Discussion
The circulation of an irrotational field round any closed curve in a simply connected region is
Answer: D
By Stokes's theorem the circulation equals the flux of the curl through a spanning surface, and an irrotational field has zero curl:
\[ \oint_{C} \mathbf{F} \cdot d\mathbf{r} \;=\; \iint_{S} \mathbf{0} \cdot \mathbf{n}\,dS \;=\; 0. \]
Simple connectedness matters: on a region with a hole the spanning surface may not exist, and the circulation can then be non-zero
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