Problem-Solving: Fall-2025
W2D2.5 Practice : Due W2 D2.5 (2 pm)
- Circulation I
S0 5402S
The circulation of a vector field \(\boldsymbol{\vec F}\) around a closed curve \(C\) is given by \[\oint_C\boldsymbol{\vec F}\cdot d\boldsymbol{\vec r}\]
For each of the vector fields below, explain whether you expect the given vector field to have positive, negative, or zero circulation counterclockwise around the closed curve \(C\) in the figure shown above. Two of the segments of \(C\) are circular arcs centered at the origin; the other two are radial line segments. \begin{align*} \hbox{I.}~~\boldsymbol{\vec G} &= x\,\boldsymbol{\hat x} + y\,\boldsymbol{\hat y} \\ \hbox{II.}~\boldsymbol{\vec H} &= y\,\boldsymbol{\hat x} - x\,\boldsymbol{\hat y} \end{align*}