Exercise · ZW-CURL-004 · ★☆☆ Basic
For \(\mathbf F=\langle z,\,x,\,y\rangle\), \(\operatorname{curl}\mathbf F\) is:
Choose one option.
Show answer
- C. \(\langle 1,\,1,\,1\rangle\)
Explanation
\(R_y-Q_z=1-0\), \(P_z-R_x=1-0\), \(Q_x-P_y=1-0\): the curl is \(\langle 1,1,1\rangle\). The field is linear, so its curl is constant.
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.
\[\operatorname{curl}\mathbf F=\nabla\times\mathbf F=\langle R_y-Q_z,\;P_z-R_x,\;Q_x-P_y\rangle\]
More practice problems: curl
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