Re: metal model of dielectric

["John S. Denker" <jsd@MONMOUTH.COM>]

At 01:29 PM 1/31/99 +0100, Ludwik Kowalski  wrote:
> "John S. Denker" wrote:
>
> > 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 the claim that the metal has effectively an infinite dielectric
constant.

This "metal model dielectric" is standard physics and standard pedagogy;
see for instance _The Feynman Lectures on Physics_ volume II, figures 10-2
and 10-3.

--- jsd