A spherical shell of inner radius a and outer radius b is made of dielectric material withfrozen polarization

P $=($k$/$r$)$ In the radial direction where k is a constant with the appropriate units and r is the distance from the center of the sphere. Calculate the electric field throughout space with the following two methods

a$)$ Calculate the induced charge densities and use Gauss's law for the electric field

b$)$Use Gauss's law for the displacement vector and from this determinethe electric field