Find the electrostatic potential outside a conducting sphere of radius a placed in an originally uniform electric field, and maintained at zero potential. Hint: Let the original field E be in the negative z direction so that E=−E0k. Then since E=−∇Φ, where Φ is the potential, we have Φ=E0z=E0rcosθ (Verify this!) for the original potential. You then want a solution of Laplace's equation ∇2u=0 which is zero at r=a and becomes u∼Φ for large r (that is, far away from the sphere). Select the solutions of Laplace's equation in spherical coordinates which have the right θ and ϕ dependence (there are just two such solutions) and find the combination which reduces to zero for r=a.