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Re: Electrostatics problem



Here is one approach:

Let Q(1) and Q(2) be the net charges put on the two conductors. Suppose
that they are both large parallel-plate conductors, and the surface charge
density is taken to be uniform on all four surfaces of the two conductors.

Then, ignoring fringe effects at the edges, the electric field produced by
any one of the four plates is perpendicular to the surfaces. Further, the
field produced by any one of the four surfaces has constant magnitude, no
matter what is the distance of the field point to the surface. (This last
statement assumes infinite size dimensions for each plate. It follows
from the fact that the field lines cannot terminate, unless they reach a
charged body.)

We have four unknowns - the total charge on the inner and outer surface of
each plate. But the condition that the field be zero inside each plate
gives two requirements on the four quantities. They are these: The outer
charge on plate #1 (and also on plate #2) is the sum of the other three
charges. Also, the outer and inner charges on each plate must add up to
known total charge on the particular plate.

The only solution to these four conditions is that the two outer charges
are the same, and are each equal to the arithmetic average of Q(1) and
Q(2). The two inner charges have opposite sign, relative to each other.
Precisely, the inner charge on plate #1 is [Q(1) - Q(2)]/2.

Note that the two results cited by Ken Fox are consistent with this.

Allen Miller
Syracuse University
Physics Department

On Wed, 24 Feb 1999, Ken Fox wrote:

I just spent a short time wrestling with this question with one of my more
intuitive AP Physics student. I am stuck.

Given two conducting metal parallel plates, as an air capacitor. If we
place equal
charges of opposite sign on each plate, we would expect to find the charge
on the inner facing surfaces. If the signs are alike, the charges would
migrate to the outer surfaces. So far so good?

Is there a clear way ( I cannot think of it) to determine the charge
distribution if the two plates are charged unequally. We tried looking at
potentials and thinking that the final potentials will tend to a minimum
but found it hard to write any meaningful expressions for that.


Any help would be appreciated.

Ken Fox
Smoky Hill High School
16100 Smoky Hill Rd
Aurora,CO 80015
303-693-1700(w)
303-850-7537(H)
kfox@stega.smoky.org