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Electric Field at the End of a Line of Charge

  1. Jan 21, 2017 #1
    Field at End of Line of Charge 2

    A charged rod of length L=7.10 m lies centered on the x axis as shown. The rod has a charge density which varies according to λ=ax^2 where a=−20.2 μC/m^3 .

    What is the x component of the electric field at a point on the x axis a distance of D=3.70 m from the end of the rod?


    media%2F71b%2F71ba0d9b-0e30-4c4b-8021-8ce735eb4fa9%2Fphp3k5qvx.png


    Relevant equations: Coulomb's Law - E=kQ/r^2


    The attempt at a solution: Ok, so part I of this problem was to calculate the total charge of the rod, which I figured out easily enough. Part II, as stated above, is to find the electric field at some point P along the axis of the line of charge. Here's my attempted solution:

    E = ∫ (kdQ/r^2)*<i> where dQ=ax^2dx where r=x. The x^2 on top and x^2 on bottom cancel out so you just end up integrating dx with bounds (D+L) and (L) and multiply by k and a. That didn't work, so I tried the equation with <xi> for the r vector and that didn't work either. I can't figure out what I'm doing wrong. Help!
     
    Last edited: Jan 21, 2017
  2. jcsd
  3. Jan 21, 2017 #2

    gneill

    User Avatar

    Staff: Mentor

    You need to integrate over the charge, from -L/2 to L/2. But the distance from the dq's to the point P is not the same as the x that "scans" the rod.
     
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