Potential at all points due to uniformly charged infinite cylinder

[oddjobmj]

Homework Statement

Infinitely long cylinder of radius R with uniform charge ρ. Calculate the electric potential at all points in space.

Homework Equations

V(a)-V(b)=-∫_b^a$\vec{E}$($\vec{r}$')°dr'$\hat{r}$

The Attempt at a Solution

Generally potential is calculated with a reference point at r=∞ but in the case of an infinite cylinder I believe the integral above would diverge because the potential at ∞ (V(∞)) would not necessarily equal zero. What I did then is simply provide an arbitrary r' vector as the reference point and went through the problem as one would normally do so with a non-infinite charged object. Is this okay? Do I have to do something extra because of the non-zero reference point?

Thank you!

 

[ehild]

It is right, but better to show your work.

ehild