Capacitor problem, another question

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

The capacitors energy paradox, as presented by Simanek on 3/28/97, is quoted 
as item #2 below. I would like to formulate it slightly differently in order 
to ask an additional question.

1) A single parallel plate capacitors (negligible fringe effect) is made 
   from metallic plates whose areas can be increased at any rate. Think
   about nylon strings to visualize the process of doubling the area of
   both plates simultaneously in time t. You can do this suddenly (but
   not at the speed of light) or adiabatically. Friction is negligible
   and the mass of each plate is very small. The first question is the
   same as before "Where did the rest of the energy go?". We have already 
   identified two alternatives, heat and e.m. waves. My prediction was
   that most of the lost electrostatic energy will appear as heat. 

   New question: "How does the answer to the first question depend on t?".
   Ludwik
...........................................................................
2)       
> Two identical parallel plate capacitors are used. One is charged with
> charge Q, so the plates have Q and -Q respectively. The other capacitor
> is still uncharged. The stored energy of the charged capacitor is CV^2/2,
> or Q^2/2C and the stored energy of the other one is zero.

> Now perfectly *resistanceless* wires are used to connect the capacitors
> as shown, being careful not to add or remove any charge from the system.

                -------------
               |             |
            -------       -------
            -------       -------
               |             | 
                -------------

> The charges redistribute, so that each capacitor has charge Q/2. The
> total stored energy (both capacitors) is now

                      2      2
                 (Q/2)    1 Q
               2 ------ = - --
                    C     4 C

> This is half as much stored energy as before. Where did the rest of the
> energy go?

> The charge redistribution can be accomplished by having the wires in place
> and a remote-controlled pair of switches complete the connection. No
> mechanical work need be done by the agent performing this operation.