2) Consider a very long cylinder with a radius a, having a permanent polarization density: P = Po (x + y) a a) Find the bound surface and volue charge densities. Write the electric potential inside and outside without determining the coefficients. b) Determine the coefficients using boundary conditions. c) If the same cylinder is made of a linear dielectric material and is inside a uniform electric field, find the polarization density within the cylinder in terms of the applied electric field ( = E). 3) C) A spherical capacitor is half-filled with dielectric material (let the relative permittivity be 7, refer to the figure. Metal spheres have the same amount of Q charges and are isolated. Determine the capacitance of the system. Find the charge density on the outer metal for each region.