Re: funny capacitor

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

In the last message I asked:

> 4) But how can one justify Cij=Cji? John
> justified it be referring to Dr. Maxwell. Can
> this be done on the basis of what is explained
> in a typical introductory physics textbook?

I suppose that a simple justification does not exist,
otherwise John would use it.

ARE THESE COMPARISONS VALID?

1) A rock is dropped from a roof. How long does
it take to hit the ground? 3 seconds. Is this the
"one and only one reproducible solution?" I think so.

But somebody may object saying that there are many
solutions. One is when my stopwatch is initially at zero,
another when the initial time is 10 seconds (and final
time is 13 s), etc.

2) Consider a common capacitor. Suppose its geometry
is such that C=100 pF. What is Q when dV=10 V? It is
1000 pC. Is this the "one and only one reproducible
solution?" I think so.

But somebody may object saying that there are many
solutions. One is for V1=0, V2=10, another is for
V1=50, V2=60, etc. Any set of two voltages is a
solution provided V2-V1 = 10.

3) JohnD was saying that the well defined V(Q) problem
(find V1, V2 and V3 when Q1, Q2 and Q3 are given) has
many solutions. How does this differ from the "many
solutions" claims in the first two items above?

4) Am I the only one to be puzzled by the contradiction.
On one hand I believe in one and only one reproducible
solution (funny capacitor with V1=-50, V2=+50 and
V3=+20) on the other I am facing a situation in which
the mathematics contradicts me. Is this an artificially
created dilemma due to different interpretations of the
meaning of the phrase "one and only one?"
Ludwik Kowalski