5.1.5 Getting agreement with the Ampère–Maxwell law
Finally, our electric and magnetic fields must satisfy the Ampère–Maxwell law in empty space. Using Equations 7.21 and 7.23, we obtain
which requires that
This condition is analogous to that obtained using Faraday's law. The Ampère–Maxwell law links the rate of change of the electric field to the spatial variation of the magnetic field.