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For what values of $a$ and $b$ does the vector field $\vec{F}=\langle ay, bx\rangle $ have zero circulation on the counterclockwise oriented unit circle centered at the origin.

A

$a=0, b=1$

B

$a=1, b=0$

C

$a=\pi, b=\pi$

D

$a=-1, b=1$

E

$a=1, b=-1$

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