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# Re: A funny capacitor.

• From: "John S. Denker" <jsd@MONMOUTH.COM>
• Date: Wed, 28 Feb 2001 20:50:37 -0500

At 08:26 PM 2/28/01 -0500, Ludwik Kowalski wrote:
I would know how to calculate C of the funny capacitor, at
least in principle, if the potential of the bottom plate were
specified,

Good.

for example zero.

Not a good choice.

In that case I would impose
potentials on vertical plates, for example, -50 and +50 V,
and used the Laplace equation to find surface charges
on each vertical plate. Then C=Q/V.

Q = C V where C is the 3x3 capacitance matrix.
You can walk through the columns by changing the imposed
voltage on each of the elements.

The boundary
conditions (potentials on three objects) is given and the
rest is just a matter of number crunching.

Yes. There exist many ways to do the crunching, including the spreadsheets
discussed in this connection last month.

> But how can the problem be solved when the lower plate is
floating.

V = C^-1 Q, for imposed Q.

Inverting a 3x3 matrix isn't very hard. A fellow named Gauss had something