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Homework Help: A Semi- Infinite Conducting Rod

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data
    25. A semi-infinite nonconducting rod (i.e. infinite in one
    direction only) has uniform positive linear charge density
    lambda. Show that the electric field at point P makes an
    angle of 45 degrees with the rod and that this result is
    independent of the distance R. (HINT: Separately find
    the parallel and perpendicular (to the rod) components
    of the electric field at P, and then compare those
    components.)

    rod
    starts
    here
    _ +++++++++++++++++++++++++ =====> very long
    | |
    |
    R |
    |
    | |
    - P <== this point is a distance R from the end
    of the rod


    2. Relevant equations
    Coulomb's Law
    E= kq/r^2

    Q= (lambda)*x and thus dQ=(lambda)*dx (assuming the semi-infinite rod beings at 0 and continues on the x-axis)

    3. The attempt at a solution

    I drew a diagram and using the problems suggestions I solved for the perpendicular component first which I called dE_y (assuming it ran with the y-axis)
    dE= (kdQ)/R^2

    Then solving for the "parallel" component, I understand that if the rod truly continues to infinity, the distance between the point and the rod will become negligible and thus the influence by the rod on the point will truly be parallel with the rod itself.

    dE_x = dEcos(theta) = (k*lambda*dx*cos(theta))/r^2
    = (k*lambda*dx*y_0)/(y_0^2+x^2)^(3/2)

    and from here it all becomes convoluted.

    Thank you for your time
     
  2. jcsd
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