Chapter 19 - Electric Charges, Forces, and Fields - Problems and Conceptual Exercises - Page 686: 70

$E=\frac{\lambda}{2\pi \epsilon_{\circ}r}$

We know that $\phi=EA$ $\phi=E(2\pi rL)$ We also know that $\phi=\frac{q}{\epsilon_{\circ}}$ $\implies E(2\pi rL)=\frac{\lambda L}{\epsilon_{\circ}}$ $\implies E=\frac{\lambda}{2\pi \epsilon_{\circ}r}$ This is the required proof.