# Infinite line of charge

Ivegottheskill
The question I've been attempting:

An infinitely long line of charge has a linear charge density of 8.00×10−12 C/m. A proton is a distance of 17.5 cm from the line and moving directly toward the line with a speed of 2700 m/s.

How close does the proton get to the line of charge?
Use 1.60×10−19 C for the magnitude of the charge on an electron, 1.67×10−27 kg for the mass of a proton, and 8.85×10−12 F/m for the permittivity of free space

From my notes and working etc. I've got:

E = lambda/2*pi*epsilon*r (where lambda = charge per unit length and epsilon = permittivity of free space)

F = E * q (where q = the charge of the proton, -1.60*10^-19, as apparently defined by the question)

I've used the F calculated to get acceleration by

a = F/m (where m = mass of proton)

I get a value of -7.88*10^7

I then use the linear acceleration formula v^2 = u^2 + 2*a*s to try and calculate s.

I get 0.04627... (4.63*10^-2)

Apparently this is incorrect however. Can anyone see where I'm messing up?

Homework Helper
The linear acceleration formula holds only when the acceleration is constant.

Try using energy conservation instead! :)

Ivegottheskill
Hmm, still having trouble,

1/2*m*v^2 + E*q*y = 0 + E*q*(unknown y value)

The formula for E that I'm using doesn't make sense to me but appears right in my notes and textbook: E = lambda (charge per unit length)/2*pi*r*epsilon(permittivity of free space)

I wouldn't think E relies on r (for a straight line of charge). Aren't field lines parallel for a line of charge? Meaning E is constant at any point in the field?

I'm not given the r value for the final state of the particle, so I can't work out either E or the unknown y on the right hand side of that formula.

Homework Helper
The "Electric Field Lines" are spread out more (1-dim), farther from the wire.
That means the E-field strength decreases as 1/r .
You need substripts to distinguish "E_final" from "E_initial" ... not equal!

You want to integrate E(r) from y_initial to y_final ...
or if this isn't for calc-based physics, use Potential.

Ivegottheskill
No, still confused out of my brain. Was doing it on Mastering Physics.com, but exceeded attempts and failed the question. I tried a billion random different formulas. Worst thing is having no idea if they were even valid to use in an equation

The answer was apparently 0.134 m, but I still can't see how. I'll probably have to see tutorial teacher or something