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Electric field of a line of charge with symmetry

  1. May 14, 2014 #1
    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[itex]\int[/itex]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=[itex]\lambda[/itex]dx and r2=x2+a2 which gave me an integral that was an arctan integral. By substituting a for x, I got [tex] E= \frac{k \lambda \pi}{2a} [/tex] in the radial direction.

    The answer should be √2k[itex]\lambda[/itex]/a upwards and perpendicular to the line of charge
     
    Last edited: May 14, 2014
  2. jcsd
  3. May 14, 2014 #2

    SammyS

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

    You failed to take that into account.


    Here's the image for the link to your problem.
    attachment.php?attachmentid=69770&stc=1&d=1400044878.png

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

    You failed to take that into account.
     

    Attached Files:

  4. May 14, 2014 #3
    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...
     
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