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Findng electric force for line of charge

  1. Apr 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the force acting on an electron located "d" distance from the midpoint of a line of charge, length "L", located on the x axis. The line of charge is positive.


    2. Relevant equations

    F(e)=kq1q2/r^2

    3. The attempt at a solution

    λ=linear density, here the charge is uniform.
    So, dq=λdx I think?
    The distance is the variable that is changing, so we should integrate the dx and the limits should be over the length of the line?

    k, e(electron) and λ are constant and can be brought out of integral... if the origin is the midpoint, then the limits of integration are -L/2 to L/2? The solution the book gives is the following:

    4keλL/(4d^2-L^2)

    I don't know where I'm going wrong with this equation, maybe I have the wrong r value?
    Is r=(d-x)^2 when dx is along the positive x axis?
    Any tips or perspectives would be great!
     
  2. jcsd
  3. Apr 30, 2012 #2

    tiny-tim

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    hi lonewolf219! :smile:
    yes
    how can a distance equal a distance squared? :confused:

    (and don't forget that force is a vector, so you'll need to integrate the component :wink:)
     
  4. Apr 30, 2012 #3
    Ah, yes, that's why I prefer energy! The electron is also along the x axis, so the angle between the line and the electron is 0, so cos(0)=1?

    Using Coulomb's formula, where denominator "r" is squared. The distance between the electron and a dx element of the line (?) can be represented by what? Is it d-x, where we don't know the value of x? Or d+x?
     
  5. Apr 30, 2012 #4

    tiny-tim

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    ah, i think the question means that the electron is on the y axis
    see above :wink:
     
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