Prove using divergence theorem

  • Thread starter grissom
  • Start date
  • #1
2
0
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.
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
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:
 

Related Threads on Prove using divergence theorem

  • Last Post
Replies
1
Views
845
Replies
7
Views
640
  • Last Post
Replies
23
Views
1K
  • Last Post
Replies
1
Views
957
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
11
Views
3K
Replies
4
Views
3K
Replies
8
Views
6K
Replies
5
Views
274
Replies
5
Views
2K
Top