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Finding the density of the matter

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the density of the matter [tex]\rho(\vec{r})[/tex] in spherical coordinate system, with the mass M, which is homogeneously placed on two rings with the radii of a (with the center in the origin) put in the xy and yz plane

    2. Relevant equations
    [tex]\int \rho(\vec{r})dV=M[/tex]
    For a unit mass in the center that would be:
    [tex]\int dx\int dy\int dz M\delta(x)\delta(y)\delta(z)=M\cdot 1\cdot 1\cdot 1[/tex]
    in cylindrical coordinates:
    [tex]\rho(\vec{r})=\frac{M}{2\pi \rho}\delta(\rho)\delta(z)[/tex]
    [tex]\int\rho(\vec{r})dV=\int_{-\infty}^\infty dz\int_0^{2\pi}d\phi\int_0^\infty \rho d\rho \cdot\frac{A}{2\pi\rho}\cdot\delta(\rho)\delta(z)=M\Rightarrow M=A[/tex]

    3. The attempt at a solution

    I don't know even how to start :( Help plz...
     
  2. jcsd
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