 Electric field of a uniformly charged infinite cylinder

For an infinite insulating cylinder of radius $R$ and uniform fixed charge density $\rho$, Gauss's law gives interior electric field $\rho \mathbf{r}/(2{ϵ}_0)$ and exterior electric field $\rho R^2\mathbf{r}/(2{ϵ}_0|\mathbf{r}{|}^2)$, where $\mathbf{r}$ is transverse displacement from its axis. The electric field is continuous at $|\mathbf{r}|=R$ when there is no separate surface charge density. The interior linear dependence makes displaced-cylinder superposition particularly simple.