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Electric field from a charged rod

  1. Sep 19, 2004 #1
    Ok, i'm inexperienced with the latex code, so excuse me.

    I'm trying to derive the expression for the electric field at a point, along the perpendicular bisector of a charged rod, of known total charge, length L, a perpendicular distance y from the rod.

    The horizontal components cancel,
    [tex]
    \frac{qy}{4\pi \varepsilon_0 L} \int_0^L \frac{dx}{((\frac{L}{2}-x)^2 +y^2)^{3/2}}
    [/tex]
    I don't think this is right, because that seems a nasty integral. Any ideas?

    Apologies if you think this is the wrong section. Thanks.
     
    Last edited: Sep 19, 2004
  2. jcsd
  3. Sep 19, 2004 #2
    I finally got the tex perfect. Can somebody please help me as soon as possible? Thanks alot.
     
  4. Sep 20, 2004 #3

    krab

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    Science Advisor

    The integral's not too bad.. Hint:
    [tex]\int (1+x^2)^{-3/2}dx=x/\sqrt{1+x^2}[/tex]
     
  5. Sep 20, 2004 #4

    ehild

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    Homework Helper
    Gold Member

    You are right, this is not right, and the integral is nasty.
    You get a much nicer integral if you place your origin at the middle of the rod, and use the angle [tex]\varphi [/tex] instead of x. See pic.

    [tex]r=\frac{y}{\cos(\varphi )} \mbox{ , } x = y \tan(\varphi )[/tex]....

    ehild
     
    Last edited: Jun 29, 2010
  6. Sep 20, 2004 #5

    ehild

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    Gold Member

    Sorry, the formula was right... But it is still nasty.

    ehild
     
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