A spherical capacitor consists of a conducting sphere of radius a and a concentric conducting spherical shell of radius b (a < b). The inner sphere was charged with a charge +Q & the outer shell was kept at zero potential. The space between the two conductors was filled with a nonuniform dielectric given by =₀ / 1+Kr Here, K is a constant.

a) Find the displacement & electric field between the two conductors.

b) Find the capacitance C of the modified capacitor.

c) Find the polarization & the bound charges.