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Ampere's law as modified by Maxwell reads

  • A.\( \nabla \times \mathbf{H} = \partial\mathbf{D}/\partial t \)
  • B.\( \nabla \cdot \mathbf{H} = \mathbf{J} + \partial\mathbf{D}/\partial t \)
  • C.\( \nabla \times \mathbf{H} = \mathbf{J} + \partial\mathbf{D}/\partial t \)
  • D.\( \nabla \times \mathbf{H} = \mathbf{J} \)

Answer: C

The conduction and displacement terms together form the total current density, whose divergence vanishes identically as the curl of anything must. In a good conductor at power frequency the second term is utterly negligible; in free space the first is absent altogether.

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