Re: funny capacitor

[Bob Sciamanda <trebor@VELOCITY.NET>]

If you add a third conducting shell of largest radius c to my previous
example, you can quickly write down:

V1 = k ( Q1/a + Q2/b + Q3/c)

V2 = k ( Q1/b + Q2/b +Q3/c)

V3 = k ( Q1/c + Q2/c + Q3/c)

Note:
1) This is invertible - the matrix of coefficients is not singular.
2) As c => infinity we revert back to our previous system.

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: Saturday, March 10, 2001 01:12 PM
Subject: Re: funny capacitor


> Bob Sciamanda wrote:
>
> > Here is your bug!  You are forcing one of your local
> > conductors to always be at the same (zero) potential
> > even when charges vary on it and other conductors.
> > You can choose any spacepoint as your potential
> > reference, but - unless it is at infinity - its potential
> > relative to other points (and infinity) will vary as the
> > charges on your N conductors vary.
>
> The "infinity" can be a conducting wall (object #4)
> which is sufficiently distant from other conductors
> (to make the net force on a probe charge, caused by
> Q1, Q2 and Q3, negligibly small). In my program the
> boundary of the enclosure was a square at |x|=101 and
> |y|=101 cells. The funny capacitor was in the center;
> it was inside the square of |x|=11 and |y|=11 cells.
> That is far enough. I can move the enclosing wall
> further away but this will also give me a singular
> matrix of Cij coefficients.
> Ludwik Kowalski