Re: Electrostatic shielding

[John Denker <jsd@MONMOUTH.COM>]

At 09:09 PM 1/31/01 -0600, Lemmerhirt, Fred wrote:
> Suppose we start with the
> positive point charge at the center of the spherical conducting shell.  The
> shell has a uniformly distributed negative charge on its inner surface and a
> uniformly distributed positive charge on its outer surface.  Now when the
> point charge moves way off center, how do we know that only the negative
> charge on the inner surface redistributes itself to compensate?

The key idea here is that there are no fields inside the metal material
that makes up the shield.

I am assuming (as usual) the low-frequency limit, and assuming there are no
gaps in the shield.

To be more specific, imagine that the shield is a thick piece of
metal.  Its inside surface is denoted Si and its outside surface is denoted
So.  We can distinguish three types of charge:
 -- Charges in the outer region, strictly outside of So.
 -- Charges "on" the shield, between Si and So inclusive.
 -- Charges inside the inner region, strictly inside Si.

It may help to visualize "field lines", imperfect as those are.  Every
field line begins on a charge and ends on the opposite charge.  There are
no fields, and therefore no field lines, inside the metal (between Si and So).

By way of contradiction, let us temporarily hypothesize that a field line
somehow penetrates the metal.  For a charge Q in the inner region we would
have:

                 Si    So
                 |     |
        -Q=======|=====|=====================Q    (hypothetical only)
                 |     |
                  metal

Such a situation cannot persist, because the electrons in the metal would
immediately re-arrange themselves to cause the new, real, lasting
configuration:

                 Si    So
                 |     |
        -Q=======Q    -Q=====================Q     (real)
                 |     |
                  metal

Note that this involves creation and migration of a pair (Q, -Q) of charges
"on" the shield, with no change in the net charge "on" the shield.

Also note that the field lines end on the surfaces;  they do not penetrate
the metal in the real situation.

We can conclude the following:

1) Charges in the outer region induce charges on So and nowhere else.

2) Charges "on" the shield arrange themselves on So and nowhere else.

3) A charge Q inside the inner region induces a charge -Q on Si and a
charge +Q on So, and nothing else.

4) The foregoing three effects add linearly and independently.

5) Re-arranging the charge inside the inner region will re-arrange the
induced charge on Si, but will have no effect on the induced charge on So,
nor on the field in the outer region.

6) An observer in the outside region, outside So, cannot tell the
difference between a charge inside the inner region and a charge "on" the
shield.  The observer can determine the total of the total of "on-shield"
and "inner" charge, but cannot say anything about the arrangement of
charges anywhere inside of So.