The Capacitor problem - once more

["JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>]

        I have read the 3 published articles in AJP on the problem of
joining 2 charged capacitors - they all seem to miss the point that the
energy loss occurs in the act of joining the two capacitors.  I have made
a simple model to clarify this fact.
        The Model:  Capacitors C_1 and C_2 are charged with respective charges
Q_A and Q_B.  We note that the electrostatic energy in the capacitors decreases
if we join the respective positive and negative terminals.  Where does the
energy go?
        Let us join the capacitors using the following method.  First join
the negative terminals.  This act clearly does not change the stored energy.
Now attach the positive terminals to the plates of a parallel plate capacitor,
where the plates are well-separated.  Call this capacitor C_3, and well-separated
means that the capacitance C_3 is practically zero.  Again there has been no
"practically" no change in the stored electrostatic energy.
        Let the separation of the C_3 plates be large, but finite.  Then the
voltage difference between the positive terminals of C_1 and C_2 induces positive
and negative charges on the plates of C_3, so that the plates attract each other.
        I leave it as an exercise to calculate the total stored energy as
a function of C_3.  It is easy to show that when C_3 is zero the stored energy
has its original value.  When C_3 is infinite (when the plates come together)
the charge on C_3 is finite and the voltage across C_3 is zero.
        We assume that the plates are free to move, so C_3 is functioning as
a switch.  Because the plates attract each other they pick up kinetic energy
which must be dissipated when the plates collide.  But when the plates collide,
the switch has been closed and the stored electrostatic energy is just that
of the two joined capacitors.
        Conclusion:  In the original statement of the problem, the energy went
into the person who joined the two capacitors, as I originally contended.  In
the "C_3" model, the energy went into the kinetic energy of the capacitor plates,
which had to be dissipated on collision.  All of this is readily calculable.
                                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