| You presumably have not proved that "magnetic forces do no
| work", because that's not true.
|
| More likely, you proved that a _static_ magnetic field does
| no work on a _test charge_.
|
| 1) If the field is in any way time-dependent, all bets are off.
| -- Betatron.
| -- Dynamo (aka electrical generator).
| -- et cetera.
|
In cases where the magnetic field is time-dependent:
dB/dt != 0
Is the magnetic force doing mechanical work? Or is it an electric force
produced by the induced electric field that is doing work? (I.e. the
non-conservative component of the electric field)