(non-conducting, of course) spherical shell has radiusaand is centered onthe origin.

(non-conducting, of course) spherical shell has radiusaand is centered onthe origin. the upper half (z > 0 orθ < π2) has a chargequniformly distributed on itssurface, and the lower half has a charge−quniformly distributed on its surface. find thepotential both inside and outside the sphere, up to fifth order in cosθ. hint: think aboutthe symmetry of the boundary conditions here with respect to the ‘equator’ (θ=π/2) –can you rule out any legendre polynomials from appearing in your solution?