Practice question · Sort into groups
Sort: which theorem relates each pair?
Groups: Divergence theorem · Stokes' theorem · Neither
- Gradient ↔ potential function
- Circulation ↔ surface integral of
- ∬_S F = ∭_V dV
- Closed surface flux ↔ volume integral of
Hints
- Ask whether the boundary is a closed surface or a closed curve.
- Divergence goes with flux; curl goes with circulation.
Show the answer
Divergence theorem: Closed surface flux ↔ volume integral of , ∬_S F = ∭_V dV
Stokes' theorem: Circulation ↔ surface integral of
Neither: Gradient ↔ potential function
Why
The divergence theorem relates flux to divergence; Stokes relates circulation to curl.
Practise The Divergence Theorem
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