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Re: funny capacitor



----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, March 05, 2001 02:57 PM
Subject: Re: funny capacitor


At 01:30 PM 3/5/01 -0500, Bob Sciamanda wrote:
The trivial case of a single conductor: Q = C V is useful. C is a
constant of geometry, even for various values of Q and V. IOW one need
not involve the the "sphere of charge at infinity" - the equations are
still valid and useful.

When I see the scalar equation
Q = C V
I assume it is shorthand for
Q = C delta V
= C (V1 - V2)

where V1 and V2 are the voltages on the two terminals of the
capacitor. That is a fine equation, valid and useful. The expression
(V1-V2) is manifestly gauge invariant.

If somebody wants to interpret
Q = C V
in terms of some "absolute" voltage V, then the equation does not look
valid to me. It begs the question of how to measure V. All the
voltmeters
I've ever seen have *two* leads, and can only measure a voltage
*difference*.
. . .

It is standard terminology in "circuit" equations (even static circuits)
to refer all voltages to some presumed "ground point" of defined zero
potential. In this sense, these circuit equations are not necessarily
"gauge invariant" - nor need they be to be useful. 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.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor