Faraday's Law and Magnetic Induction: Cause and Effect, Experiment and Theory

Faraday's Law of induction is often stated as "a change in magnetic flux causes an electro-motive force (EMF)"; or, more cautiously, "a change in magnetic flux is associated with an EMF". It is as well that the more cautious form exists, because the first "causes" form can be shown to be incompatible with the usual expression V=-partial derivative(t)Phi, where V is EMF, partial derivative(t) is a time derivative, and Phi is the magnetic flux.This is not, however, to deny the causality as reasonably inferred from experimental observation-it is the equation for Faraday's Law of induction which does not represent the claimed cause-and-effect relationship. Unusually, in this induction scenario, the apparent experimental causality does not match up with that of the mathematical model. Here we investigate a selection of different approaches, trying to see how an explicitly causal mathematical equation, which attempts to encapsulate the experimental ideas of "a change in magnetic flux causes an EMF", might arise. We see that although it is easy to find mathematical models where changes in magnetic flux or field have an effect on the electric current, the same is not true for the EMF.