How to find a $C^1$ vector field

Question

Let $S=\{(x,y,z):x^2+y^2+z^2=4\}$. Find a $C^1$ vector field ${\bf F}$ on $\mathbb{R}^3$ such that $$\iint_S {\bf F}\cdot d{\bf S}=\text{Area}(S).$$

I'm not even sure how to start this one...looking for a hint

Answer 1

Hint. Take ${\bf F}$ orthogonal to the spherical surface such that $${\bf F}\cdot d{\bf S}=dS.$$