Re: Capacitor problem

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Fri, 28 Mar 1997, Mark Shapiro wrote:

> 	The "lost" energy goes to electromagnetic radiation.  The system
> oscillates!
>
> Mark
>
> Dr. Mark H. Shapiro
> Physics Department
> California State University, Fullerton
> P.O. Box 6866
> Fullerton, California 92834-6866

Some people have no restraint. But then, I guess the problem *was* too
easy. Still, as someone pointed out to me recently, even good and correct
answers should not be left lying unexamined. 

One might add that the oscillation damps to zero as the oscillator loses
energy through radiation, during the charge redistribution, leading to the
static configuration described in the problem.

One can, at this point mention the problem of the water tanks. Two
identical cylindrical water tanks are connected at the bottom by a pipe
with a valve which is closed.  One is filled with water to height h, the
other is empty. The valve is opened and water flows. Finally the tanks
reach equilibrium with each being filled to height h/2. 

But the potential energy of the water in the tanks is only half that of
the potential energy in the one initially filled tank. Where did the
energy go?

Not radiation here. Energy is simply dissipated by heating the water and
tanks, due to viscousity of the water. If there were zero friction and
viscosity, one assumes the level in the water levels would oscillate up
and down forever.

Some versions of the capacitor problem do not specify resistanceless wire,
and I've seen them give the answer "The energy goes into heating the wire"
without ever considering the energy loss resulting from oscillation and
radiation. But even if both mechanisms of energy loss are present, the
final equilibrium situation has half the energy one started with. Now if
the capacitors weren't of identical capacitance, the result wouldn't be
exactly one half. What would it be, and would that depend on the size of
the resistance?

In these problems, when the two things are identical, one initially has
all the energy and then the energy is distributed between both, is the
resulting energy *always* half the initial energy, no matter what objects
we are talking about, and what methods of energy transfer? If so, why?
Is there a more general and universal theorem applicable here?

	--Donald

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Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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