What Produces a Magnetic Field?

Most recent answer: 06/04/2016

on page 18-2 of Feynmans Lectures on Physics he gives the classic Integration to prove there is a mag field in the capacitor. The claim is it s a changing Electric field that produces the mag field between the plates. But this field is not the same as the field around the wire. Reducing the capacitor to L shaped conduction paths (no loss of generality) it is clear that the mag field is anticyclical compared to the charging current in the wire. It is also clear that the mag field is produced by charging currents, not by Maxwell's famous dE/dt term.
- barry (age 79)

You raise an interesting philosophical argument about what "produced" the magnetic field (B). Was it the current flowing in the wires? Or was it the local changing electric field (E)? On closer inspection the question is meaningless. The pattern of current flow itself could not have happened without causing the change of E. Therefore there's no way to reason about what would have happened if the same current had flowed without the changing E and thus no meaningful way to say one or the other is the "true cause". What we can say is that any pattern of current flow that doesn't include any current in the little region we're looking at and that gives the same dE/dt will always give the same curl of B there. Any pattern that gives a different dE/dt will always give a different curl of B there. That's why it's often more convenient to think of dE/dt as the "cause" of the curl of B, although you're free to say that its the currents instead.

Mike W.

(published on 06/04/2016)