Exercise · ZW-CONSERVATIVE-FIELD-009 · ★★★ Advanced
Two different paths from \(A\) to \(B\) give different line integrals of \(\mathbf F\). What follows?
Choose one option.
Show answer
- C. \(\mathbf F\) is not conservative
Explanation
A conservative field gives \(f(B)-f(A)\) along any path. If two paths differ, no such potential exists.
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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