Re: Electrostatic shielding

[Bob Sciamanda <trebor@VELOCITY.NET>]

One must prove that, regardless of the geometry, the imposed fixed charge
and the inside surface charge together produce a net E=0 throughout the
conducting material - **without the help or hindrance of the outside surface
charge**.  If this is so, then the outer surface charge must always take
that unique configuration which, by itself, contributes E=0 in the
conducting material.

But the first statement must be proven, not merely stated.  I have not yet
seen a rigorous proof of that statement - though I believe it is so.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
www.velocity.net/~trebor
----- Original Message -----
From: "John Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, February 01, 2001 7:50 AM
Subject: Re: Electrostatic shielding


> At 01:56 AM 2/1/01 -0500, Bob Sciamanda wrote:
>
> > 1) The charges will settle to an arrangement in which the conducting
> > material is an equipotential volume (E=0) under the combined effects of
the
> > three items, the imposed charge, the inner surface charge and the outer
> > surface charge.
>
> That's narrowly true, but not very useful, since the metal can freely make
> essentially infinite electron/hole pairs and redistribute them, thereby
> changing the inner-surface charge and the outer-surface charge;  only the
> sum of those two quantities is conserved.
>
> > 2) In the case of the single imposed charge centered inside a hollow,
> > conducting sphere the imposed central charge and the inner surface charge
> > alone accomplish this as a pair, and the outer surface charge also does
so
> > (contributes zero E and constant V throughout the conducting material).
>
> I don't know what that is trying to say.  I'll ignore it and proceed.
>
> > 3) Two questions:
> >
> > a) If the imposed charge moves off center will the inner surface charge
> > still settle so that it and the imposed charge still (as a pair)
contribute
> > zero E in the conducting material.
>
> Yes.  The key idea is that there is no field inside the material.  The
> mobile charges guarantee it.  At DC the conductor is an equipotential
> throughout its bulk.
>
> >   If so, the outer surface charge must
> > still contribute zero E (constant V) and so will not be re=arranged.
>
> Right.
>
> > b) If a) is so for the sphere, is it true for the generally shaped hollow
> > conductor enclosing a fixed imposed charge.
>
> Right.
>
> ==============================================================
>
> Observers on the outside cannot tell the difference between
>
>
>                  Si    So
>                   |     |
>                   |     |
>          -Q=======Q    -Q=====================Q     (real)
>                   |     |
>                   |     |
>                    metal
>
> and
>
>                  Si    So
>                   |     |
>          -Q=======Q     |
>                   |    -Q=====================Q     (real)
>                   |     |
>                   |     |
>                    metal
>
> and
>
>                  Si    So
>                   |     |
>                   |     |
>                   |    -Q=====================Q     (real)
>          -Q=======Q     |
>                   |     |
>                    metal
>
>
> Remember that the -Q on the outer surface will move in response to
electric
> fields, and (in the DC limit) electric fields only, and there is no
> electric field inside the material.