Problem 4: Spherical charge distribution Griffiths (example 3.9) derives the exact potential V(r, 0) everywhere outside a spherical shell of radius R which has a surface charge distribution o( R, 0) = k cos(0). (a) Calculate the dipole moment of this object, and also the total charge on this object. (b) Use the methods of the multipole expansion (Griffiths p. 151) to find an approximate form for the potential far from the sphere. You can stop with the leading nonzero term. Now compare with Griffiths' exact formula from the earlier example. What does this tell you about the quadrupole moment (and higher moments) of this surface charge distribution