Problem #1 (40 points): PHY 3323 Exam II A metal sphere of radius a carries a charge Q. It is surrounded, out to radius b, by linear dielectric material of relative permittivity 6. (a) (10 points) Find the electric field E in the regions r> b,a <r<b and r<a; (b) (10 points) Find polarization vector P and the bound charge densigy ps in the region a <r<b; (c) (10 points) Find the bound surface charge density σ, and total bound charge Q, at ra and r = b. (d) (10 points) Calculate the potential V for r > b, a <r< band r<a. (Hint: V-P-(P)+rsine de 1 (sin &P)+ rsine de a b