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Re: funny capacitor



At 03:40 PM 3/5/01 -0500, Bob Sciamanda wrote:
The equation set
Qi = SUM Cij Vj
is valid when all Vj's are measured from some (any) agreed point of zero
potential. Given that specification, the Cij are functions only of
geometry. Changing the values of the Vj's (still measured from the same
"ground") does not conserve system charge in general, but preserves the
values of the Cij.

... which is exactly what I've been saying all along. That's a direct
consequence of gauge invariance.

I'm not sure why Bob felt the need to mention this. Cij is still gauge
invariant, and it's still singular and non-invertible.

It is standard terminology in "circuit" equations (even static circuits)
to refer all voltages to some presumed "ground point" of defined zero
potential.

I wouldn't have said "presumed" or "defined", but rather "chosen". It is
an arbitrary choice. You are free to choose any reference point you like
-- just don't think your choice is binding on anybody else.

And I wouldn't have said "even" static circuits. Actually it's _only_ for
static circuits that you can do this. For non-Kirchhoff AC circuits, i.e.
in the presence of stray fields, the voltage you measure depends not only
on where you attach the reference lead of your voltmeter, but on the path
that the lead-wires take. People who think that "ground" is a well-defined
concept tend to be mystified by "ground loops".