"A sphere of homogeneous linear dielectric material is palcced in an otherwise uniform electric field E. Find the electric field inside the sphere." Griffiths uses separation of variables to solve laplace's equation in the interior of the sphere. I have two questions. (1) How can you try to solve laplace's equation? isn't there bound charge in the dielectric (so the charge isn't 0?) laplace's equation can only be solved in regions where the charge is zero, right? or is that only free charge? (2) Why can't we use gauss's law for dielectrics (integral of the displacement flux equals the enclosed free charge) to find the field? is it because there is no free charge?