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Re: Confused by a derivation.



I said:
I agree it is tricky in that if you try this approach but take Q1=Q and
Q2
= -Q at the onset, the algebra encounters an indeterminacy

I now think this conclusion was due to an algebraic error on my part. I
retract this statement. If you're careful I think it works out even if you
take equal and opposite charges on the plates at the outset (it may depend
on your algebraic manipulations).

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Bob Sciamanda" <trebor@VELOCITY.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, February 04, 2002 1:10 PM
Subject: Re: Confused by a derivation.


From: "Michael Edmiston" <edmiston@BLUFFTON.EDU>

. . .. Given a parallel plate
capacitor and using nothing but Gauss' Law, can you calculate the
field
inside the gap. If so, what assumptions are you making?

Do the problem of two parallel conducting sheets carrying total charge
Q1
and Q2, arbitray choices.
Let the Q1 sheet be left of the Q2 sheet.
Let the four surface charge layers be, from left to right: q1 q2 q3 q4 .

We use a Gauss' law result that the field of a single sheet is
everywhere
sigma/2epsilon

Then we force the net field in each conductor to zero and get:

q1 -q2 -q3 -q4 = 0 and
q1 +q2 +q3 -q4 =0

We also have
q1 +q2 = Q1 and
q3 +q4 = Q2

The above 4 equations yield (check my algebra!):
q1 = q4 = (Q1 + Q2)/2 and
q2 = -q3 = (Q1 - Q2)/2

For the case Q1 = - Q2 this says all charge goes to the inside surfaces.

I agree it is tricky in that if you try this approach but take Q1=Q and
Q2
= -Q at the onset, the algebra encounters an indeterminacy.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor