From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Thu, 3 Jun 1999 10:48:05 -0500
Hi all-
I reply to Michael and Brian in the context of Michael's first posting:
*******************************************************************
I disagree with Jack Uretsky's analysis that the person connecting the
capacitors absorbs the energy. In his experimental description he may
be correct, but he has changed the experiment drastically.
I think my spring pendulum analogy can help us here.
In the original case, simply connecting the two charged capacitors
together is like letting loose of a stretched spring pendulum. The
spring pendulum either oscillates forever (no friction) or dissipates
kinetic energy into thermal energy over some period of time. Likewise
the suddenly-connected capacitors oscillate forever (E-energy to
B-energy and vice-versa) or else energy is radiated via some
combination of thermal energy or as E&M waves.
************************************
Now hold on there, fellows! We are NOT describing an "experiment",
we are discussing the solution of a problem posed to illustrate certain physical
principles. The difference is crucial. In discussing an experiment we need to
know the detailed setup, so that we can pick out the crucial elements. In
discussing the posed problem, we are dealing with an idealization.
The problem is posed in a manner that emphasizes the storage of
electrostatic energy. The context is to emphasize the physical principle presented
in a chapter on (ideal) condensers. The problem is not unrealistic - one builds
circuits regularly that minimize stray inductance (very short leads) and radiation.
The problem therefore idealizes realistic circuitry and is therefore appropriate to
the context in which it is presented.
In that context, and only in that context, the correct answer to the question,
"where did the energy go?", is "into the person who joined the capacitors", or,
equivalently, "into the switch".
Michael raises the question of what is an appropriate analogy. The burden,
I think, is on the analogizer. The usual test of a physical analogy is that
it compares two systems that obey the same differential equations. Thus, a
spring-mass system can be analogized to an L-C circuit, with L compared to mass
and C compared to the inverse spring constant. That is not an appropriate analogy
to a problem that has been set up to make inductive effects insignificant.
There probably is a 2-spring analogy in which the springs are stretched
and then connected with either a fixed force or a fixed displacement, but I'll
leave the details to the list. What is important is that there is no mass in
the analogy problem, because the problem is not posed as one involving SHM.
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