Chapter 22 Problem 38

Problem

Charged concentric rods

A very long solid nonconducting cylinder of radius $R_{1}$ is uniformly charged with a charge density $\rho _{e}$. It is surrounded by a concentric cylindrical tube of inner radius $R_{2}$ and outer radius $R_{3}$, and it too carries a uniform charge density $\rho _{e}$ Determine the electric field as a function of the distance R from the center of the cylinders for

(a) $0<R<R_{1}$

(b) $R_{1}<R<R_{2}$

(c) $R_{2}<R<R_{3}$

(d) $R>R_{3}$

plot $E$ as a function of $R$ from $R=0$ to $R=20$cm Assume the cylinders are very long compared to $R_{3}$.