After all these years, I still get the feeling that I really do not
understand Maxwell's equations. This was brought home again when I
watched the Mechanical Universe episode dealing with Faraday's discovery
of magnetic induction.

The example given was that of a toroidal solenoid with a few turns of wire looped through the toroid. There is no field outside the toroid so there is not flux cutting of the wire in the loop. The induced emf is given by the rate of change of total flux through the loop. The Maxwell equation describing this is

del x E = -B/t.

So my question is: How do you go from Maxwell's equations to describe the emf produced by a wire moving through a magnetic field?

If you bring in the theory of relativity to explain that motion through a magnetic field is Lorentz transformed to modify the magnetic field into a combination of electric as well as magnetic field, then explain what happens to the flux linkage law given above.

Bill

The example given was that of a toroidal solenoid with a few turns of wire looped through the toroid. There is no field outside the toroid so there is not flux cutting of the wire in the loop. The induced emf is given by the rate of change of total flux through the loop. The Maxwell equation describing this is

del x E = -B/t.

So my question is: How do you go from Maxwell's equations to describe the emf produced by a wire moving through a magnetic field?

If you bring in the theory of relativity to explain that motion through a magnetic field is Lorentz transformed to modify the magnetic field into a combination of electric as well as magnetic field, then explain what happens to the flux linkage law given above.

Bill