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Re: funny capacitor



Bob Sciamanda wrote:

Please give these authors their due. They do not harbor this
"misconception". The non-invertibility arises only when ....

Here is how I see this problem. Laplace equation allows us to
find charges when potentials are given. It does not allow us,
as far as I know, to calculate the boundary conditions (V1, V2,
V3, V4 on metallic pieces) when net charges are given. For
example, consider three floating rods bombarded by beams
of alpha particles and electrons. Suppose we know that Q1=2 nC,
Q2=-3 nC and Q3=0.5 nC. Find the resulting potentials on the
rods. Assume the geometry is the same as in our funny capacitor.

How to solve this problem? We begin by finding the Cij
coefficients by the Laplace method. This is only a preliminary
step toward what we really want. What is next? I used to think
that once the Cij are know I can find the Bij coefficients at once
by inverting the Q=C*V equation. But now I know that,
contrary to what many authors say, the matrix inversion is
algebraically impossible. So we need another method to
calculate Bij from Cij. John is offering a method. The authors
of textbook offer a method which does not work.

Is this a fair description of what has been accomplished under
this thread? I did not try to solve the "floating conductors"
problem yet but I assume it will work. Why not? Once the Bij
are known we would calculate potentials for any given set of
charges. I think that John exposed a serious misconception, an
unjustified claim that the matrix inversion is possible.
Ludwik Kowalski