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The identity \( \nabla \cdot (\nabla \times \mathbf{A}) \) is equal to

  • A.zero for any vector field A
  • B.the Laplacian of A, taken component by component
  • C.the curl of the divergence of A
  • D.the magnitude of the curl of A

Answer: A

A curl field has no sources, so its divergence vanishes identically. This is why the magnetic flux density, being the curl of the vector potential, satisfies \( \nabla \cdot \mathbf{B} = 0 \) and magnetic monopoles do not appear.

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