Back EMF (motor) - a moving magnetic field (flux) will cause a conductor loop (copper wire/winding) to rotate - a MOTOR

only if the loop is shorted and that is not always the case.

...

Of course you are right but the question goes beyond that. I know you know everything I'm going to say here, but let me make the point because the idea that a flux variation can be the cause of anything is quite penalizing for the understanding of cause and effect relationships.

If the flux were a cause, it would be non-local because the electrons are not in the flux but in the conductor of the induced circuit. A flux variation is therefore not the cause of anything in a circuit.

The one and only cause is the force on the electron in the induced circuit, which is F=q.E where E is the local electric field.

So why can we evaluate E from the variation of the flux?

To understand, we need to find Faraday's law.

Emf = ∮E.dl integral of the electric field E on the circuit l of which dl is an element

E.dl = ∬(∇xE).n.dS Stokes' theorem applied to E, S surface bounded by l

∇xE = -∂B/∂t Maxwell

so ∮E.dl = -∬(∂B/∂t).n.dS

Φ = ∬B.n.dS definition of flux, B and n are vectors, n is the unit vector, normal to the surface S of the circuit

-dΦ/dt = -∂(∬B.n.dS)/∂t = -∬∂B/∂t .n.dS

hence:

∮E.dl = -dΦ/dt Faraday's law, Q.E.D.

The flux variation is only a convenient mathematical means from Stokes' theorem, but it is not a physical cause of action on the charges in the induced circuit. Only the electric field at the position of a charge creates a force.

One could also obtain the electric field from the potential vector, E=-∂A/∂t, or from relativity by applying the Lorentz transforms to the electric field of the charges at the source of the magnetic field, as seen by the charges in the induced circuit. Everything is very coherent, the magnetic field is a deceptive artifice,

**the only cause is the Coulomb force**.