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Re: Conserving Q/Faraday



REPOSTING
I do not remember if I already replied to what John Denker wrote.

I agree on the infinite epsilon. My epsilon=1 corresponds to a very
thin layer of P2. John was dealing with P2 which is nearly equal to
the spacing between P1 and P3, as it should be when comparing P2 to
a dielectric filling the space.

Good point, John.

"John S. Denker" wrote:

At 01:29 PM 1/31/99 +0100, Ludwik Kowalski wrote:
"John S. Denker" wrote:

First, let's replace the insulating dielectric by a conducting dielectric;
that is, we build a three-plate capacitor as follows:

P1 P2 P3
P1 P2 P3
P1 P2 P3
wwwwwwwP1 P2 P3wwwwww
P1 P2 P3
P1 P2 P3
P1 P2 P3

where "w" indicates a wire, and P2 is the "dielectric" plate. The
advantage of this scheme is that we can unambiguously talk about the
voltage on P2.

... the combination of insulator plus P2 makes a fine dielectric,
increasing the capacitance of the P1/P3 capacitor.

Actually, this is not correct. Suppose P2 is exactly in the middle.
You are comparing C1 of one capacitor (in which plates are separated
by d) with the equivalent capacitance C2 of two capacitors connected
in series. Each of these two has C=2*C1 (assuming d/2) and the effective
C2 is the same as C1. The equality of C1 and C2 is not limited to a
case in which P2 is exactly in the middle.

I stand by what I wrote. The standard procedure when putting dielectric
substances into a capacitor is to keep *constant* the distance between the
capacitor plates P1 and P3. I assumed all my readers knew that. Otherwise
the whole concept of dielectric constant goes out the window.

As the "metal dielectric" P2 fills more and more of the space between P1
and P3, the capacitance of the P1/P3 capacitor increases without bound,
justifying my claim that the metal has effectively an infinite dielectric
constant.

The viewpoint I have take is absolutely standard; see for instance _The
Feynman Lectures on Physics_ volume II, figures 10-2 and 10-3.

--- jsdÒ