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, πR2L: \[\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, πR2L: Qenc=ρπR2L Thus, applying Gauss’ Law outside the cylinder, gives the electric field for r>R: ∫EdA=Qencϵ0E2πrL=ρπR2Lϵ0∴ Inside the cylind…
