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Homework Help: Prove using divergence theorem

  1. Mar 25, 2010 #1
    Use the divergence theorem to show that [tex]\oint\oint[/tex]s (nXF)dS = [tex]\int\int\int[/tex]R ([tex]\nabla[/tex]XF)dV.

    The divergence theorem states: [tex]\oint\oint[/tex]s (n.F)dS = [tex]\int\int\int[/tex]R ([tex]\nabla[/tex].F)dV.

    The difference is switching from dot product to cross product. I have no idea how to start. Can someone please point me in the right direction. Any help is appreciated.
     
  2. jcsd
  3. Mar 25, 2010 #2

    gabbagabbahey

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    Hint: For any constant (position independent) vector [itex]\textbf{c}[/itex], the following is true (It's worthwhile if you prove this to yourself by looking at individual components)

    [tex]\textbf{c}\cdot\int\int_{\mathcal{S}}\textbf{A}dS=\int\int_{\mathcal{S}}(\textbf{c}\cdot\textbf{A})dS[/tex]

    What happens if you let [itex]\textbf{A}=\textbf{n}\times\textbf{F}[/itex] and apply the triple scalar product rule?:wink:
     
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