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
Keywords:Maxwell’s equations, wave equations, Sagnac effect, ring laser gyro
On the base of two systems of Maxwell’s equations for the electromagnetic field vectors E and B in a uniformly rotating frame of reference, which were first proposed in the works by L.I. Schiff [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 first 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 different form; 3) the structure of equations for vectors E and B in the first 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 different laws; 4) the structure of the wave equations in the second case is symmetric. Hence, the propagation of these field 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.
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