Electric Field of a Hollow Cylidrical Conductor

[Zook104]

Consider a hollow cylindrical conductor in vacuum with its axis aligned with
the z-axis, and with a positive surface charge density σ. The direction of the
electric field is radial and its magnitude E is only a function of the distance r
from the z-axis, E = E(r).

Use Gauss' law to obtain the magnitude of the electric field at r < R and
at r ≥ R, where R is the radius of the conductor.

I don't know whether I have got my brain stuck in a rut but I can't for the life of me solve this. Any and all help will be greatly appreciated :D

 

[BruceW]

hey, welcome to physicsforums!
Try using Gauss' law, as it says. What kind of Gaussian surface should you use to take advantage of the symmetry?

 

[Zook104]

A cylindrical surface? With surface area of 2$\pi$rl ?

 

[Zook104]

Or should I just use a circular one because the conductor is infinite either side?

 

[BruceW]

Use the cylinder with surface area of 2*PI*r*l
Do the calculation using the information they have given you, and it should all come out nicely. (Even though the conductor is infinite, it doesn't go bad).

 

[rude man]

A cylindrical surface? With surface area of 2$\pi$rl ?

Go with that one.

 

[Zook104]

Excellent I believe I have got the correct answer :D Thank you so much for your help