I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

Regards,

Erland Gadde