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Electric field on a one dimensional line

  1. Apr 9, 2010 #1
    1. The problem statement, all variables and given/known data

    An electric charge Q has been evenly divided over a line with the lenght L. Calculate the electric field in the field spot X0. X0 > L

    2. Relevant equations



    3. The attempt at a solution

    E = 0SL(dQ/(4*pi*E0*X0^2))

    0SL = the integral over 0 to L >_<

    dQ = Q*dx/L , I think...

    E = (Q/(4*pi*E0*(X0^2)*L))*0SL(dx)

    E = (Q/(4*pi*E0*(X0^2)*L))*L

    this is not a correct answer so i wonder where Im failing.


    The right answer should be (Q/(4*pi*E0))*(1/(L(X0 - L)) - 1/(L*X0))
     
  2. jcsd
  3. Apr 9, 2010 #2
    The equation

    [tex]E = \frac{1}{{4\pi {\varepsilon _0}}}\int_0^L {\frac{{dQ}}{{{x_0}^2}}} [/tex]

    has an error in it.

    This is correct.

    Your first equation just needs a small modification. As it currently stands, your equation has constant "[itex]r[/itex]", but [itex]r[/itex] is supposed to be the distance between [itex]dx[/itex] and [itex]x_0[/itex], and the position of [itex]dx[/itex] varies between [itex]0[/itex] and [itex]L[/itex].
     
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