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Stokes's theorem relates

  • A.a surface integral of the curl to a line integral round the bounding curve
  • B.a volume integral of the divergence to a surface integral of the flux
  • C.a line integral of the gradient to the difference of the scalar at the ends
  • D.a surface integral of the divergence to a volume integral of the curl

Answer: A

Correct answer: a surface integral of the curl to a line integral round the bounding curve

\[ \int_S (\nabla\times\mathbf{A})\cdot d\mathbf{s} = \oint_C \mathbf{A}\cdot d\mathbf{l}. \] It is the two-dimensional counterpart of the divergence theorem, converting circulation over a surface into circulation round its edge - and it is what connects the two forms of Ampere’s law.

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