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**Example text**

2). '( t) = -r r, Sn 2 I' I 'I f(r',w) j[wr-klr-r'lld •d \ w. 3 ). 13) with t lr--r'l ,=f-. 14) where ( denotes the retarded time. which is defined as the time at which the signal 26 I. Basic Electromagnetic Theory arriving at the position r at the time t is emitted at the position r'. Note that the signal emitted at the position r' is propagated at the speed u over the distance between the two positions. 15) 1 r p(r', t') dv. 4). 1 with the aid of the Fourier analysis described in the preceding section.

12). 3) 22 I. w)ejwr]. 6). The plane wave is defined as a transverse electromagnetic wave for which equiphase surfaces or wave fronts are infinite planes perpendicular to the direction of wave propagation. In addition, the amplitudes of electric and magnetic field vectors for the plane wave are constant on the equiphase surface. 8) where E0 and H0 are constant vectors, and k is also a constant vector directed in the direction of wave propagation. 6 ), the magnitude of k proves to be equal to w/u.

5 Transformation of Frequency and Wave Numbers In the preceding section, we have found the constitutive relations for a moving nondispersive medium by transforming the constitutive relations from the inertial system where the material medium is at rest to the inertial system where it is moving. However, if we wish to obtain the constitutive relations for moving dispersive media, the transformation formulas for frequency and wave numbers are required in addition to those for field vectors. In this section, we investigate how frequency and wave numbers are transformed under the Lorentz transformation.