Re: funny capacitor

[Bob Sciamanda <trebor@VELOCITY.NET>]

Please give these authors their due.  They do not harbor this
"misconception".  The non-invertibility arises only when one insists that
only states with the same total system charge be considered in Qi = SUM
Cij Vj  (the Vj's are then no longer independent variables).  These
authors do not impose this constraint.  (I know of only one person who
does :)

Whether or not conservation of charge is a property of the universe, it
need not be a property of a system which I choose to study.   Eg: I can
place charges on a capacitor's electrodes with a variety of values of net
total charge - a set of states worthy of study and modeling.  These
authors are considering this general possibility and are defining for each
system of N conductors a single set of Cij which depend only on geometry
and the choice of Voltage reference point .  These Cij are then a property
of the N conductor system and describe the Qi vs Vj relations for all
possible system states - not just those with a given, fixed total charge.

I've said 'nuff . . . I quit!  :)

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Ludwik Kowalski" <KowalskiL@MAIL.MONTCLAIR.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, March 06, 2001 01:26 PM
Subject: Re: funny capacitor


> . . .
> In that university textbook the V=B*Q matrix is introduced in
> the context of the principle of superposition. Then the authors
> say: "SOLVING THESE EQUATIONS WITH RESPECT TO
> CHARGES, one can see that, inversely, charges are linear
> functions of potentials."  . . .
>
> It would be interesting to trace the origin of the misconception . . .
> . . . It is true
> that linear relations exist between charges and potentials in both
> ways (when Q are independent variables, and when V are
> independent variables). What is not true is that Cij can be
> calculated from Bij, or vice versa, by the matrix inversion
> method. . . .