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Two perpendicular charged infinite lines

  1. Jun 25, 2014 #1
    1. The problem statement, all variables and given/known data
    On a long dielectric line a charge with density ##10^{-3}## is applied one half with positive charge and the other half with negative charge. Perpendicular to the first line and 5 cm away from it we have another line with the same charge density and also half of it is positive while the other half is negative. Points on the line where the charge changes from positive to negative, are the closest. (meaning they are 5 cm apart). Determine the vector of force between the lines.


    2. Relevant equations



    3. The attempt at a solution

    I hope at least some of the things written below are ok:

    Density of charge is ##\rho =e/l## meaning ##de=\rho \frac{dx}{l}##.

    Vector from the origin to the point on horizontal line ##\vec r=(x,0,h)## if ##h## is the distance between the lines. Vector from the origin to the point on vertical line is ##\vec r^{'}=(0,y,0)##

    So finally
    ##dF=dedE=\frac{\rho ^2}{l^2}dxdy\frac{1}{4\pi \epsilon _0}\frac{(x,-y,h)}{(x^2+y^2+z^2)^{3/2}}##

    But if I integrate this from ##-\infty ## to ##\infty ## the integral does not converge... Did I do anything wrong or is this simply the correct answer? :/
     
  2. jcsd
  3. Jun 25, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    e is usually the (negative) charge of a single electron, using it for an arbitrary charge is a bit confusing.

    Where did you take into account that the two halves have opposite charge?
     
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