Griffiths 4.15: A thick spherical shell of inner radius a and outer radius b is made up of dielectric material with a frozen in polarization. P = k / r in the r-hat direction. There is no free charge (why?). Find the electric field inside and out.
The Attempt at a Solution
I have the solution, but the only part that I don't understand is why the polarization is negative at r=a (pointing inwards, why not radially out like at b?). This may be trivial, but a thorough explanation would be helpful, and perhaps and generalization to other cases. Also they tell us there is no free charge, but could someone explain why physically? Thank you