6.3 Exercise 18

Charge is distributed uniformly with a density $\rho$ 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

$\begin{matrix} \\ \\ E = \frac{\rho r}{2 \epsilon_{0}} & & & \left(r \leq R\right) ; \\ E = \frac{\rho R^{2}}{2 \epsilon_{0} r} & & & \left(r \geq R\right) .\end{matrix}$