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The expression \( \nabla \times (\nabla \times \mathbf{A}) \) may be expanded as

  • A.\( \nabla(\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A} \)
  • B.\( \nabla^2 \mathbf{A} - \nabla(\nabla \cdot \mathbf{A}) \)
  • C.zero
  • D.\( \nabla \cdot (\nabla \times \mathbf{A}) \)

Answer: A

This identity is what turns Maxwell's equations into the wave equation: substituting it and using the vanishing divergence in a source-free region leaves the Laplacian of the field equal to its second time derivative multiplied by a constant.

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