Re: Confused by a derivation.

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Now bc is confusewd;  see below

"Carl E. Mungan" wrote:

> John D's comments, as usual, strike to the heart of the matter. Just
> to summarize them in explicit detail, in case Ludwik or anyone else
> is still confused.
>
> Take a metal plate. Each side has area A. Put charge Q onto this
> conductor. Let sigma be defined as s = Q/A.
>
> Half the charge goes to either side:
>
> + + + + + +
> ===========
> + + + + + +
>
> Each side thus has charge density s/2. Compute the fields everywhere
> by superposing the fields (s/2)/(2*eps0) due to the infinite sheet
> charge on each side. The result is zero inside the plate and s/2*eps0
> outside each sheet. This is the standard textbook result for either
> an insulating or a conducting plate.
>
> Now bring a plate of the same dimensions with equal and opposite
> charge -Q nearby. Consequently, all of the charge on each plate
> redistributes to the internally facing surfaces:
>
> ===========
> +++++++++++
>
> -----------
> ===========
>
> The charged sides now have charge density +/-s. We again superpose
> the fields  (+/-s)/(2*eps0) due to each of these two infinite sheet
> charges. The result is s/eps0 between the two sheets and zero
> everywhere else (ie. in the bulk of each plate and outside the
> capacitor). This is again the standard textbook result.
>
> All clear? Carl

not really  Unless I'm missreading, you've changed the definition of G's
law.   with + & - charges on their respective plates the charges reside
on the insides (except for fringing), as you wrote.  Therefore, a G.
pillbox with flat sides in a conductor and between will enclose one
Q/area; the field will be (Q/area) / kappa sub zero. (no dielectric).
Not: "We again superpose the fields  (+/-s)/(2*eps0) due to each of
these two infinite sheet charges."

If one uses two insulating sheets with + & - charges (respectively)
evenly distributed.  A G pb enclosing both plates will "prove" no field
out side the plates.  Adding two G pb's, each enclosing one plate only,
give again (Q/area) / kappa sub zero.

Now my ?.  Why must one add the fields due to two insulating plates with
two G pb's, (very confortable w/ this) and not in the case of conducting
plates.





> --
> Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
>        U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
> mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/