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Re: Electric Field Question



P.S.
It seems that two concentric shells with net charges +Q and +Q
(or -Q an -Q) represent a charged capacitor. Why not? There
is an electric field between the two equally charged electrodes.

Will the system be discharged by touching the electrodes
with a conducting rod, for example, by somebody sitting on the
surface of the smaller shell? It depends on what is meant by
"discharged." The rod will allow the positive charge to move
from the the smaller shell to the outer surface of the larger
shell. The field between the electrodes will disappear. The
inner shell will become neutral but the charge on the outer
shell will double. And somebody outside the system will continue
observing a constant E = k*(2*Q)/r^2. How would he know
that these processes occured inside?

A spherical capacitor with two equal charges of the same sign?
It would be confusing to call such setup a capacitor. What would
be a better name?" I would say that the word "capcitor" is
reserved for a setup with two equal charges of opposite sign.
Ludwik Kowalski

Tina asked what happens when charges [on concentric spheres]
have the same sign, for example, both positive. All textbooks show
how lines are distributed for two positive or two negative point
charges. Lines are like hands "saying don't come to me,I do not
like you." Does something like this happen for lines due to net
charges on two concentric spheres? Not at all.

In this case all field lines are radial and they point toward infinity.
Consider +Q on the smaller metallic sphere only. Charges are
distributed uniformly on its outer surface. They polarize the larger
metallic shell. Lines originating on the outer surface of the smaller
shell terminate on the inner surface of the larger shell. And lines
originating on the outer surface of the larger shell go to infinity.

Up to this point the larger shell was neutral. When a net charge
+Q is deposited on the larger shell it goes to its outer surface. This
creates additional lines radiating from the surface of this shell
toward infinity. (These additional line are the same as one would
have if the smaller shell had a zero net charge.) The E outside the
two spheres is the same as for a point charge of +2*Q.
Ludwik Kowalski

Rick Tarara wrote:

If q(a) and q(b) are equal in magnitude and opposite in sign--then yes,
outside the spheres the field is zero.

To see this:

a) Use Gauss' law with your surface outside both spheres. The NET enclosed
charge is zero hence the field is zero.

b) Look at the field lines that must start at + charges (or infinity) and
end at negative charges (or infinity). With an equal number of charges, you
have one line per set of + and - charge. All lines start and end between
the inner surface of the outer shell and the outer surface of the inner
shell. No field lines left over--so no external field.

If the magnitude of the charges are not the same, then (a) can calculate the
field, and (b) can help visualize the field.

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

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----- Original Message -----
From: "Tina Fanetti" <FanettT@QUEST.WITCC.CC.IA.US>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, February 05, 2002 11:58 AM
Subject: Electric Field Question

Okay, my students have stumped me.

Say you have a hollow metallic spherical shell of radius a with charge
q(a). Concentric to that is a hollow metallic spherical shell of radius b
with charge q(b).

Now we get what happens when the charges are the same sign.

Now what through me off is what if q(a) and q(b) have opposite signs.
What would the electric field be outside both spheres. I realize it won't
change the answer inside sphere a or inbetween the spheres. But will the
electric field outside the spheres be zero? I can't imagine they would
cancel out?

Thanks
Tina

Tina Fanetti
Physics Instructor
Western Iowa Technical Community College
4647 Stone Ave
Sioux City IA 51102
712-274-8733 ext 1429