I believe this problem is somewhat analogous to a spring pendulum. If
I do work to displace the mass of a spring pendulum, in the long run,
where does my work go? Initially it is passing back and forth between
potential energy and kinetic energy. But assuming any amount of
friction, it eventually ends up as thermal energy. If we want to
imagine the absence of "nonconservative forces" (i.e. we want to rule
out any thermal energy changes) then the pendulum oscillates forever.
Now let's look at the two capacitors. When we hook them together we
make a loop. That means we have inductance. Therefore we have made an
RC circuit. If we want to imagine the absence of any thermal processes
(no resistance and no polarization effects in the dielectric) then the
circuit will oscillate forever, passing energy back and forth between
the electric field (capacitance) and magnetic field (inductance).
However, given any tendency to put energy into the thermal realm
(which will certainly happen in the wires, capacitor plates, and
dielectric) then the "missing energy" will show up as thermal energy.
Additionally, at some frequency of oscillation and some wire
orientations, radiated electromagnetic waves can become important (i.e.
how good of an antenna is the wire geometry for the frequency of
oscillation we have?). However, for typical capacitors and wires in
the lab I assume that resistive losses and heating of the dielectric
will transfer that "missing energy" into the thermal realm pretty
quickly.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817