Re: Confused by a derivation.

[Bob Sciamanda <trebor@VELOCITY.NET>]

Michael, I'm not sure what you require for the field calculation (the
field in terms of what?). But you can get the field in terms of the charge
density on one of the inner plates by the simple Gauss' law application to
which you refer.  You said:

> This means in order to find the E inside a capacitor you have to have
one
> end of the gaussian surface inside the gap . . .  The location of the
far end would either be inside one plate
> or outside the capacitor.  At this point you need additional
information.
> If the far end is inside a plate then you need to know all the charge is
on
> the inner surface of that plate.

You do not need to know that all of the charge is on the inner surface.
Your Gaussian cylinder, with the far end inside one plate gives (for the
net field, due to everything, wherever it is) E =  sigma/epsilon,  where
sigma is the charge density on an inside surface, ie  the total charge on
only that inside surface divided by the area of only that inside surface.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Michael Edmiston" <edmiston@BLUFFTON.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, February 04, 2002 9:39 PM
Subject: Re: Confused by a derivation.


> Okay.  It took me a while... but now I get what Bob Sciamanda did to get
> some of the algebra I said I didn't understand.  He is using the
> superposition principle to find fields in various places in and around
the
> parallel-plate capacitor.  I thought he was using Gauss' Law.
>
> Of course the reason I thought he was using Gauss' Law was because
that's
> the way Ludwick posed the original question, and that's the way I wrote
my
> original response to Ludwick.  I said, and I maintain, solving for the
field
> inside a capacitor using Gauss' Law (and nothing else) is not obvious.
>
> In my understanding, using the superposition principle is not using
Gauss'
> Law.  Using GL to find the field at a spot means (1) knowing what the
net
> charge is inside an appropriate gaussian surface, (2) having the point
of
> interest reside at an appropriate place on some portion of that gaussian
> surface, (3) finding the flux through that portion of the surface using
> Gauss' Law, (4) using the flux and area and symmetry to deduce the
electric
> field at that point.
>
> This means in order to find the E inside a capacitor you have to have
one
> end of the gaussian surface inside the gap.  A wise choice of surface
would
> dictate this portion of the surface is flat and parallel to the plates.
> Another wise choice would make the other parts of the surface
perpendicular
> to the plates except for the far end.  The far end also be flat and
parallel
> to the plates.  The location of the far end would either be inside one
plate
> or outside the capacitor.  At this point you need additional
information.
> If the far end is inside a plate then you need to know all the charge is
on
> the inner surface of that plate.  If the far end is outside the
capacitor
> then you need to know the field there is zero.  If you don't know one of
> these things you can't calculate the field in the capacitor gap using
this
> method, i.e. using Gauss' Law.  And... I don't see how you can show
either
> of these things using Gauss' Law.  Yes, you can show these using the
> superposition principle.  But I thought that was not allowed.  I thought
the
> question was, "Can you calculate the field using Gauss' Law?"
>
>
> Michael D. Edmiston, Ph.D.                      Phone/voice-mail:
419-358-3270
> Professor of Chemistry & Physics        FAX:
419-358-3323
> Chairman, Science Department            E-Mail
edmiston@bluffton.edu
> Bluffton College
> 280 West College Avenue
> Bluffton, OH 45817