Inter-charge forces in relativistic classical electrodynamics: electromagnetic induction in different reference frames

The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for the electric field of a moving charge predicts that the inductive force vanishes in the frame in which the magnet is in motion and the test charge at rest. In contrast, consistent results, in different frames, are given by the recently derived formulae of relativistic classical electrodynamics. PACS 03.30.+p 03.50.De In the introduction of his 1905 paper on special relativity [1] Einstein discussed the phenomenon of elecromagnetic induction, discovered by Faraday, viewed either from a frame in which the magnet is motion, or from one in which it is at rest. In this letter a careful re-analysis of this problem is performed in terms of the force on a test charge of magnitude q in the vicinity of a magnet. The force on the charge, due to electromagnetic induction, is calculated in both the inertial frame, S, in which the magnet is a rest and the test charge is in motion as well as the frame, S’, in which the magnet is in motion and the test charge is at rest. Three different methods are used to perform the calculation: (i) Application of the Faraday-Lenz Law. (ii) Application of the Lorentz Force Law, using standard formulae of Classical Electromagnetism [2, 3] (CEM) for the electric and magnetic fields of a uniformly moving charge. (iii) The formulae of Relativistic Classical Electrodynamics (RCED) [4, 5], a covariant formalism developed recently by the present author, are used to calculate directly inter-charge forces. The corresponding formulae are: Faraday-Lenz Law ~ F = q ~ E, − 1 c ∂φ ∂t = ∫