You have changed the problem! Originally, the connections were
"resistanceless". In that case the rate of change of the E-fields will be
very large, and the induced B-fields will be very large. Essentially all
the energy loss is to radiation. The system oscillates because of the
stray inductance of the plates and the connections. The oscillations die
out because of the radiation resistance and whatever resistance the plates
have (not much if they are more than paper thin).
If you allow the connections to have resistance, then some of the
energy loss will be thermal (integral of the I^2R losses). The remaining
will be to radiation.
I don't see what the issue is here Ludwig. You seem to be overly
concerned about some energy leaving the system as EM radiation, but not as
thermal energy.
Dr. Mark H. Shapiro
Physics Department
California State University, Fullerton
P.O. Box 6866
Fullerton, California 92834-6866