• Українська
  • English

<Prev | >

Current issue   Ukr. J. Phys. 2017, Vol. 62, N 2, p.99-105
https://doi.org/10.15407/ujpe62.02.0099    Paper

Bondarenko E.A.

National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
(Bldg 28, 37, Prosp. Peremohy, Kyiv 03056, Ukraine; e-mail: ea_bndrk@ukr.net)

Two Systems of Maxwell's Equations and Two Corresponding Systems of Wave Equations for Electromagnetic Field Vectors E and B in a Rotating Frame of Reference: a Linear Approximation

Section: Fields and Elementary Particles
Original Author's Text: English

Abstract:  On the base of two systems of Maxwell’s equations for the electromagnetic feld vectors E and B in a uniformly rotating frame of reference, which were frst proposed in the works by L.I. Schif [Proc. Natl. Acad. Sci. USA 25, 391 (1939)] and W. Irvine [Physica 30, 1160 (1964)], two corresponding systems of wave equations are derived (to the frst order in Ω). The analysis of these systems implies that: 1) the factor of rotation causes the arising of longitudinal E- and B-components of electromagnetic waves, which interact with the transversal ones; 2) the wave equations for the vector E in both systems of equations have the same form, while the equations for the vector B have diferent form; 3) the structure of equations for vectors E and B in the frst case is asymmetric. Therefore, the propagation of the E- and B-components of electromagnetic waves in a rotating frame of reference will be governed by qualitatively diferent laws; 4) the structure of the wave equations in the second case is symmetric. Hence, the propagation of these feld components will be governed by similar laws. It is also shown that, in the approximation of transversal electromagnetic waves, the distinction between the two systems of wave equations for the vectors E and B vanishes: both are transformed into two identical sets of separate (independent of one another) wave equations for the vector E and the vector B of a simpler (and already known from the literature) form.

Key words: Maxwell’s equations, wave equations, Sagnac efect, ring laser gyro.

References:

  1. L.I. Schif. A question in general relativity. Proc. Natl. Acad. Sci. USA 25, 391 (1939).
     CrossRef
  2. W. Irvine. Electrodynamics in a rotating system of reference. Physica 30, 1160 (1964).
     CrossRef
  3. L.N.Menegozzi,W.E. Lamb, jr. Theory of a ring laser. Phys. Rev. A 8, 2103 (1973).
     CrossRef
  4. K.T. McDonald. Electrodynamics of rotating systems (Princeton University, 2008); http://physics.princeton.edu/mcdonald/examples/rotatingEM.pdf.
  5. G.A. Korn, T.M. Korn. Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).
  6. G. Lianis, D.Whicker. Electromagnetic phenomena in rotating media. Arch. Ration. Mech. Anal. 57, 325 (1975).
     CrossRef
  7. S.G. Zeiger, Yu.L. Klimontovich, P.S. Landa, E.G. Lariontsev, E.E. Fradkin. Wave and Fluctuation Processes in Lasers (Nauka, 1974) (in Russian).
  8. W.W. Chow, J. Gea-Banacloche, L.M. Pedrotti, V.E. Sanders, W. Schleich, M.O. Scully. The ring laser gyro. Rev. Mod. Phys. 57, 61 (1985).
     CrossRef