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# Re: A funny capacitor.

On Tue, 27 Feb 2001, Ludwik Kowalski wrote:

Instead of asking "which of the two setup has a larger C?"
I can now ask "which of the setups should take more Q from
the battery?" Why should the presence of the third plate
require a larger Q?

Things might become slightly clearer if we specifically depict the two new
capacitors formed by the extra plate.

Change this:

B

* *
* *
******* ******* C2
* *
* *

*********

Into this:

B

* *
* *
******* ******* C2
* * * *
* * * *
* *
* *
* *
* *
******* *****
* *
* *
********* *********
C3 C4
********* *********
* *
* *
* *
*************

However, the added plate does not approach the *backs* of the two
capacitor plates, instead it approaches the gap region. It causes charge
on the original two plates to migrate towards the extra plate, and acts to
"intercept" flux lines connected to that charge, therefore it partially
shields the original two plates from each others' effects. As far as the
charge is concerned, the two original plates are rotating to face the
extra plate. As a result, the original capacitor's value would decrease
even as the extra capacitance of C(added) = 1/(1/c3 + 1/c4) causes the
total capacitance to increase. Arguements using forces and potential
energy show that the drop in value of C2 is more than made up by the extra

I don't see other ways to simplify this problem, so perhaps it's in the
same realm as calculating charge distributions on conductors of arbitrary