2. (a) Consider a polarized sphere of radius R. The polarization is given by P =...

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2. (a) Consider a polarized sphere of radius R. The polarization is given by P = AVx2 + y² + z² î. Here f is the unit vector along the radial direction and A is a constant. Find all the volume and surface bound charges, p and op. Find the electric fields inside and outside the sphere. (b) Now consider a spherical shell with inner radius a and outer radius b. The space in a <r < b is filled with a dielectric material and the polarization is given by P r. Here B is a Va2+y²+z2 constant. Find all the volume and surface bound charges, p, and op. Find the electric fields in three regions r < a, a <r < b, and r > b. 2. (a) Consider a polarized sphere of radius R. The polarization is given by P = AVx2 + y² + z² î. Here f is the unit vector along the radial direction and A is a constant. Find all the volume and surface bound charges, p and op. Find the electric fields inside and outside the sphere. (b) Now consider a spherical shell with inner radius a and outer radius b. The space in a <r < b is filled with a dielectric material and the polarization is given by P r. Here B is a Va2+y²+z2 constant. Find all the volume and surface bound charges, p, and op. Find the electric fields in three regions r < a, a <r < b, and r > b.