Ludwig wrote:
* * * *
.. . . .
3) The calculations were performed by using the formula for the current
i(t) in the serial LCR circuit. The reference used was "Principles of
Electricity" by Page and Adams (fourth edition, 1969). As usual, the
formula for i(t) is parametrized in terms of Q(0)=initial charge,
alpha=0.5*R/L and omega_zero= sqrt[1/(L*C)-alph^2). In our problem:
q(0)=1, alpha=0.5*R/L=25000 and omega-zero=66144, all in SI units).
The formula, derived on pages 300-301), is:
i(t)=i(0)*exp(-alpha*t)*sin((omega_zero*t)
where i(0)=[(omega_zero^2+alph^2)*C*V(0)]/omega_zero. Note that our
V(0)=100 volts and C*V(0) is the initial charge on the capacitor, Q(0).
4) Once the formula is written it can be used to find H (as an integral
of i^2*R*dt between zero and infinity). Analytical integration is
likely to be easy but being out of practice with this craft I simply
wrote a short program to do this numerically on my Mac. The energies of
the e.m. waves were then calculated as 0.5*C*V^2-H. All exotic forms of
energy (neutrinos, gravitons, etc.) were ignored.
.. . . .
Ludwik Kowalski
* * *
Ludwig,
I'll go out on a limb and predict that if you do the integration
carefully, ALL of the capacitor's original energy will go into Ohmic
heating. The differential equation whose integral you are using I(t) does
not know of any radiation mechanism; it states Kirchoff's loop law which
says energy is totally accounted for by the terms in the equation. You
would have to include a term which sinks energy by way of some "radiation
resistance". Math is not magic; neither is it a source of new physical
information; it is logic, and its conclusions will only make explicit what
is already implicitly in the premises which it was handed.