Exercise · ZW-STOKES-THEOREM-007 · ★★☆ Intermediate
If \(\iint_S(\nabla\times\mathbf F)\cdot d\mathbf S=4\) with \(S\) oriented upward, what is it after reversing the orientation of \(S\) (downward normal)?
Choose one option.
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- A. \(-4\)
Explanation
Reversing the normal also reverses the boundary direction, and the flux changes sign.
Review the concept: Stokes' Theorem
Stokes' theorem relates the circulation of a field \(\mathbf F\) along the closed curve \(C\) bounding an oriented surface \(S\) to the flux of the curl of \(\mathbf F\) through \(S\).
\[\oint_C\mathbf F\cdot d\mathbf r=\iint_S(\nabla\times\mathbf F)\cdot d\mathbf S\]
More practice problems: stokes' theorem
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