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E Field from Distribution of Charge

  1. Jan 31, 2010 #1

    A thin rod of length L has a non-uniform charge per unit length λ(x) given by

    λ(x) = A x2 where A = 3 µC/m3

    and x is measured in meters from the origin.

    (a) Find the net charge on the rod for L = 2.9 m.
    Q = 2.439e-5

    (b) Find the net x-, y-, and z-components of the electric field at the origin.
    Ex = ?
    Ey = 0N/C
    Ez = 0N/C

    HELP: Draw a diagram showing the contribution dE to the electric field at the origin produced by the infinitesimal amount of charge between x and x + dx. Check that your diagram shows the correct direction of dE.
    HELP: Write down an integral expression that follows from your diagram and perform the necessary integration. Check that your expression has an overall algebraic sign that corresponds to the vector in your diagram.

    So the first part was easy I just had to integrate the function given. But w/ part b I'm at a loss. I really don't understand why the net x component at the origin isn't zero. I tried integrating like the help said and I got E = (2Kλ)/y and I don't see how that helps, if I put 0 in for y that's obviously impossible. Can someone explain this and give me some hints on how to do this?
  2. jcsd
  3. Feb 1, 2010 #2
    Every part of the rod has a positive charge. The entire rod is to the right of the origin, so eacht part of the rod will produce a leftwards force on a positive test charge at the origin. So the electric field at the origin can't be 0.

    What is the charge of the section of the rod between x and x + dx ?

    How far is this section from the origin?

    What is the contribution of this section to the electric field at the origin (Coulombs law)

    now integrate this over the length of the rod
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