Question

A hollow metal sphere has inner radius a and outer radius b. The hollow sphere has charge +2 Q. A point charge + Q sits at the center of the hollow sphere.

A)Determine the magnitude of the electric field in the region

r?a. (The correct answer does not depend on:

Q, ??0, r.)

B) Determine the magnitude of the electric field in the region

a<r<b

C)Determine the magnitude of the electric field in the region

r?b

D)How much charge is on the inside surface of the hollow sphere?

E)How much charge is on the exterior surface?

Answer 1

"Determine the magnitude of the electric field in the region r<a."
From Gauss' Law:
E(4?r^2) = +Q/?o
E = +Q/[(4??o)r^2]

"Determine the magnitude of the electric field in the region a<r<b"
The electric field inside of a conductor (with no current) is zero.

"Determine the magnitude of the electric field in the region r>b."
Again, from Gauss' Law:
E(4?r^2) = +3Q/?o
E = +3Q/[(4??o)r^2]

"How much charge is on the inside surface of the hollow sphere?"
For the electric field in the region a<r<b to be zero, the charge on this surface would be equal in magnitude, but opposite in sign to the point charge in the center: -Q.

"How much charge is on the exterior surface?"
If the conductor has a total charge of +2Q and the charge on the inner surface is -Q, the charge on the outside surface would be: +2Q - (-Q) = +3Q