Prove Vector Integration: Closed Surface S = 0

[aj06]

Homework Statement

Prove $$\int\int_{S}r \times dS=0$$
for any closed surface S.

Homework Equations

The Attempt at a Solution

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

 

[gabbagabbahey]

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.

 

[aj06]

the value of r= x^2+y^2+z^2

 

[gabbagabbahey]

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]. <br /> <br /> Second, is this the entirety of your attempt at the problem? What does this have to do with computing the integral<br /> <br /> $$\int\int_{\mathcal{S}}\textbf{r}\times d\textbf{S}$$<br /> <br /> ??[/tex]

 

[aj06]

i don't know sir...

 

[gabbagabbahey]

Try applying the divergence theorem to the vector field $\textbf{c}\times\textbf{r}$, where $\textbf{c}$ is any constant (position independent) vector... What does that give you?

 

[aj06]

thank you sir...
but can i have the complete solution of it sir..
thank you

 

[gabbagabbahey]

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.