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Simplifiyng the proof of conservative field using rottor properties

  1. Aug 13, 2009 #1
    [tex]\vec{F}=(\frac{x}{\sqrt{x^2+y^2+z^2}},\frac{y}{\sqrt{x^2+y^2+z^2}},\frac{z}{\sqrt{x^2+y^2+z^2}})[/tex]
    [tex]
    \vec{r}=(x,y,z)
    [/tex]

    [tex]
    |r|=\sqrt{x^2+y^2+z^2}[/tex]

    [tex]\vec{F}=(\frac{x}{|r|},\frac{y}{|r|},\frac{z}{|r|})[/tex]

    so its [tex]F=\frac{r}{|r|}[/tex]

    i need to prove that F is a conservative field
    where (x,y,z) differs (0,0,0)
    so i need to show that rot f is 0
    but for rottor i need a determinant
    is there a way to do a rot on simpler way?
     
  2. jcsd
  3. Aug 13, 2009 #2
    A conservative field is also irrotational. Take the curl of the field and show that it is equal to zero. (It is).
     
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