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Electric field from a line of charge

  1. Jul 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Positive charge q= 7.81pC is spread uniformly along a thin nonconducting rod of length L=14.5cm. What are the magnitude and direction (relative to the direction of the x axis) of the E-field produce at pt P, at distance R = 6.00 cm from the rod along its perpendicular bisector.

    2. Relevant equations

    dE= (kdQ)/r^2


    3. The attempt at a solution

    dQ = charge density (a) * dL --> dE = intergral from -L/2 to L/2 of (k*a*dL)/(R^2 + L^2/4)
    E= k*a/ (R^2 + L^2/4) * L ---> charge density (a)= Q/L
    E = kQ/(R^2 + L^2/4)

    It might be a bit hard to understand all the broken notations. Sorry. I also tried to attached a diagram, please look at that to clarify. I don't think I set up the integral correctly. Help please! Thanks
     

    Attached Files:

  2. jcsd
  3. Jul 20, 2009 #2
    Assuming the line of charge is vertical, you only need to consider the x-components of the force; the y-components will cancel out. Why? Symmetry.

    Can you find an expression for the x-component of the force?

    If so, just integrate that over the integration region and you'll have your answer.
     
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