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Homework Help: Outward flux problem

  1. Nov 27, 2005 #1
    Let D be a "nice" bounded domain in R3 with boundary surface S and let F =-k del(1/r). Show that the outward flux over S is [tex]k4\pi[/tex] if the origin lies in D and 0 if the origin lies outside D U S.

    I don't understand the notation for F. What is del of 1/r?
     
  2. jcsd
  3. Nov 27, 2005 #2
    Can anyone help?
     
  4. Nov 27, 2005 #3

    Physics Monkey

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    Del is just a notation for the gradient operator. The vector field is [tex] - k \vec{\nabla}\left(\frac{1}{r}\right) = k \frac{1}{r^2}\hat{r} [/tex].

    As for your problem, use Gauss' Theorem to calculate the integral. Be very careful when your surface encloses the origin.
     
  5. Nov 27, 2005 #4
    By [tex]\hat{r}[/tex], you mean the unit vector in the direction of (x,y,z)?
     
  6. Nov 27, 2005 #5

    Physics Monkey

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    Yes, [tex] \hat{r} = \frac{\vec{r}}{r} [/tex].
     
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