Charged cylinder with charge inside, find force

[youknow]

Problem is:
You have a non-uniformly charged solid cylinder along x-axis who's volume charge density (ρ=ρ°+vx), v is constant, changes according to where you are in reference to center of cylinder (origin). At center there is a charge q. Find force felt by the charge due to the cylinder. I know that I have to use F=Eq, but I am having trouble finding the electric field felt by the charge due to cylinder. Is that even possible?

Homework Statement

Homework Equations

F=Eq
Gauss's law

The Attempt at a Solution

 

[member 553083]

Yes, it is possible to find the electric field felt by the charge due to the cylinder. You can use Gauss's law to calculate the electric field. The electric field at any point is given by: E = (1/ε0)*Integral of ρdV over the entire volume of the cylinder where ρ is the volume charge density. The electric field at the center of the cylinder is simply q/4πε0, where q is the total charge on the cylinder.