Exercise · ZW-CURL-007 · ★★☆ Intermediate
For which value of \(k\) does \(\mathbf F=\langle kxy,\,x^2+z,\,y\rangle\) have zero curl?
Choose one option.
Show answer
- C. \(k=2\)
Explanation
The \(\mathbf i\) and \(\mathbf j\) components are already \(0\) (\(R_y-Q_z=1-1\), \(P_z-R_x=0\)). It remains \(Q_x-P_y=2x-kx=0\), i.e. \(k=2\).
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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