Re: funny capacitor

["John S. Denker" <jsd@MONMOUTH.COM>]

At 04:58 AM 3/6/01 -0500, Bob Sciamanda wrote:
> Qi = SUM Cij Vj is invertible because it is NOT gauge invariant

I suspect we have a communication problem because Cij means different
things to different people:  if it means the *full* capacitance matrix
that's one thing, and if it means the *diminished* capacitance matrix
that's another thing.

> In practice one can invert the Cij of a particular geometry

In practice, the following is the *full* capacitance matrix Cij for a
particular geometry:
        2.86,  -0.460, -1.15,  -1.25
       -0.460,  2.86,  -1.15,  -1.25
       -1.15,  -1.15,   3.26,  -0.96
       -1.25,  -1.25,  -0.96,   3.46

I would be very impressed if anybody can invert this, where by "invert" I
mean exhibit a matrix B such that B C = I, the identity matrix.

OTOH, starting from the *full* capacitance matrix it is possible to form a
number of different *diminished* capacitance matrices, and these
*diminished* capacitance matrices are invertible.

The *full* capacitance matrix is gauge invariant and manifestly
charge-conserving.  The *diminished* capacitance matrix is neither.