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... Why does the result (half the energy goes
elsewhere) *not* depend on these particular details? If the only loss were
radiative, you'd get 1/2 for the energy loss. If the only loss were
resistive, you'd get 1/2. If it is a combination of both, you'd get 1/2.
I chose identical capacitors, which is one reason you get 1/2, but that
was only for convenience of discussion. The principle (if there is one)
could be applied to any pair of unequal capacitors, and the resulting
fractional energy loss would be a different value.
...
...
Well, yes, this is an example of the sort of general principle I was
fishing for. I'm not sure how we'll apply it to the capacitor problem.
Another example would be the Thevinin and Norton theorems which tell us
that a circuit will behave in a certain manner with respect to two
terminals *no matter what combinations of emfs and resistors* the circuit
is made up of.
I was really hoping that someone more math savvy than I knew already what
principle might apply to the capacitor problem, and jump in and enligten
us all. Maybe there is no such principle, and this thread will die.
It's one of those things that tantalizes, making one think that when a
precise result is *so independent of specific details*, then there *ought
to be* a general principle predicting that result. Maybe that's the
clearest statement of my concern that I've been able to state so far. When
I posted this I fully expected someone to say "What's the matter, Donald,
didn't you learn Schwartzengruber's Dissipative Energy Particition
Principle in college"? (I made that up.)