Exercise · ZW-CURL-001 · ★☆☆ Basic
Compute \(\operatorname{curl}\mathbf F\) for \(\mathbf F=\langle -y,\,x,\,0\rangle\).
Choose one option.
Show answer
- B. \(\langle 0,\,0,\,2\rangle\)
Explanation
Only the \(\mathbf k\) component survives: \(Q_x-P_y=1-(-1)=2\). The other two are \(0\). Reversing the subtraction would give \(-2\).
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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