(g) From part (f), what must be the charge on the outer surface of the hollow sphere? Qouter 1 A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric fields at all locations. (Assume Q is positive. Use the following as necessary: Q, ε 0, a, b, c and r. Do not substitute numerical values; use variables only.) Insulator Conductor (a) Find the charge contained within a sphere of radius r < a. qin = 1 (b) From this value, find the magnitude of the electric field for r < a. E = 1 (c) What charge is contained within a sphere of radius r when a < r < b? ain = 1 × (d) From this value, find the magnitude of the electric field for r when a < r < b. E = 1 (e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r? E = 1 (f) From this value, what must be the charge on the inner surface of the hollow sphere? Qinner = 1 ×

(g) From part (f), what must be the charge on the outer surface of the hollow sphere? Qouter 1 A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric fields at all locations. (Assume Q is positive. Use the following as necessary: Q, ε 0, a, b, c and r. Do not substitute numerical values; use variables only.) Insulator Conductor (a) Find the charge contained within a sphere of radius r < a. qin = 1 (b) From this value, find the magnitude of the electric field for r < a. E = 1 (c) What charge is contained within a sphere of radius r when a < r < b? ain = 1 × (d) From this value, find the magnitude of the electric field for r when a < r < b. E = 1 (e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r? E = 1 (f) From this value, what must be the charge on the inner surface of the hollow sphere? Qinner = 1 ×