Using the method of images, discuss the problem of a point charge q inside a hollow, grounded, conducting sphere of inner radius a. Find
(a) the potential inside the sphere;
(b) the induced surface-charge density;
(c) the magnitude and direction of the force acting on q.
(d) Is there any change in the solution if the sphere is kept at a fixed potential V? If the sphere has a total charge Q on its inner and outer surfaces?