Cylindrical charged surface

1. May 26, 2015

erisedk

1. The problem statement, all variables and given/known data
An infinitely long cylindrical surface of circular cross-section is uniformly charged lengthwise with the surface density σ = A cosΦ where Φ is the polar angle of the cylindrical coordinate system whose z axis coincides with the axis of the the given surface. Find the magnitude and direction of the electric field strength vector on the z axis.

Source: Irodov

2. Relevant equations

3. The attempt at a solution
Since σ depends only on Φ, according to cylindrical coordinate system, σ is different on different planes that pass through z = 0. I just don't know where to begin, I looked up the answer and it didn't make sense to me very much.
Please just tell me how to start!

2. May 26, 2015

theodoros.mihos

On axes x,y make the expretion of electric field components E_x, E_y for the field on the x=0, y=0 and take integrals to whole circle and z. May polar coordinates be more useful.
Also may Gauss's law be useful.

3. May 26, 2015

haruspex

Don't you mean through r=0?
Consider a section through it at some value of z. What does the charge distribution look like? Does it vary with z?