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A vector calculus problem

  1. May 26, 2004 #1
    Hi All,

    I've been working through a series of vector calculus problems and I need some help to get started with this one. Anyone care to help?

    The problem is:

    Evaluate [tex]\oint_{s} r.n.dS[/tex] where S is a closed surface.

    Cheers
     
  2. jcsd
  3. May 26, 2004 #2

    arildno

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    What is the meaning of this?
    a)[tex]\int_{S}r\vec{n}\cdot{d}\vec{S}[/tex]
    b)[tex]\int_{S}\vec{r}\cdot\vec{n}dS[/tex]
     
  4. May 26, 2004 #3
    b)

    sorry I didn't know how to do the vector symbol.
     
  5. May 26, 2004 #4

    arildno

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    Use the divergence theorem:
    [tex]\vec{r}=x\vec{i}+y\vec{j}+z\vec{k}[/tex]
    Hence, the answer is 3V, where V is the volume.
     
  6. May 26, 2004 #5
    Ok I'll give it a try. Hmm I keep noticing the divergence theorem popping up.
     
  7. May 26, 2004 #6
    OK then:

    [tex]\int_{S}\vec{r}\cdot\vec{n}dS = \int_{V}\nabla\cdot\vec{r}dV[/tex]

    Therefore
    [tex]\int_{V}\nabla\cdot\vec{r}dV=\int_{V}3dV[/tex]
    [tex]=3V[/tex]
     
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