Question

Problem A solid conducting sphere of radius a is at the center of a hollow conducting sphere of inner radius b and outer radius c. The solid sphere carries a charge q > 0, the outer sphere carries an excess charge of -3q on its outer surface. derive expressions for the magnitude of the electric field in the following regions Final answers not given.]

Answer 1

a) Field inside the conductor is zero

b) Field outside the solid conductor is due to +q

c) Field inside the conducting shell is zero.

d) +q charge on the solid sphere induces a charge of -q on the interior of the outer sphere. This induces a charge of +q on the exterior of the outer sphere.So the total charge on the exterior surface of the outer sphere is -3q+q=-2q. Hence the electric field outside is

The magnitude is

e) Surface charge density at r = a is

f) +q charge on the solid sphere induces a charge of -q on the interior of the outer sphere. Hence the surface charge density at r = b is

g) The charge at r = c is 2q as explained above. Hence the charge density at r = c is