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Electric field of line charge with non uniform charge densit

  1. Feb 14, 2015 #1
    1. The problem statement, all variables and given/known data
    A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis.

    2. Relevant equations
    E = kQ/r^2

    3. The attempt at a solution
    dq=axdx

    y component of E = kaxdx/(x^2+y^2) cosθ = kaxdxy/(x^2+y^2)^(3/2)
    after integrating from x = -L/2 to L/2 it comes out to be 0 which makes sense because the positive side cancels out the negative side of the charge charge distribution.

    x component of E = kaxdx/(x^2+y^2) sinθ = kax^2dx/(x^2+y^2)^(3/2)
    I can't figure out how to do the integral though
     
  2. jcsd
  3. Feb 15, 2015 #2

    ehild

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    Try integration by parts.
     
  4. Feb 15, 2015 #3

    rude man

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    Try Wolfram Alpha or a table of integrals!
     
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