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Re: Confused by a derivation.



Ludwik Kowalski wrote:

I am not very happy; perhaps somebody else will come
with an acceptable derivation.

I don't understand what there is to be unhappy about.

1) There is a slightly unfortunate ambiguity in the definition
of area: If you buy some aluminum foil that is 2 feet wide
and 25 feet long, you've got 50 square feet of aluminum foil.
That's enough to cover 50 square feet of real estate. But if
you want to paint it (both sides) you need to buy 100 square
feet worth of paint, so in this unusual sense your foil has
100 (not 50) square feet of "area" -- but when talking about
the two-sided area of thin objects you must be super-explicit
that you are referring to the two-sided area.

2) Every field line ends on a charge.

2a) For one plate of a parallel-plate capacitor, all the
field lines go out one side. This is required by overall
charge neutrality (we're assuming the capacitor is being
operated as a 2-terminal device in accordance with
Kerchhoff's "law") so it remains true even for non-flat
capacitors (e.g. a coaxial cylindrical capacitor).

2b) For a single isolated flat plate, half the lines go
out one side and half go out the other. This should be
obvious by symmetry for a flat plate. It's not obvious
(and not true :-) for non-flat plates.

The maximum field (per unit charge) is 2x greater in
case (2a) than in case (2b). I don't see a problem here.

If somebody sees a problem, please explain.