This is not actually a homework question, just something I am wondering about. A specified charge density dependent on /theta is glued over the surface of a spherical shell and you are asked to find the potential inside and outside the sphere, which is done in the example using separation of variables. My question is - why cant you use Gauss's Law to find E and then find V from it (I see that wouldnt give the right answer, but why?)? Is it because the charge density depends on the angle? So Gauss's Law can only be used when the only dependence in the problem is on the radius?