A hollow metal sphere has inner radius a and outer radius b . The hollow sphere

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. (Answer is multiplied by Q/(pi*epsilon0*r^2) and does not depend on Q, pi,epsilon0, or r)

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

r?b. (Answer is multiplied by Q/(pi*epsilon0*r^2) and does not depend on Q, pi,epsilon0, or r)

d)How much charge is on the inside surface of the hollow sphere? (Answer is multiplied by Q and does not depend on Q)

e)How much charge is on the exterior surface? (Answer is multiplied by Q and does not depend on Q)

Explanation / Answer

"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

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