Discussion
True or false: the flux of a field through a closed surface must vanish if the field is solenoidal.
Answer: D
Solenoidal means \( \nabla \cdot \mathbf{F} = 0 \), so the divergence theorem gives
\[ \oiint_{S} \mathbf{F} \cdot \mathbf{n}\,dS \;=\; \iiint_{V} 0\,dV \;=\; 0 \]
for every closed surface in the region, whatever its shape or position. This is what \"source-free\" means in integral terms
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