A spherical conductor of radius R₁ is surrounded by a polarizable medium which extends from R₁ to R₂ with dielectric constant κ.

(a) The conductor has charge Q. Find E everywhere and confirm that the total polarization charge is zero.
(b) The conductor is grounded and the entire system is placed in a uniform electric field E₀. Find the electrostatic potential everywhere and determine how much charge is drawn up from ground to the conductor.