Exercise · ZW-CURL-008 · ★★☆ Intermediate
At a point, \(\operatorname{curl}\mathbf F=\langle 0,\,0,\,3\rangle\). Near that point, the field tends to spin a small object:
Choose one option.
A about the \(x\)-axis, counterclockwise B about the \(z\)-axis, clockwise as seen from above C about the \(z\)-axis, counterclockwise as seen from above D not at all; it only pushes it along the \(z\) direction Show answer C. about the \(z\)-axis, counterclockwise as seen from above← Back to the question
Explanation The curl points along the axis of rotation and, by the right-hand rule, the sense is counterclockwise seen from the tip of the vector. Its length (here \(3\)) is twice the local angular speed.
Review the concept: Curl The curl of a vector field \(\mathbf F=\langle P,Q,R\rangle\) is the vector field that measures, at each point, the field's tendency to rotate, with axis and rate of rotation given by its direction and length.
\[\operatorname{curl}\mathbf F=\nabla\times\mathbf F=\langle R_y-Q_z,\;P_z-R_x,\;Q_x-P_y\rangle\]
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