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The Laplacian of a scalar field is

  • A.the divergence of the curl of that field
  • B.the divergence of the gradient of that field
  • C.the curl of the gradient of that field
  • D.the gradient of the divergence of that field

Answer: B

Correct answer: the divergence of the gradient of that field

\[ \nabla^2 V = \nabla\cdot(\nabla V). \] The gradient turns the scalar into a vector and the divergence turns it back into a scalar. The other combinations offered are either identically zero - the curl of a gradient and the divergence of a curl both vanish - or are not defined for a scalar at all.

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