Exterior Multipoles for a Specied Potential on a Sphere (a) Let go(R, 6, ) be specied values of the electrostatic potential on the surface of a sphere. Show that the general form of an exterior, spherical multipole expansion implies that 00 8 R 5+1 90(1') = Z Z (7) ng(52)fd9'go(R,Q')Y;1(S2') r > R. (:0 m= (b) The eight octants of a spherical shell are maintained at alternating electrostatic potentials :|:V as shown below in perspective View (a) and looking down the z-axis from above in (b). h h W \"V (a) ('3) Use the results of part (a) to nd the asymptotic (r > 00) form of the potential produced by the shell. Z