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Re: Gauss' law and displacement current



At 03:49 PM 4/19/01 -0400, Carl E. Mungan wrote:

When you close the switch and
turn on the current, why does the electric field inside the capacitor
change

I don't think it does -- not until some nonzero time has elapsed. Please
explain.

This is why I think I haven't accounted for the charges properly. You
can't change the fluxes without changing the charges. I'm still
stumped. More help anyone?

In case anyone missed my question the first time around, here it is
again. Consider two identical RC circuits, with both capacitors half
charged up. In circuit A, there is no current running into the
capacitor. In circuit B, there is. For both circuits, surround the
positive plate with a Gaussian surface cutting across the wire
connected to the plate. The right-hand side of Gauss' law seems to be
the same for both circuits because both capacitors carry the same
charge; the left-hand side is different for both circuits because the
electric field in the lead wire decreases the net flux for circuit B.
(Since both capacitors carry the same charge, I assume the electric
field inside both capacitors is the same.) What's wrong with my
analysis?

I'm still mystified by the question. We all know there's a misconception
lurking here somewhere, but the scenario has not been described in enough
detail to permit nailing down the exact nature of the misconception.

*) Perhaps a diagram would help.

*) Perhaps it would help to consider variations on the question. For
instance, would the same question arise if the capacitor were replaced with
a resistor?

*) Perhaps it would help to pay special attention to the following common
areas of confusion:
-- Current is not the same as charge. A long straight wire (even a
non-superconducting wire) can carry a current without having any net charge
at typical places along its length.
-- Field is not the same as flux.
-- To apply Gauss's law, you can't just look at the magnitude of the
flux; you have to be careful about signs, and about directions of vectors.
-- Current (i.e. flow or "flux" of electrons) is not the same as magnetic
flux which is not the same as electric flux.
-- Kirchhoff's "laws" are only approximations to the real physics.
-- In particular, if a wire is thin, it has only a small capacitance per
unit length, so you can change its voltage with only a small amount of
charge. OTOH if you want to look closely there will be *some* charge
involved.