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Re: funny capacitor



Ludwik wrote:
Many textbook authors discuss equations (2) and (1) shown
below. They often emphasize that by knowing Cij we can
calculate Bij, or vice versa.

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

and

V1=B12*Q1 + B12*Q2 + B13*Q3
V2=B21*Q1 + B22*Q2 + B23*Q3 Equation (1)
V3=B31*Q1 + B32*Q2 + B33*Q3

But JohnD discovered that this is not true. How come that
others were wrong for so long? As an example let me quote
from "Fundamentals of Electricity and Magnetism" by A.F.
Kip. [By the way, is it the same public lecturer you
mentioned this morning, John?]

Referring to three conductors Kip begins with Equation 1
and justifies it by "the principle of superposition and the
uniqueness theorem." Then he writes that (1) "can be
inverted to solve for the charges". The (2) are presented
as the result of the inversion of (1). Any comments?
Ludwik Kowalski >
*************************************************
I venture that the answer is that the textbook authors are not restricting
themselves to the cases where the total charge on the system of conductors
is always the same, as one imposes different sets of potentials/charges on
the conductors.
Eg: 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.

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