Re: Confused by a derivation.

["Carl E. Mungan" <mungan@USNA.EDU>]

>  > 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.

But that IS s/eps0. Okay? As John D said, you can do superposition or
you can do Gauss' law and both methods give the same answer.

> It is not at all obvious that the field
>     due to two isolated planes of charge is the same as the
>     field due to charges residing on conducting plates.

But it IS so (neglecting fringe fields and charge pile-up on the
sharp corners at the edges). Whether the plates are conducting or
insulating is a red herring. Put +Q and -Q on two conducting plates.
The field in-between will be s/eps0. Now repeat for two insulating
plates (where you manually spread the charge out uniformly over the
surfaces - doesn't matter whether you do it only on one side or
both). You get the same field for conductors or insulators.

> The problem is that you cannot get an isolated plate to look like one
> component of a parallel pair (without an external E-field).  <snip>
> The field inside the conductor is not zero 'because the
> fields cancel', but 'because there are no lines there at all'.

I consider this to be mere semantics. I can say they cancel, you can
say there are none. We're both right, that's the beauty of linear
superposition. Carl
--
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/