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The wave equation for the electric field in a source-free region follows from Maxwell's equations by

  • A.taking the curl of the Faraday equation and substituting the Ampere equation
  • B.taking the divergence of both curl equations and adding them
  • C.differentiating the two divergence equations with respect to time
  • D.eliminating the constitutive relations between the four equations

Answer: A

The curl of a curl expands into a gradient of a divergence minus a Laplacian, and in a source-free region the divergence term vanishes, leaving the Laplacian equal to a second time derivative. That is the wave equation, and its solutions travel at the speed set by the medium.

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