Generalization of Faradays Law of Induction: Some Examples

Abstract

The induced electromotive force and Faradays law of induction, due to a time-dependant magnetic field, are more conveniently written on the covering space. In this paper, we consider the induced electromotive force in the loop on a covering space which is generated by them time derivative the external magnetic field enclosed that loop.  The total induced electromotive force is derived by summing over all the contributions coming from the infinite winding numbers on the covering space. Illustrative examples of different time-dependent magnetic field are examined and analytical closed form expressions for the total induced electromotive force are derived. Our results, for all these examples, show the explicit dependence of the electromotive force on the ratio between the self-inductance and the resistance of the loop and they reduce to the well-known result when the limit of this ratio gpoes to zero.