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Re: funny capacitor



At 10:33 AM 3/6/01 -0500, Bob Sciamanda wrote:
The "full" (your term) capacitance matrix Cij which you are defining
restricts the validity of the equation Qi=SUM CijVj to states with the
same total charge, SUM Qi.

I consider that a feature, not a bug. It makes manifest the law of
conservation of charge.

There is no one set of Cij that is a property
only of geometry and the choice of voltage reference point.

Au contraire, the full capacitance matrix Cij depends only on geometry, and
it is independent of choice of voltage reference point.

This is not very useful.

My opinion differs. I see fine uses for the full capacitance matrix, and
also for the various diminished capacitance matrices to which it gives rise.

If I have an isolated system of two
separated conductors, I would like an equation Qi=SUM Cij Vj which defines
the Cij as properties of the system geometry (and the gauge) and are
independent of the total system charge, so that I can consider cases in
which Q1 = -Q2, or Q1=2*Q2, or Q1 = -3*Q2, or etc, using the same set of
Cij. I want to use the same Cij to describe all various ways of
depositing charges on these conductors, holding fixed only the geometry
and the voltage reference space-point.

If that's what you want, then that's what you want, and it's OK with
me. You are free to want whatever you want. In this case you can get what
you want by choosing one of the diminished capacitance matrices.

Adding the constraint of fixed total charge
is doing a very different, and severely restricted, problem.

Using the full capacitance matrix requires me to live within the
restrictions of charge conservation and gauge invariance. This hardly
seems like a severe restriction!

The full capacitance matrix doesn't impose any restrictions that weren't
already imposed by the basic laws of physics.