Exercise · ZW-DIVERGENCE-THEOREM-005 · ★☆☆ Basic
Let \(\mathbf F=\langle yz,xz,xy\rangle\). What is its outward flux through the unit sphere?
Choose one option.
Show answer
- C. \(0\)
Explanation
\(\nabla\cdot\mathbf F=0+0+0=0\), so the triple integral vanishes and the flux is \(0\) through any smooth closed surface.
Review the concept: Divergence Theorem
The divergence theorem relates the flux of a field \(\mathbf F\) through a closed surface \(S\), with outward normal, to the triple integral of its divergence over the solid \(E\) that \(S\) encloses.
\[\iint_S\mathbf F\cdot d\mathbf S=\iiint_E\nabla\cdot\mathbf F\,dV\]
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