Exercise · ZW-CONSERVATIVE-FIELD-005 · ★☆☆ Basic
If \(\mathbf F\) is conservative and \(C\) is a closed curve, then \(\oint_C\mathbf F\cdot d\mathbf r\) equals:
Choose one option.
Show answer
- A. \(0\)
Explanation
On a closed curve the endpoints coincide, so \(f(B)-f(A)=0\).
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 \(\mathbf F\).
\[\mathbf F=\nabla f\]
More practice problems: conservative field
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