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How to calculate this integral?

  1. Jul 22, 2011 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=37435&stc=1&d=1311346104.jpg


    2. Relevant equations



    3. The attempt at a solution
    Can I use this substitution?
    attachment.php?attachmentid=37436&stc=1&d=1311346104.jpg
     

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  2. jcsd
  3. Jul 22, 2011 #2

    hunt_mat

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    Looks good, what does it come out to?
     
  4. Jul 22, 2011 #3
    attachment.php?attachmentid=37439&stc=1&d=1311346670.jpg

    I am not sure for 2 things.

    1. Since z is not a constant, does the derivative yield dz?
    2. How can I write the range properly?
     

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  5. Jul 22, 2011 #4

    hunt_mat

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    You're fixing a point z and calculating the electric field there, the limits are easy, you have [itex]L=\tan\theta[/itex] and so the upper limit is [itex]\theta =\tan^{-1}L[/itex], the lower on is just 0.
     
    Last edited: Jul 22, 2011
  6. Jul 22, 2011 #5
    Thx!
     
  7. Jul 22, 2011 #6

    SammyS

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    For your limits of integration look at your triangle. (The angle you labeled L is actually θ.) If x = 0, then sin θ = 0 and if x = L, then sin θ = L/√(L2+z2) .
     
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