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Faraday's law in differential form reads

  • A.\( \nabla \times \mathbf{E} = 0 \)
  • B.\( \nabla \times \mathbf{B} = -\partial\mathbf{E}/\partial t \)
  • C.\( \nabla \times \mathbf{E} = -\partial\mathbf{B}/\partial t \)
  • D.\( \nabla \cdot \mathbf{E} = -\partial\mathbf{B}/\partial t \)

Answer: C

A changing magnetic field gives the electric field a curl, so the electric field is no longer conservative and no single-valued scalar potential exists. Stokes's theorem converts this into the familiar integral statement about an electromotive force round a loop.

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