matter, D and H. Here, we note that D and H are well defined both inside and outside of matter, as are the true electric and magnetic fields, E and B. Since the fields D and H are simply useful in calculating E and B when matter is present, to avoid confusion, we will refer to E and B as fundamental fields, and to D and H as auxiliary fields.
18. H. Ohanian and R. Ruffini, Ref. 9, pp. 322-323.
19. L. Schiff, "A question in general relativity," Proc. Natl. Acad. Sci. USA 25, 391-395 (1939).
20. C. T. Ridgely, "The electrodynamics of a rotating material medium." M.S. thesis, California State University, Long Beach, 1996, p. 30.
21. See, for example, A. O. Barut, Electrodynamics and Classical Theory of Fields and Particles (Dover, New York, 1980), p. 19.
22. G. Modesitt, "Maxwell's equations in a rotating reference frame," Am. J. Phys. 38, 1487-1489 (1970).