Electrostatic Potential of cylindrical surface

[greygasher]

Homework Statement

The figure shows a section of a cylindrical surface, height h and radius R. The curved surface extends from the z-axis to the y-axis only and has a charge density given by σ(z)= σ₀z where σ₀is some constant. ind the electrostatic potental at a. (a is at the origin)

I'm sorry I'm not sure how to get the picture up here. It's not that complicated, just a cylindrical shell but it's cut in a way that nothing cancels out (as I hope is obvious from the problem description)

Homework Equations

(1) Laplace/Poisson

or

(2)

The Attempt at a Solution

I'm really kind of at a loss. I could solve the Laplace for cylindrical coordinates (as that is where our lectures have been heading) but I feel like there's absolutely no symmetry to exploit and it would be way too much work. I would almost just want to find the electric field and integrate to get the potential, but we've never really done (nor can I find much help online with) a varying charge density. So I get stuck with finding the enclosed charge.
If I end up needing to use Laplace, I'd like some help with my boundary conditions and probably making sense of the whole mess. I can follow the derivation alright but the solution is a hair away from being over my head.

 

[cragar]

what about integrating the charge density over the area.
$$V(r)= \int_{a}^{b}\frac{\sigma}{4\pi\epsilon_0r}da$$