Question

A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a. (a) Find the surface charge density on the inner surface and on the outer surface, (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and the outer surfaces? (c) Find the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).

Answer 1

Given: The sphere is uncharged metallic sphere.
Due to induction the charge induced at the inner surface = –Q, and that outer surface = +Q.
(a) Hence the surface charge density at inner and outer surfaces = charge/total surface area

(b) Again if another charge ‘q’ is added to the surface. We have inner surface charge density = – Q/4πa², because the added charge does not affect it. 

On the other hand the external surface charge density =  Q + q/4πa² as the ‘q’ gets added up. 

(c) For electric field let us assume an imaginary surface area inside the sphere at a distance ‘x’ from centre. This is same in both the cases as the ‘q’ in ineffective.