(a) Let (R, , ) be specified values of the electrostatic potential on the surface of a sphere. Show that the general form of an

(a) Let ϕ(R, θ, φ) be specified values of the electrostatic potential on the surface of a sphere. Show that the general form of an exterior, spherical multipole expansion implies that

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).

Use the results of part (a) to find the asymptotic (r →∞) form of the potential produced by the shell.

(r) = {+1 (3) () | d(R, )Y#m () r > R.