Abstract
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity v (including a velocity more than c). We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.
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Chubykalo, A., Espinoza, A., Flores, R. et al. Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics. Found Phys Lett 19, 37–49 (2006). https://doi.org/10.1007/s10702-006-1847-y
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DOI: https://doi.org/10.1007/s10702-006-1847-y