Re: Confused by a derivation.

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

Ludwik Kowalski wrote:
> But two layers of sigma in a capacitor reside on metallic
      ^^^
> plates and each plate produces E"=sigma/eps_o.


The highlighted factor of "two" is the problem.

To say it another way, do _not_ try to think in terms of
thin plates.  Make sure your plate is thick enough to
have its front surface distinct from its back surface.
Even if the area and charge on the "rim" of the plate
is negligible, you need a way to keep track of the
front-surface charge as distinct from the back-surface
charge.

1) For an isolated single plate with _frontal_ area A,
if you put a charge Q on the plate, the charge density
will be Q/2A, because the _total_ area is 2A not A.

2) If you then make a similar plate be one plate of a
parallel-plate capacitor, all the charge will run
around to the inside face.  You will have a charge
of Q/A on one face and zero on the other face.

The gaussian integral correctly reports the total
charge in either case.