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Название: The Faraday induction law in relativity theory
Авторы: Kholmetskii A.L., Missevitch O.V.
We analyze the transformation properties of Faraday’s law in an empty space and its relationship
with Maxwell’s equations. In our analysis we express the Faraday’s law via the fourpotential
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.