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).