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Electric field above one end of a straight line segment?

  1. Aug 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the electric field a distance z above one end of a straight line segment of length L, which carries a uniform line charge λ. Check that your formula is consistent with what you would expect for the case z>>L

    2. Relevant equations

    KQ/r2

    3. The attempt at a solution

    I first considered the x component of the field and integrated

    Kλx*dx/(x2+z2)3/2 from 0 to L

    I then considered the y component of the field and integrated

    Kλz*dx/(x2+z2)3/2

    Finally I used pythagorean theorem on both these terms to find the total field.

    The problem became pretty cumbersome (which is why I didn't follow all the calculations through in this post). Is my method correct, or am I way off here?
     
  2. jcsd
  3. Aug 24, 2012 #2
    Looks good to me. So, when you combine the x and y components of the field using the Pythagorean theorem, you are effectively calculating the magnitude of the electric field. I don't think you need to do that, although you certainly can do. I would think it sufficient to say the x and y components separately. The point is that the x component should vanish in the [itex]x>>L[/itex] limit and the y component should become [itex]k \lambda L / z^2[/itex].
     
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