What is the kinetic energy of the proton?

[Millimole]

Homework Statement

An infinitely long line of charge has linear charge density λ = 3.00 pC/m. A proton is at
a distance d = 14.5 cm from the line and moving directly toward the line at v = 2.00 km/s.
a. (3 points) What is the kinetic energy of the proton?
b. (15 points) How close does the proton get to the line of charge?

Homework Equations

K=.5mv²
E(line of charge)=($$\lambda$$/(2$$\Pi$$$$\epsilon$$subnought))*1/r
W=Kfinal-Kinitial
W=Uinitial-Ufinal
U=k(q1q2)/r

The Attempt at a Solution

First let me apologize for my lack of understanding how to input formulas into the forum. I found the latex reference tool thing but when I click something it just inserts a bunch of garbletygoop that makes my head explode a little. Yes, garbletygoop.

Part a is just a simple application of the kinetic energy equation, yielding 3.34×10^−21 J. This part is just a lead in for how to work part b. To find out how close the proton comes to the line of charge, I realized that we are really looking for the turning point of the proton, or the point at which kinetic energy equals zero. Since W=Kfinal-Kinitial, this means the work done is -Kinitial, which we just solved for in part a.

Next I plugged this into the equation W=Uinitial-Ufinal. So, -Kinitial=Uinitial-Ufinal. I know the distance (r) for the Uinitial equation, and the distance (r) for the Ufinal equation is my variable. Seemed pretty straight forward. But then I realized that my electric potential energy equations were for two point charges, not for a point charge and a line of charge. I can find no such equation, and honestly my calculus skills are not such that I can derive one of my own. Suggestions?

 

[LiorE]

The assumption is that the line generates a certain potential (which you should have/be able to calculate) throughout space and that the proton moves inside that potential. You are not supposed to take into account the potential that the proton creates when you work out its equations of motion.

In any case, since the equation that relates the potentials to the charges is linear, the potential of a line of charge and a point charge is a sum of the potentials of each.

Also, if you were needed to calculate the potential that the proton creates in space as it moves, you would have to take into account that it accelerates and thus creates radiation - and that isn't an electrostatic problem anymore.