Find the magnitude of the electric field at a point 4 cm away from a line charge of density 2 × 10^-8 C / m.

Flux through cylinder

$\overrightarrow{\mathrm{E}}\cdot \overrightarrow{\mathrm{A}}=\mathrm{E}\left(2\mathrm{\pi rL}\right)+\mathrm{O}=\frac{{\mathrm{q}}_{\text{in }}}{{\mathrm{ϵ}}_0}$

flux through cylindrical force is zero as  $\overrightarrow{\mathrm{E}}\perp \overrightarrow{\mathrm{A}}$

$\begin{array}{l}\mathrm{E}\times 2\mathrm{\pi }\left(4\times {10}^{-2}\right)\mathrm{\ell }=\frac{{\mathrm{q}}_{\text{in }}}{{\mathrm{E}}_0}\\ \Rightarrow \mathrm{E}\times \left(2\mathrm{\pi }\times 4\times {10}^{-2}\right)\times \mathrm{\ell }=\frac{2\times {10}^{-8}\times \mathrm{\ell }}{{\mathrm{\epsilon }}_0}\\ \Rightarrow \mathrm{E}=\frac{{10}^{-6}}{4{\mathrm{\pi \epsilon }}_0}=9\times {10}^3\end{array}$