Re: Conserving Q/Faraday

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

"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.
>
> Metal has effectively an infinite dielectric constant, but as long as P2 is
> separated from P1 and P3 by an air gap (or other insulator), the
> combination of insulator plus P2 makes a fine dielectric, ...
>
> 1.1) The first thing to notice is that even if there were a huge net Q on
> P2, it would have no effect on the operation of the P1/P2 capacitor, which
> could still be treated as a two-terminal device, with no change in
> capacitance.

I like this idea of treating a metallic P2 as if it were a dielectric
plate. By induction two "layers of bound charges" appear in P2 when E>0.
But only dielectric materials in which molecules are not permanently
polarized can be modeled in this way. The macroscopic dipole moment of
P2 becomes zero as soon as E becomes zero. In many materials that moment
does not become zero after the field is off, unless the temperature is
high enough to destroy the order on molecular orientations rapidly.

> , ... 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.

My inclination would be to say that the "relative dielectric constant"
of P2 is one; because C1=C2. What kind of evidence support statement
that "metal has effectively an infinite dielectric constant"? We are
both idealizing by ignoring a finite leakage current.

Ludwik Kowalski