= Electric field of a uniformly charged infinite cylinder
{title2=$\mathbf E_{\rm in}=\rho\mathbf r/(2\epsilon_0)$}
For an infinite insulating cylinder of <radius> $R$ and uniform fixed <charge density> $\rho$, <Gauss's law> gives interior <electric field> $\rho\mathbf r/(2\epsilon_0)$ and exterior <electric field> $\rho R^2\mathbf r/(2\epsilon_0|\mathbf r|^2)$, 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.
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