Laplace equation in spherical coordinates with some symmetry given a sphere with the radius r and the potential on its surface specified by vo k sin2 (1) where k is a constant and 0 is the polar angle. a) which symmetry does the potential obey? calculate the potential inside and outside the sphere the sphere b) calculate the surface charge density o(0) on hints use the ansatz for the symmetry which is derived in the lectures or from griffths chapter 3. use the boundary conditions to simplify the expression, i. e. get rid of some terms compare the coefficients to get the unknown coefficients using the ansatz and the boundary condition