1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integral over a sphere with the dirac delta function
Loading...