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Homework Help: Integral over a sphere with the dirac delta function

  1. Aug 7, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\[
    \underset{\left|\underline{\xi}\right|=1}{\int}\delta_{0}\left(\underline{\xi}\cdot\underline{z}\right)dS_{\xi}=\intop_{0}^{2\pi}d\varphi\intop_{-r}^{+r}\delta_{0}\left(\varsigma\right)\frac{d\varsigma}{r}=\frac{2\pi}{r}\]
    [/tex]

    The [tex]\delta_{0}[/tex] is the dirac delta function.


    the following variable substitution has been made,
    [tex]\[
    \varsigma=\underline{\xi}\cdot\underline{z}=rcos\theta\]
    [/tex]



    2. Relevant equations

    I am not really sure whether its over the surface of the sphere or the Volume,

    the problem and the solution are given above, I want to know how it has been solved.
    What is the Jacobian Determinant for the problem ?

    3. The attempt at a solution

    I always end up with [tex]2\pi[/tex]
     
    Last edited: Aug 7, 2009
  2. jcsd
  3. Aug 7, 2009 #2
    hey guys,

    thanx a lot but i got it finally.

    by the way... i posted this problem in another section too and i dont know how to delete it...

    Thanx...
     
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