# Can an ungrounded conductive cavity provide electrostatic shielding?

This comes from Electromagnetic Fields and Waves by Lorrain et al, page 77 on a Hollow, ungrounded conductor enclosing a charged body:

The surface charge density at a given point on the outside surface of the conductor is independent of the distribution of Q in the cavity. It is the same as if the conductor were solid and carried a net charge Q.

1) I don't believe this. As I move +Q around the inside of the cavity, this will affect the distribution of $-Q$ on the inside surface, which must also affect $+Q$ on the outside surface to keep $E=0$ inside the cavity conductor.

Inversely, the field inside the cavity is independent of the field outside the conductor. The conductor then acts as an *electrostatic shield.

2) I don't believe this either for similar reasons. The external fields will affect the distribution of $+Q$ on the outer surface, which must affect the distribution of $-Q$ on the inner surface and therefore the electrostatic field inside the cavity, to maintain $E = 0$ inside the conductor.

So am I correct to disbelieve that an ungrounded conductive cavity can provide electrostatic shielding for the reasons 1. and 2. above?

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These are a little bit tricky and can be confusing, but no, standard E&M is correct on shielding.

1) Electric charges inside a conductor are shielded from the outside. One does this by giving the shield an equal and opposite charge. This charge will rearrange so as to eliminate the field inside the shield (which is conductive). Thus there will be no electric field in the conductor. And since the total assemblage, (shield plus charges) has zero charge, there is no field outside the shield.

2) First consider a solid conductor in the presence of an external charge. You agree that the conductor ends up with a surface charge which cancels the fields inside the shield (otherwise current would flow which is not a static situation). Now imagine hollowing out the conductor. Since the metal you're removing is entirely from regions where there is no electric field, you haven't changed anything. The interior hole will now have no electric field.

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You didn't answer my points in the question about the distribution of charge, but thanks anyway:) (1) In my example, there is a charge inside the cavity, so the total charge is Q. (2) There is an opposite charge on the inside surface of the interior hole to that on the surface. – Larry Harson Feb 1 '12 at 15:00
The question "does the conductor produce a field outside of itself?" is answered simply by "is there a net charge inside of the conductor?" That is, if the charge on the conductor cancels the charge inside it, there will be no net external charge. So for your example, there will be an external field, but its form will be different from that of the interior charge. – Carl Brannen Feb 2 '12 at 1:52

As I move +Q around the inside of the cavity, this will affect the distribution of −Q on the inside surface, which must also affect +Q on the outside surface to keep E=0 inside the cavity conductor.

The second "must" is wrong. The change in distribution of the -Q on the inside surface alone will cancel out the electric field generated by the cavity charge +Q out of the inside surface.

The external fields will affect the distribution of +Q on the outer surface, which must affect the distribution of −Q on the inner surface and therefore the electrostatic field inside the cavity, to maintain E=0 inside the conductor.

This "must" is wrong too. The total electric field of cavity charges and the inside surface charges is zero in the area outside of the inside surface, and the total electric field of outside electric field and the outside surface charges is zero inside the outside surface. The result is a net zero field in the intersection of these two area, namely, the area between the inside surface and the outside surface, a.k.a the conductor. These two parts change independently.

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