Chapter 6, Problem 53P

Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that

   $E=\frac{pr}{2{\epsilon }_0}$ $\left(r\le R\right);$

   $E=\frac{p{R}^2}{2{\epsilon }_{0}r}$ $\left(r\ge R\right).$