Practice question · Multiple choice
A vector field has everywhere inside a closed surface . What is the total flux of out through ?
Hints
- Divergence theorem: .
- The volume integral of zero is zero, no matter how the field swirls or how strong it is at the boundary.
Show the answer
D. Exactly zero, no sources inside means nothing net flows out
Why
Zero divergence means every region passes along exactly what it receives, flow in equals flow out. Incompressible water and magnetic fields () obey this: no net flux ever escapes a closed surface.
Practise The Divergence Theorem
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