Electric field of an infinite charged rod

[fluidistic]

Homework Statement

I tried to derive the electric field of an infinite (non conductor and conductor, I believe it is the same) charged rod.

Homework Equations

$$\oint \vec E d \vec A = \frac{Q_{\text {enclosed}}}{\varepsilon _0}$$.

The Attempt at a Solution

I could do all, except at the end... when he wrote that $$\oint \vec E d \vec A=E 2 \pi rL$$. I understand that $$\oint d\vec A = 2\pi rL$$, but I don't understand how he could pass the $$E$$ outside the line integral, as if $$E$$ was constant. Because it isn't constant, $$E$$ depends on $$r$$.

I would have understood this step if we were to derive the electric field due to an infinite charged plane, where $$E$$ does not depend on the distance between a charged particle and the plane.

Can you explain me why does $$\oint \vec E d \vec A=E 2 \pi rL$$?
Thanks in advance!Here's the link : http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/ElectricForce/LineChargeDer.html .
(look at the very bottom of the page)

 

[fluidistic]

Nevermind, I got it. E is constant over the cylinder' surface!