From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Thu, 3 Jun 1999 11:04:46 -0500
Hi Mark:
You write:
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If I understand Jack right, then we can bring the C3 plates together in
infinitesmal steps, keeping the charge in pseudo-equilibrium, and absorbing
the "excess" energy as we do so. In this case, it seems that it does not
matter if the connecting wires are superconducting or not. Or is my
intuition faulty here?
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Not faulty.
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Indeed, this is the other extreme from closing the switch so quickly that
the charge does not start to redistribute until the switch is closed
(remember there is inductance), which is the case I had in mind before, as I
now understand it.
Jack's case, with the plates coming together under their own attraction is
more interesting if we include in the problem the L of the circuit, since
the current would seem to be non-zero as the plates collide, which means
that a current oscillation continues after the collision.
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Putting L in the circuit makes a different problem. If you
want to teach about storage of energy in capacitors, stick with the
idealization that does the job. Follow the KISS principle.
If, by the way, you want to do an experimental demo in connection
with this unit, make the voltage difference across the two capacitors big
enough so you get a little spark when you make the final connection.
The spark is part of the energy dissipation.
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Now what about elastic plates that will bounce back after colliding...
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That's easy, if the collision is elastic. When the plates touch
the charge across C_3 is neutralized so that the electrostatic energy
is that of the joined capacitors. The plates bounce away from each other
and travel forever with kinetic energy equal to the missing electrostatic
energy.
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography