Consider a solid insulating sphere of radius R that is coated with an electrical conductor of thickness d < R as shown below. The insulating sphere has a charge +4Q uniformly distributed throughout its volume. The conducting layer has a total charge -2Q on it. d P1 P2 P3 +4Q -20 Insulating sphere with conducting coating (a) What is the volume charge density p in the insulating sphere? Express your answer in terms of R and Q. (b) Use Gauss's law to find the electric field vector E, at the point P at position z = -R/2 on the x-axis as shown in the figure. Be sure your answer makes clear both the direction and magnitude of E. You may express your answer either in terms of p or Q. (c) Describe the distribution of charge in the conducting layer. Be sure to specify how much total charge is on its inner surface, how much charge is inside it (volume charge density), and how much total charge is on its outer surface. (d) What is the electric field vector , at the point P, at position a = R+d/2 on the x-axis? (e) What is the electric field vector E, at the point Ps at position r = 3R on the x-axis?