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Homework Help: E field above a plane

  1. Feb 3, 2009 #1
    1. The problem statement, all variables and given/known data
    This is problem 47(chapter 21) in the text book - Physics for engineers and scientists (Giancoli)
    Uniformly charged wire has length L, where point 0 is the mid point. Show that the field at P, perpendicular distance x from 0 is

    E= (lambda/2*pi*epsilon_0) *(L/x*sqrt(L^2+4x^2)


    2. Relevant equations


    3. The attempt at a solution

    I tried solving it, I got E = - (lambda/2pi*epsilon_0)*[1/sqrt(L^2+4x^2)-1/2x)
    Is something wrong with my integration?

    My attempt is correct until

    E= lamda/r^2*4pi*epsilon_0 * integration (cos theta)dl

    After this, I use cos theta = x/r (r is the hypotenuse = sqrt (L^2+4x^2))

    I am trying to do this instead of taking r=x cos theta.
     
  2. jcsd
  3. Feb 3, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    Looks like something wrong with the "(cos theta)dl."
    I'll use A instead of theta. And z in place of your l, running from -L/2 to L/2.
    I get some constants times integral of cos(A)/(x^2 + z^2)*dz
    Since tan(A) = z/x, I can use z = x*tan(A) to simplify the integral.
    And dz = x*sec^2(A) dA
    After the dust settles on this change of variable, I get integral of cos(A)dA.

    Not the difference from your integral: I have dA where you have dl
    I end up with the given answer.
     
  4. Feb 3, 2009 #3
    If I use r=cos theta/x, then i get the correct result.
    I am trying to get there without that substitution and just cos theta = x/sqrt(x^2+(l/2)^2)
    huh. Doesn't work if I use the integral but does work if I take l/2 as y initially. The whole term becomes (x^2+y^2) and then apply limit to get answer.
     
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