The problems states: An inverted hemispherical bowl of radius R carries a uniform surface charge density σ. Find the potential difference between the north pole and the center. I was able to do the problem and got the correct answer the book gives, which is (Rσ/2ε0)(√2 - 1). My professor, however asks that we do an assessment, or check, of our answer for every problem. This is where I am having troubles. I figured I could use Poisson's Equation to show that the Laplacian of the answer is -σ/ε0, but I can't seem to get this. Any other ideas?