Question

A solid spherical conducting shell has inner radius a and outer radius 2a. At the center of the shell is located a point charge +Q. What must the excess charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

(A) –5Q

(B) +3Q

(C) –4Q

(D) +4Q

(E) –3Q

Answer 1

The correct option is: (A) –5Q

Explanation:

The charge density is Q/area which is Q/4πr2 so for the inner surface it is Qinner/4πa2 and for the outer surface it is Qouter/16πa2. For these to be equal Qouter must be 4Qinner. Because of the +Q charge inside, there is a charge of –Q induced on the inner surface, which means the outer surface must have charge –4Q. Thus the total charge on the shell is –5Q.