Originally Posted by

**craig** Show, using Stokes' Theorm, that

$\displaystyle \oint_C \phi \nabla \phi \cdot \mathbf{dl} = 0$

Firstly Stokes gives us:

$\displaystyle \oint_C \phi \nabla \phi \cdot \mathbf{dl} = \int_S \nabla \times [\phi \nabla \phi] \cdot \mathbf{dS}$

Expanding $\displaystyle \nabla \times [\phi (\nabla \phi)]$ gives:

$\displaystyle \phi \nabla \times \nabla \phi + \nabla \phi \times \nabla \phi$

The second part of this is zero for any vector, so this leaves the integral as:

$\displaystyle \int_S \phi \nabla \times \nabla \phi \cdot \mathbf{dS}$

Anyone any ideas?

Cheers in advance!