Integrating n.curl F and n^grad(phi) on a Closed Surface

[Tiggy]

I am trying to show for a closed surface
the integral n.curlF ds and
the integral n^grad(phi) ds
both equal zero.

Any ideas? Do I need to use identities such as div curl F=0
I can't seem to find a way to make the integrands equal zero.

Thanks

 

[Siberius]

does ^ mean a cross product? If that is the case, then what do you mean by the integral of a vector being equal to zero? Do you mean the vector (0,0,0)?

 

[AlphaNumeric]

Siberius, I assume dS is actually a vector too, Tiggy just didn't put in the 'dot' to make it a scalar.

Tiggy, Stokes Theorem is that for a nice surface/volume you have the relation

$$\int_{V}d\eta = \int_{\partial V}\eta$$

You're asking to find $$\int_{S = \partial V}\eta$$ where $$\eta$$ is the integrands you've given. Can you work out their divergences? The first one is quite clearly zero by the identity you mention. The second one is zero by the fact $$a.(b \times a) = 0$$, even when $$a = \nabla$$ (proof by suffix notation).