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