\nabla \cdot B=0,
so \int\nabla \cdot B dv=0,
then \int B \cdot \widehat{n}da=0,
let B=\nabla \times A,
then \int\nabla \times A \cdot \widehat{n}da=0,
thus A=\nabla\varphi[/itex], thus [tex]B=\nabla \times A=\nabla \times\nabla\varphi=0
I know something is wrong with that but I am not sure...