Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: funny capacitor.



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