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Electric Field off the end of a Rod

  1. Aug 23, 2007 #1
    1. The problem statement, all variables and given/known data
    "A thin rod carries a total charge Q distributed uniformly over its length, L. Use integration to show that the electric field strength a distance x along the rod's direction from either end of the rod is
    [tex]E=\frac{kQ}{\left[ x(x+L) \right]}[/tex]."


    2. Relevant equations
    [tex]E = \int dE = \int \frac{k dq}{r^2}[/tex]


    3. The attempt at a solution
    Somehow the [itex]r^2[/itex] on the bottom turns into an [itex]x(x+L)[/itex] AND the dq turns into a Q. I really don't understand how they integrated this problem.
     
    Last edited: Aug 23, 2007
  2. jcsd
  3. Aug 23, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Draw yourself a diagram and define a variable that will represent the position of the charge element dq. (I'll call it "y".) Then to convert your generic expression into one specific to this problem:
    (1) express dq in terms of dy (hint: what's the charge per unit length?)
    (2) express the distance between dq and the point in question (hint: this will involve L, x, and y)

    Once you've done that, integrate with respect to y over the length of the rod. Only then will you get the result you're looking for.
     
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