Originally Posted by

**ojones** OK, I think I understand what's going on. Your teacher is correct in that the 2-form in the example can't be exact. This is because if it were, the flux through any closed surface would have to be zero. However, we know from Gauss's Law that the flux through any closed surface containing the origin must be E (compare your field with the electric field generated by a point charge at the origin). The exampe is not wrong either. The author doesn't claim that a vector potential for the field exists globally. He considers small open balls (which presumably don't include the origin). He states clearly that these potentials can't be patched together to give a global one.

I'll need to think a little bit more about his suggestion as to how to show f is not exact.