1. The problem statement, all variables and given/known data This question refers to Griffiths E and M book. An uncharged conducting sphere of radius a is coated with a thick insulating shell (dielectric constant \epsilon_r) out to radius b. This object is now placed in an otherwise uniform electric field [itex]\bfE_0[/itex]. Find the electric field in the insulator. 2. Relevant equations 3. The attempt at a solution So, I wrote down the boundary conditions and I can't seem to find solutions that match them. Since the electric field vanishes inside of a conductor. The solution inside the dielectric must be constant at r=a. Its derivative must vanish at r=a since there is no free charge on that surface. I don't see how we can obtain that unless the potential is constant inside the conductor. But then how can you meet the boundary conditions for the r=b where the potential is not constant!