• Support PF! Buy your school textbooks, materials and every day products Here!

Proving a vector Identity

  • #1
208
0

Homework Statement


Let the domain D be bounded by the surface S as in the divergence theorem, and assume that all fields satisfy the appropriate differentiability conditions.
Suppose that:
[tex]\nabla\cdot\vec{V}=0[/tex]
[tex]\vec{W}=\nabla\phi with \phi = 0 on S[/tex]
prove:
[tex]\int\int\int_{D}\vec{V}\cdot\vec{W}dV=0[/tex]

This problem is in the Laplace's, Poisson's and Greens Formulas section. Truthfully I'm not sure where to even get started here. If anyone could give me a push in the right direction I would appreciate it greatly.
 

Answers and Replies

  • #2
208
0
nevermind; got it!
 
  • #3
208
0
I used a vector identity, but can someone please help me do this one without an identity. This is in a greens identities section, but none of the greens identities look like they would work. Is it right of me to say that
[tex] \vec{V} = curl \vec{G}[/tex]

where g i ssome vector potential? or would this not help me at all?
 

Related Threads for: Proving a vector Identity

  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
6
Views
782
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
892
Replies
29
Views
4K
Replies
1
Views
6K
Replies
14
Views
3K
Replies
11
Views
6K
Top