Re: Capacitor and Force

Heres the problem, due to John Perry.

My assumption about ceramic caps was wrong. I didn't know it was layered.

Since one has layers the charge is distributed between each layer. Suppose
there are 2n interleaved layers and charge Q. Then each layer has charge
Q/n. Every layer experiences a force between every other but almost all
cancel out.

By assuming all the charge Q was on just one plate seperated by a distance r
was wrong(Which is how jus 2 plates would actually work).

Some initial investigation shows that the layers have a significant effect
in reducing the force. No only is the charge on each plate reduced by Q/n
but the distance between the first and last is increased because of all the
layers inbetween. So treating a ceramic cap as a parallel plate cap is wrong
as I did it. (using CV to get the charge and assuming it was on each plate
because it should be Q/n but I have no idea what n is).

So there are forces there but they are much smaller than what I was
thinking. For a very large parallel plate cap one has C = e*A/d, Q = C*V, F
= k*(Q/d)^2 = k*(e*A/d*V/d)^2 = k*(e*A*V/d^2)^2.

For A = 1/4 m^2, V = 10V, d = 1mm, one gets F = 4N. This is without a
dielectric in a vacuum. I imagine that that if one inserts a
dielectric(which they will probably have to if they want to insulate it)
that it will cut the charge in half because the dielectric sorta acts as a
layer itself. In any case it should be an order of magnitude approximation.

Note that increasing d = 2mm gives F = 0.2N so the F is heavily dependent on
d. (obviously it is d^(-4)). Changing d by a factor of 10 changes F by a
factor of 10000.

Jon



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