Exercise · ZW-CONSERVATIVE-FIELD-007 · ★★☆ Intermediate
For which value of \(a\) is the field \(\mathbf F=\langle axy,\,x^2\rangle\) conservative?
Choose one option.
Show answer
- B. \(a=2\)
Explanation
We need \(P_y=Q_x\): \(ax=2x\), so \(a=2\). Then \(\mathbf F=\nabla(x^2y)\).
Review the concept: Conservative field
A vector field \(\mathbf F\) is conservative if it is the gradient of a scalar function \(f\), called a potential function of \(\mathbf F\).
\[\mathbf F=\nabla f\]
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