Need help finding the electric potential

[JFuld]

Homework Statement

calculate the electric potential for the following:

A cylindrical cable with a center rod of diameter a surrounded by a gap and a
thick pipe with inner and outer radii b & c. The charge distribution on the inner rod
is ρ = k cos(sπ/2a), and the outer rod has a uniform charge density such that the total
system is neutral.

Homework Equations

V=-integral E.dl
gausses law

The Attempt at a Solution

i calculated the electric field everywhere, but I am not sure how to go about calculating V.

My best guess is to calculate V the cylinder, setting my reference point at infinity and then work my way inside the cylinder, calculating V in each region.

But since the total system is neutral, the integral gives V=0 for outside the cylinder, which I have a feeling is incorrect...

My book doesn't really have any examples or explanations for charge distributions of this type so I just wanted to know if I am on the right track.

 

[Simon Bridge]

this is sort of a cylindrical capacitor isn't it?
https://www.physicsforums.com/showthread.php?t=246762

The key is to use cylindrical coordinates.
Notice that the field depends only on radius.
Choose cylindrical gaussian surfaces.

Some people find the differential form more useful.