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Integral Over a Sphere with dirac delta function

  1. Aug 7, 2009 #1
    Hi,

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

    the problem and the solution are given below, I want to know how it has been solved.
    The [tex]\delta_{0}[/tex] is the dirac delta function.

    [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 following variable substitution has been made,

    [tex]\[
    \varsigma=\underline{\xi}\cdot\underline{z}=rcos\theta\]
    [/tex]

    Thanx a lot.
     
  2. jcsd
  3. Aug 7, 2009 #2
    hey,

    I Just got it,

    I used this substitution.

    [tex]
    \[
    \intop_{0}^{\pi}\intop_{0}^{2\pi}f(cos\varphi sin\theta,sin\varphi sin\theta,cos\theta)sin\theta d\theta d\varphi\][/tex]

    the radius that i used in the variable substitution is not the same as the unit radius.
     
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