On Equivalent Expressions for the Faraday's Law of Induction

TL;DR

This paper rigorously proves the equivalence of various forms of Faraday's law of induction, clarifying misconceptions and highlighting limitations of common derivations in textbooks from a mathematical perspective.

Contribution

It provides a rigorous proof of the equivalence of different formulations of Faraday's law, addressing misconceptions and emphasizing the conditions under which these forms are valid.

Findings

Different forms of Faraday's law are mathematically equivalent under certain conditions.

Many textbook derivations are only valid in special cases.

The paper clarifies misconceptions about the law's general applicability.

Abstract

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 circumstances and not satisfactory under a mathematical point of view.