4. A spherical shell of radius R has a nonuniform potential V0 (:9) = 16 cos2 (:9), where k is a constant and I9 is the polar angle. (a) What is the general solution V039) to Laplace's equation for the region outside the sphere, before applying boundary conditions at r = R? Take the reference potential to be zero at innity and simplify as much as possible. (b) Express the given surface potential V009) in terms of Legendre poly nomials (Table 3.1 in the textbook may be helpful). (c) Apply the boundary condition at the sphere surface and solve for V('r, 6) outside the sphere.