Abstract
In Chap. 4 of our lecture course we shall become acquainted with the wave equations of macroscopic generalized electrodynamics (Sect. 4.1) and we show their distinctive features compared with the classic case (described in Chap. 3). The consequence of the Stokes–Helmholtz theorem (Sect. 1.3.1) about the fact that an electric field has the vortex and potential components is a significant feature of wave equation formation in generalized electrodynamics. This allows (as was done in Sect. 3.2) equations to obtained for the vector and scalar potentials. At this, the absence of a necessity to use the calibration relationships of Lorentz and Coulomb, respectively, is the essential feature. In this case, the one pair of wave equations obtained defines the transverse electromagnetic waves, whereas the second one defines the longitudinal waves.
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Notes
- 1.
Nefyodov E.I., Khublaryan M.G. Passing of the axis-symmetric screw flow through the channel of given profile (in Russian). Izvestia AS USSR, series Mechan. and Machinery, 1964, No 3, p. 173–176.
- 2.
In usual physics, a four-vector is a combination of the three-dimensional space and the fourth coordinate of time. In our consideration of electrodynamics, a four-vector is a combination of the three-dimensional vector potential \( \overrightarrow{A} \) and the one-dimensional scalar potential φ. This interpretation helps us to describe generalized electrodynamics more precisely. The term “four-vector” was proposed by A. Sommerfeld in 1910. Four-vectors were first considered by A. Poincaré (1905) and then by H. Minkovski.
- 3.
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Nefyodov, E.I., Smolskiy, S.M. (2019). Wave Equations of Macroscopic Generalized Electrodynamics. In: Electromagnetic Fields and Waves. Textbooks in Telecommunication Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-90847-2_4
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