Problem No 6 There is a solid metal sphere of radius $R$, which is cut into two parts along a plane in such a way that the outer surface of the smaller part of the sphere is $\pi R^2$. The cut surfaces are coated with a negligibly thin insulating layer, and the two parts are put together so that the original shape of the sphere is restored. Initially the sphere is electrically neutral. Then the smaller part of the sphere is given a positive electric charge $+Q$; the larger part of the sphere remains neutral. Find (a) the charge distribution along the sphere; (b) the electrostatic interaction force between the two pieces of the sphere; (c) the electrostatic energy of the sphere.   Acknowledgment: This problem is contributed by Gyula Honyek.