Image: A 2D circulating vector field with closed curve
The vector field $\dlvf(x,y) = (y,-x)$ tends to circulate in the clockwise direction. The green curve is the ellipse
\begin{align*}
\frac{x^2}{4}+\frac{y^2}{9} =1
\end{align*}
oriented counterclockwise. The circulation calculated by the line integral of $\dlvf$ over the curve should be negative.
Image file: vector_field_circulate_closed_curve.png
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