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3-dimensional charge density for a finite thin wire

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Express the 3D charge density [tex]\rho[/tex] for a thin wire with length Z and uniform linear charge density [tex]\lambda[/tex] along the z-axis in terms of a two-dimensional dirac-delta function.


    2. Relevant equations

    The three dimensional charge density is the total charge over a volume.


    3. The attempt at a solution

    I am not sure how to proceed with this question. Last night I attempted to calculate the electric field components, which I believe I did correctly, but was heavy in the algebra. I had intended to use Gauss law to calculate the charge density from the Electric field, hoping that a delta function would pop out somewhere. I talked to my professor today and he told me I was using the wrong approach, and that the solution to this problem is much simpler. Unfortunately I'm not sure I entirely understand how to use the dirac-delta function, and I feel stuck. I'm not sure how to start this problem. All I know is that

    [tex]Q=\int^{Z}_{0}\lambda dz[/tex]

    This integral just evaluates to [tex]\lambda Z[/tex].

    I have no idea how to proceed. Any help would be appreciated.

    Thanks.
     
  2. jcsd
  3. Sep 23, 2009 #2

    kuruman

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