The Faraday induction law in relativity theory

Abstract

We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of four-velocity, defined on a circuit under its deforming motion. The obtained equations show one more facet of the physical meaning of electromagnetic potentials, where the motional and transformer parts of the flux rule are incorporated into a common phenomenon, reflecting the dependence of four-potential on spatial and time coordinates, correspondingly. It has been explicitly shown that for filamentary closed deforming circuit the flux rule is Lorentz-invariant. At the same time, analyzing a transformation of e.m.f., we revealed a controversy: due to causal requirements, the e.m.f. should be the value of fixed sign, whereas the Lorentz invariance of flux rule admits the cases, where the e.m.f. might change its sign for different inertial observers. Possible resolutions of this controversy are discussed.