Re: A funny capacitor.

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Referring to this:

Q1=C11*V1 + C12*V2 + C13*V3
Q2=C21*V1 + C22*V2 + C23*V3                (Equations 2)
Q3=C31*V1 + C32*V2 + C33*V3

John wrote:

> You will discover the following facts, which will soon come in handy:
>
> Gauge invariance requires Cij to be symmetric:
>          Cij = Cji                              (equation 3)
>
> Charge conservation requires each row (and/or column) to sum to zero
>          SUM_j Cij = 0    for all i     (equation 4)
> assuming (!) the sum runs over all relevant objects.

1) I was aware of equations 3 and 4. Equation 3 reminds of
    Newton's third law. The influence of object 2 on object 1
    is as strong as the influence of object 1 on object 2. Here
    we refer to influences (Q affecting V) not forces. Can it
    be said that N3 is a consequence of "gauge invariance"?

2) I am not sure I understand the last line in the above quote.
    It refers to equation 4. For example, can I write:

    C11+C12+C31=0   and   C11+C12+C13=0 ?

How does the equation 4 follow from the law of
conservation of charges?
Ludwik Kowalski