I am to show: closed integral {phi (grad phi)} X (n^)dS=0
I see I am to use Divergence theorem.Can you please help?

It would help if you would use LaTeX. Do you mean this?


\int\phi\nabla\phi\times\hat{n}dS=0

exactly.I meant to learn Latex.But my exams are always wrapping me up.

You can see the source LaTeX code by clicking on "quote" and looking at somebody's post. It isn't too hard to learn.

Most special symbols in LaTeX are produced with a backslash and a name. For example, to get the greek letter "alpha", you'd just type \alpha

More information is in a sticky thread in this forum.

exactly.

Well in that case I'm not too sure of how to proceed myself. The divergence theorem says:

\int_{\partial V}\vec{F}\cdot\hat{n}dS=\int_V\nabla\cdot\vec{F}dV

The left side of the theorem involves the dot product of a vector field \vec{F} with \hat{n}. But your integrand contains a cross product. So to apply the theorem you'll have to find a way to transform your cross product into a dot product.

One suggestion: cross your integral with a constant vector \vec{a} that you can move inside the integral. Then use the identity \vec{a}\times(\vec{b}\times\vec{c})=(\vec{a}\cdot \vec{c})\vec{b}-(\vec{a}\cdot\vec{b})\vec{c}.

That would be cumbersomw.Well,I got it. express
(n^)=((n^).i)i+((n^).j)j+((n^).k)k
Now,apply divergence theorem.