1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper
    Gold Member

    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:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove using divergence theorem
Loading...