# Homework Help: Electric field and charge density

1. Jul 3, 2009

### peaceandlove

1. The problem statement, all variables and given/known data
A uniform line charge of density λ lies on the x axis between x=0 and x=L. Its total charge is 11 nC. The electric field at x=2L is (500 N/C)ˆı. Find the electric field at x=3L. Answer in units of N/C.

2. Relevant equations

3. The attempt at a solution
I have no clue where to even begin...I know that eventually I need to obtain a relationship between E(2L) and E(3L) but besides that I'm totally lost.

2. Jul 3, 2009

### LowlyPion

Develop an integral for a charged line segment along the x-axis. Won't that then tell you what the relationship between distance along x and field strength?

3. Jul 3, 2009

### peaceandlove

I can't seem to get the integral right... I got (1/4(pi)e_0)*(qQ/(d(d+L)). Perhaps I calculated it wrong because I'm not sure what q is.

4. Jul 3, 2009

### LowlyPion

What you don't know is what L is.

By giving you the field intensity at 2L, then they are telling you what it is. But rather than calculate it out I'd just go to the ratio and figure the L based on the ratio of the dependency on L.

For instance you should get a result based on the charges being arranged 1L to 2L, and when measured at 3L, the field will be evaluated with the charges 2L to 3L away.

5. Jul 3, 2009

### peaceandlove

Do I do that using the integral I developed? And if so does that mean the one I came up with is correct?

6. Jul 3, 2009

### LowlyPion

Sorry, I didn't work out your integral. I simply note that you should have an equation of the form

E = kλ∫ 1/r2 = - K/r

where K is the grouped constants (which will cancel out) and r is evaluated from 1 to 2, or 2 to 3.
Then take the ratio of the equations right?

E3/500 = (K*(1/2 - 1/3))/(K*(1-1/2)