Discussion
The divergence of a curl, \( \nabla \cdot (\nabla \times \mathbf{A}) \), is
Answer: C
Expanding gives six mixed third derivatives that cancel in pairs, so
\[ \nabla \cdot (\nabla \times \mathbf{A}) \;=\; 0. \]
Every curl field is therefore solenoidal, which is why a solenoidal field can be represented by a vector potential and why magnetic flux density, having zero divergence, is written as the curl of one
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