Chapter 22, Problem 38P

(II) A very long solid nonconducting cylinder of radius R₁ is uniformly charged with a charge density ρ_E. It is surrounded by a concentric cylindrical tube of inner radius R₂ and outer radius R₃ as shown in Fig. 22–36, and it too carries a uniform charge density ρ_E. Determine the electric field as a function of the distance R from the center of the cylinders for (a) 0 < R < R₁, (b) R₁ < R < R₂, (c) R₂ < R < R₃, and (d) R > R₃. (e) If ρ_E = 15 μC/m³ and $R_1=\frac{1}{2}{R}_2=\frac{1}{3}{R}_3=5.0\text{cm}$, plot E as a function of R from R = 0 to R = 20.0 cm. Assume the cylinders are very long compared to R₃.

FIGURE 22–36 Problem 38.