Re: Electrostatic shielding

[William Beaty <billb@ESKIMO.COM>]

On Wed, 31 Jan 2001, Bernard G. Cleyet & Nancy Ann Seese wrote:

> The macroscopic answer is that charge is conserved, therefore, the same
> charge (amount and sign) that is inside is on the outside.  If the
> inside charge contacts the inside of the sphere it neutralizes the
> charge induced on the inside and leaves the outside charge unchanged.

> The lack of "communication" is true only in the static case.

And that's a key point.  It doesn't matter how slowly we place the charge
into the cage.  It could take centuries, yet the outside of the cage still
ends up with an alike charge of equal quantity to the charge placed inside
the cage (assuming that the cage is truely "floating" with no leakage
paths to other objects.)  If the metal prevents communication between
inside and outside, how can we understand this?

As the charge moves slowly from outside to inside, it remains in
"communication" with both surfaces of the cage!  The induced charge on the
inner and outer surface can redistribute itself as needed. However, once
the charge is entirely inside (and assuming that the hole in the cage is
very small,) the inner and outer surfaces are no longer in communication.
The charge on the outside of the cage can no longer "sense" the charged
object within.  The situation vaguely resembles the "charging" of a
two-plate capacitor, followed by removing it from the power supply!  Once
the charged object is inside, we can now briefly connect the outer surface
of the cage to ground, and the external surface charge will be removed (it
will spread to the earth,) yet this has no effects on anything inside
(well, if there was a spark, a bit of high-freq noise might penetrate.)

Does THAT solve the controversy?

Usually "static " and "pseudostatic" are the same, i.e. if we move things
very slowly (let it take centuries) then we can assume that the static
case is always in force.  "Pseudostatic" doesn't seem to work in the case
of inserting a charged object through a hole in a conductive shell.  The
charges rearrange themselves no matter how slowly we transport the object.
And the macroscopic "shielding effect" increases from zero to infinity as
the object moves from outside to inside.

> P.s. I'm rather certain the q inside the sphere will experience a (net)
> force if it's not in the center

I believe so.  Unlike a hollow shell of mass, the induced opposite charges
on the inner surface of the conductive cage will move adjacent to the
approaching charged object (it will see an "image charge" below the
surface, and experience a dipole attraction force when it's very near the
surface.)

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