How to modal a voltage gradient from a single cylinder

[Wondering]

Hello,

I am a bit trumped. I know how to calculate the voltage of a single uniform cylinder:

V(r) = (-q/2 Pi ep0) Ln(r/R0) + V0

q: Charge density
r: radius from outside of the cylinder. r >= R0
R0: radius of the uniform cylinder
V0: applied voltage to the cylinder

Here is my problem. How do I modal this given that I do not know the charge density. I will simply have a conducting cylinder with a voltage applied to it and no current will be flowing.
This can be done for a sphere because I can use the capacitive formula of a sphere and substitute. But the cap. equation for a cylinder does not allow a single cylinder.

Let me know.

 

[Wondering]

I am referring to the voltage gradient outside of the solid cylinder. I need to know how to remove the charge term or replace it with a numerical value.