Electromagnetic Waves

If we consider waves propagating in one direction, say x-direction then
the fundamental solution is:
u(x, t) = Ae ik(x−vt) + Be −ik(x+vt)
which represents waves traveling to the right and to the left with
propagation velocities v which is called phase velocity of the wave.
⋆ From the divergence relations of (1) by applying (6) we get
(8)
n · E = 0 and n · B = 0 (9)
This means that E (or E) and B (or B) are both perpendicular to the
direction of propagation n. Such a wave is called transverse wave.
⋆ The curl equations provide a further restriction
B = √ µɛn × E and E = − 1
√µɛ n × B (10)
The combination of equations (9) and (10) suggests that the vectors n, E
and B form an orthonormal set.
Also, if n is real, then (10) implies that that E and B have the same
phase.
Electromagnetic Waves