Question

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, ε₀ , a, b, c and r. Do not substitute numerical values; use variables only.) 

(a) Find the charge contained within a sphere of radius r < a. 

(b) From this value, find the magnitude of the electric field for r < a. 

(c) What charge is contained within a sphere of radius r when a < r < b? 

(d) From this value, find the magnitude of the electric field for r when a < r < b. 

(e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r? 

(f) From this value, what must be the charge on the inner surface of the hollow sphere? 

(g) From part (f), what must be the charge on the outer surface of the hollow sphere? 

(h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density? 

• surface a 

• surface b 

• surface c

Answer 1