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Illustration Point at which a Vector Field is Fivergence-Free (Source-Free)

Point at which a Vector Field is Fivergence-Free (Source-Free)
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If the divergence \(\nabla \cdot \boldsymbol{F}\) of a vector field \(\boldsymbol{F}\) vanishes at the location \((x,y,z)\):\[ \nabla \cdot \boldsymbol{F}(x,y,z) = 0 \]then at the location \((x,y,z)\) there is neither a source nor a sink of the vector field \(\boldsymbol{F}\). If this point is enclosed by an arbitrary surface, then the vector field 'flows' out of the surface as much as into it. Or the vector field is zero.