5.1.3 Getting agreement with Faraday's law
Substituting Equation 7.21 into Faraday's law gives
This shows that a propagating electric wave is automatically accompanied by a transverse magnetic wave. The magnetic field oscillates in the y-direction, which is perpendicular to the direction of propagation and to the electric field. Expressing the magnetic field as
Equation 7.22 requires that
This condition makes good sense. Faraday's law links the rate of change of the magnetic field to the spatial variation of the electric field. The consequences of this condition will be explored at the end of our analysis, after agreement with the remaining two Maxwell equations has been checked.