Re: Electrostatic shielding [long!]

[William Beaty <billb@ESKIMO.COM>]

On Thu, 1 Feb 2001, John Mallinckrodt wrote:

> > 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.
>
> I think Bob's question is at the very heart of the confusion here.
> Proving this isn't easy!  Fortunately it's already been done for
> us in the form of the "existence-uniqueness theorem" that applies
> to solutions of Laplace's equation.

Once the charged object is inside the faraday cage, the charge on the
outside has no connections with the inside.  Yet how did that charge on
the outside come to be there?  The history of events reveals that it was
created by the act of inserting the charged object into the cage!
Charge-separation arose when the charged object went through the hole.
Since charge is conserved, the only way to get some charge into the cage
is to pass it through the surface (through a hole.)

If we only look at the final state of the system, we can honestly say that
the charge on the outside of the cage has nothing to do with the charged
object found inside.  But if we watch a charged object being inserted and
withdrawn from a faraday cage, we can observe the outside surface charge
"magically" appearing and vanishing.  Obviously it was caused by the
charged object.  But once the charge-separation has been set up (and the
charged object is totally within the cage,)  the external surface charge
is no longer BEING created by the charged object.  This doesn't alter the
fact that the surface charge outside the cage WAS created by the act of
inserting the charged object through the hole.

> Conclusion:  The *only* way to affect the charge on the outer
> surface or the fields outside the conductor is to change the *net*
> charge inside the cavity.

I agree.  Unfortunately, in order to get some *net* charge into a Faraday
cage, we must *change* the net charge inside the cavity, and that affects
both the charge on the outer surface and the fields outside.

Wait a minute.  We could also assemble the faraday cage around the charged
object (using neutral cage walls, of course.)  A similar situation would
occur: the act of assembling the cage would cause a charge-separation, and
we'd again end up with equal and opposite quantities of charge on the
inner and outer surfaces of the cage.

I guess we need to imagine that the cage and its contained object was
created during the big bang.  That way the charged object within the cage
need never pass through its boundaries, and it has nothing at all to do
with the charges on the outside surface of the cage!  :)

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William J. Beaty                                  SCIENCE HOBBYIST website
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