Discussion
The divergence of the curl of a vector field is
Answer: D
The divergence of the curl of any vector field is zero.
Writing it out, \(\nabla\cdot(\nabla\times\vec{F})\) is a sum of mixed second partial derivatives that cancel in pairs, such as \(\partial^{2}F_{z}/\partial x\partial y - \partial^{2}F_{z}/\partial y\partial x\), for any field with continuous second derivatives.
It is a scalar identity, not related to the magnitude or direction of the field or of its curl, so the other three options are wrong.
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