Electric Field in a shell

Question

My current understanding is:

• Electric field inside a metal shell = 0 since the net charge enclosed is zero.

• Electric field inside a conductor =0, but the electric field in a cavity of the conductor can be calculated.

The question I faced states that:

Figure 3: Spherical conducting shell with inner radius a and outer radius b. Point charge q1 is located at the centre of the hollow shell. In Figure 3 the central point charge is q1 = +2Q and there is a net negative charge -Q on the spherical conducting shell. Which of the following statements about the electric field magnitude E is true?

a) E is Q/(4(pi)(Epsilon 0)r^2) for all r > b.

b) E is zero for all r < b.

Shouldn't these both be true then?

Answer 1

The conductor is hollow. You are correct that there is no electric field within the conductor, but that does not mean that there is no electric field in the cavity. Approach the problem from this direction:

1. You know that there must not be any electric field within the conductor.
2. There is a charge of $2Q$ inside the hollow conductor.
3. In order to make (1) work with (2), charges will have to move through the conductor and emerge on a surface. A particular amount of charge needs to emerge on the inner surface, that with radius $a$. This surface charge has to exactly neutralize the charge in the middle of the cavity.
4. Charges are conserved. The charges on the inner surface have to come from somewhere. Again look at (1), they cannot come from the interior. They must come from the outer surface. The charge on the outside is given in this problem, so we already know how much charge there is on the outside.
5. For the far field ($r > b$), remember that with (3) we have exactly canceled the electric field within the conductor, so does the field of the inner charge reach outside ($r > b$)?

From this you should be able to conclude that only one answer is correct and which one it is.