Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2017 / Paper 2 / 13 / c / Solution

Differentiate the components directly:Thus $\boxed{\nabla \times \mathbf{F}=0}$. The field is smooth on all of ${\mathbb{R}}^3$, a simply connected domain, so the zero-curl condition is sufficient for a conservative vector field. The domain condition matters: zero curl alone need not imply a global potential on a region with holes.