Vector integration

  • Thread starter aj06
  • Start date
  • #1
aj06
5
0

Homework Statement


Prove [tex] \int\int_{S}r \times dS=0 [/tex]
for any closed surface S.


Homework Equations





The Attempt at a Solution


i used divergence theorem but i didn't make it...
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
7
i used divergence theorem but i didn't make it...

Well, how far did you make it with that? Show us what you've got and we'll be better able to help you.
 
  • #3
aj06
5
0
the value of r= x^2+y^2+z^2
 
  • #4
gabbagabbahey
Homework Helper
Gold Member
5,002
7
the value of r= x^2+y^2+z^2

First,

[tex]r=||\textbf{r}||=\sqrt{x^2+y^2+z^2}\neq x^2+y^2+z^2[/itex].

Second, is this the entirety of your attempt at the problem? What does this have to do with computing the integral

[tex]\int\int_{\mathcal{S}}\textbf{r}\times d\textbf{S}[/tex]

??
 
  • #5
aj06
5
0
i dont know sir...
 
  • #6
gabbagabbahey
Homework Helper
Gold Member
5,002
7
Try applying the divergence theorem to the vector field [itex]\textbf{c}\times\textbf{r}[/itex], where [itex]\textbf{c}[/itex] is any constant (position independent) vector.... What does that give you?
 
  • #7
aj06
5
0
thank you sir...
but can i have the complete solution of it sir..
thank you
 
  • #8
gabbagabbahey
Homework Helper
Gold Member
5,002
7
but can i have the complete solution of it sir..

No. We do not provide complete solutions here. It is unethical and it doesn't really help you learn any problem solving skills.

You need to make some effort and show your work in order to receive further help.
 

Suggested for: Vector integration

Replies
5
Views
339
Replies
13
Views
507
Replies
2
Views
325
Replies
58
Views
895
  • Last Post
Replies
3
Views
493
  • Last Post
Replies
8
Views
540
Replies
7
Views
519
Replies
12
Views
304
Top