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? What about if the sphere has a total charge Q on its inner and outer surfaces?