On equivalent expressions for the Faraday's law of induction

in this paper we give a rigorous proof of the equivalence of some different forms of faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and papers are only valid under very special circunstances, thus are not satisfactory under a mathematical point of view. we show also that faraday's law of induction is a relativistic invariant law in a very precise mathematical sense.