Outside of the cylinder (\(r>R\)), the total charge enclosed is the total charge on a length, \(L\), of the cylinder, which has a volume, \(\pi R^2 L\): \[\begin{aligned} Q^{enc}=\rho \pi R^2 L\end{al...Outside of the cylinder (\(r>R\)), the total charge enclosed is the total charge on a length, \(L\), of the cylinder, which has a volume, \(\pi R^2 L\): \[\begin{aligned} Q^{enc}=\rho \pi R^2 L\end{aligned}\] Thus, applying Gauss’ Law outside the cylinder, gives the electric field for \(r>R\): \[\begin{aligned} \int E dA &= \frac{Q_{enc}}{\epsilon_0}\\ E 2\pi rL &= \frac{\rho \pi R^2 L}{\epsilon_0}\\ \therefore E(r) &= \frac{\rho R^2}{2\epsilon_0r}\quad(r\geq R)\end{aligned}\] Inside the cylind…
