The role of the virtual work in Faraday's law

TL;DR

This paper explores how the concept of virtual work offers new insights into Faraday's law, clarifying the nature of induced electric fields and the non-conservative aspects of magnetic forces in practical scenarios.

Contribution

It introduces the use of virtual work and virtual conservativity concepts to better understand electromagnetic induction and the nature of magnetic forces.

Findings

Virtual work clarifies the nature of induced electric fields.

Magnetic forces can be non-conservative mathematically but practically treated as conservative.

The relation between emf and external work is analyzed in moving circuits.

Abstract

In the context of Faraday's induction law, we show that the concept of virtual work provides another point of view to clarify the nature of the induced electric field, as well as the fact that the integral over a closed path of the induced electric field is not the work performed by a unit charge. The usefulness of the concept of virtual conservativity is discussed. Further, we study the relation between the electromotive force and the real work done by an external agent to keep a circuit at constant velocity. From this discussion it is observed that magnetic forces can be non-conservative from the mathematical point of view, but can be treated as conservative for all practical purposes.