1. The problem statement, all variables and given/known data Find the potential in the interior of a sphere of unit radius when the potential on the surface f(θ)=cos^2(θ). 2. Relevant equations 3. The attempt at a solution I think the correct procedure is to apply uniqueness theorem.We know when the potential at every point of the surface is given,and the potential in that region obeys Laplace's (Here, Poisson'sequation),the potential function is unique. So,I think it would be the same inside the sphere. Please check if it is correct.