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Re: induced emf again



A reminder: This thread has drifted away from its nominal
subject.

To keep things in perspective: Fundamentally, the induced
EMF doesn't care about the charges.

The formula is
voltage = flux dot
or more specifically
voltage induced around the loop = (d/dt) flux through the loop

The foregoing equations are independent of the charges (or
lack thereof) in, on, or near the chosen loop.

1) In the absence of a material loop, you can use an imaginary
loop and the induced-EMF law applies just fine.

2) In the presence of charges in the vicinity of the loop, the
field produced by the charges is simply superposed on the
field produced by they flux dot.

The total voltage around the loop is unchanged. The local
voltage-drops are re-arranged: a little more voltage-drop
here and a little less there.

This is easily visualized by considering a C-shaped conductor
in a changing magnetic field. Choose a loop that follows the
shape of the C, inside the material except where it has to cross
the gap. There will be no field in the bulk of the conductor.
There will be a concentrated field in the gap. If the gap is at
its usual 3:00 position, that's where the field will be. If you
rotate the C so that the gap is at another position, say the 7:00
position, then that's where the field will be. In all cases the
total voltage-drop around the loop is unchanged.

===========

If the question is "what is the induced voltage" you don't
need to say anything about the charges.

In contrast, if the question is "what are the charges" then
you need to know the EMF plus various details about the shape
of the nearby conductors et cetera.

If you want to be retentive about it, you need to know
innumerable details about the conductors, so that you can
figure out the surface charges that must be present to
steer the currents in the conductor. But in practice, you
can usually just make the Kirchhoff approximations, which
assert that the surface charges on the wires (i.e. everywhere
except inside capacitors) are uninteresting because they
make a negligible contribution to the energy budget and
don't do anything except enforce the constraints -- and
the constraints are more conveniently expressed as constraints,
not expressed in terms of the surface charges.