Calculating Proton's Closest Approach to a Line of Charge

[totalmajor]

Homework Statement

An infinitely long line of charge has linear charge density 4.00 10-12 C/m. A proton (mass 1.67 10-27 kg, charge +1.60 10-19 C) is 18.0 cm from the line and moving directly toward the line at 1.20 103 m/s. How close does the proton get to the line of charge?

Homework Equations

kq/r

The Attempt at a Solution

Hi guys,
This is one of the toughest problems we've had all year, and no matter who I ask, they're all stuck on it.

I know the basic equations for voltage and work but finding how close the proton gets seems nearly impossible. Is it okay if you guys can just lead me in the right direction to something I can work with?
Thanks a lot,
Peter

 

[Dick]

You need a formula for the potential of the line charge. You can get this pretty easily by first calculating the field using a gaussian cylinder outside of the line charge and then integrating the field to get the potential.

 

[kamerling]

Find the electric field around the conductor. (use Gauss' law). Then integrate
to get the potential energy of the proton as a function of the distance to the conductor.