Walker, Halliday & Resnick — Gauss' Law: Problem 32

32 Figure 23-38a shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure 23-38b gives the radial component E of the electric field versus radial distance r from the common axis, and $E_s = 6.0 \times 10^3$ N/C. What is the shell’s linear charge density?