Dwight-Bewley paradox

The concept of motional induced EMF is implicitly based on a reference frame relative to which the magnetic field pattern is unchanging or stationary, and uses the relative velocity v between the frame and the conductor in the expression B v l. For ease of conception, the velocity may be taken as that between the field pattern itself and the conductor. Where there are multiple field patterns in relative motion, no “velocity” can be ascribed to the resultant field pattern relative to any object, fixed or moving. Therefore the EMF induced in a conductor situated in such a field cannot be expressed as a single motional EMF, but must be found by superposition of EMFs induced by the individual fluxes. From the impossibility of applying the B v l rule to the resultant flux, Bewley concludes that the EMF in the conductor is not motional but variational. It is shown here, mathematically from a consideration of reference frames, and physically from the fact of electromechanical energy conversion taking place, that Bewley´s assertion is invalid and that the EMF is in fact motional, not variational. The B v l rule is then generalised for application to such situations