# Electric field of a line of charge with symmetry

1. May 14, 2014

### Regtic

1. The problem statement, all variables and given/known data
http://imgur.com/W4Ntkfb

2. Relevant equations
E=KQ/R2
e= electric field
Q = charge
R = radius from point to charge
K is a constant, 9x109

3. The attempt at a solution
http://imgur.com/4CTEwDw

If my handwriting sucks, I basically did the standard integral of k$\int$dq /r2 but kept the r hat vector since there is symmetry and I know that the magnitude will be be in the y direction. I used dq=$\lambda$dx and r2=x2+a2 which gave me an integral that was an arctan integral. By substituting a for x, I got $$E= \frac{k \lambda \pi}{2a}$$ in the radial direction.

The answer should be √2k$\lambda$/a upwards and perpendicular to the line of charge

Last edited: May 14, 2014
2. May 14, 2014

### SammyS

Staff Emeritus
$\hat{r}\$ depends on x, it's not constant.

You failed to take that into account.

$\hat{r}\$ depends on x, it's not constant.

You failed to take that into account.

#### Attached Files:

• ###### W4Ntkfb.png
File size:
25.5 KB
Views:
164
3. May 14, 2014

### Regtic

Oh right it's not constant in direction... was just thinking of that as a constant. Derp, shouldn't be studying this late. Thank you. Redid it with Ey and got it.

also it seems whenever I post photos directly into the forum they become ridiculously large, or maybe that's just photos from Iphone...