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Re: A funny capacitor.



On Mon, 26 Feb 2001, Ludwik Kowalski wrote:

William Beaty wrote:

I think it will be larger, since such a plate will be attracted and
accelerate towards the other plates, exchanging electromagnetic
PE for mechanical KE just as when two oppositely-charged
plates fall together and voltage measured between the plates falls
(and since charge is constant, capacitance value must rise as
the 3rd plate is sucked inwards.)

OK, one more condition should have been specified: positions of
plates are fixed.

Yes. I'm reasoning that if the two plates approaching each other will
decrease the stored energy and increase the capacitance, the same is true
if your 3rd plate approaches.


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Assuming the totally inserted plate has the thickness d1 while the
distance between the original plates is d2, and ignoring the bulging
of E lines near the edges, the capacitance is C=eps_o*A/(d2-d1),
where A is the area. In this case C after inserting the plate is indeed
larger than C before inserting it. But what does this have to do
with the origibal problem?

It's the same problem intuitively, I've just "morphed" the shape of your
3rd plate a bit, and I reason that if inserting the above "metal cube"
causes the capacitance to uniformly increase as it approaches the gap,
then bringing in a perpendicular plate must also cause an increase for
similar reasons. I see that bringing a conductive object near the gap
between the two plates tends to replace "empty space" with two new
capacitors in series, where the plate area of the "new" capacitors is
approximately the same as the capacitor that they've "usurped", yet the
average distance between the new plate and each of the original plates
adds up to LOTS LESS than one half of the original distance, so the two
new capacitors have MORE that twice the capacitance of the space they've
"usurped", therefore in series their presence must increase the total
capacitance. Only an infinitely thin plate inserted parallel to the
original two plates would not act this way. Yes, my thinking is very
visual and handwavy. It's informed guessing while thinking aloud. I
start talking, then monitor my own "bullshit detector" to see if
half-subconscious analysis agrees with what I'm saying. I end up with an
understanding of what's happening, but it doesn't give me total certainty,
and cannot supply any hard numbers. If we need certainty and hard
numbers, I sure wouldn't do it that way.



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