Conditions on the Wave Field

CONDITIONS ON THE WAVE FIELD

If the plane polarized waves is propagating along x-axis having electric vector along the y-axis, we have

Ey ≠ 0, Ez = Ex = 0 and 

Similarly for magnetic field vector

Hz ≠ 0, Hy = Hx = 0

Therefore, the wave equations for plane electromagnetic wave reduce to

since at the given value of x, Ey and Hz are constant at any instant. Further and are varying only in x-direction which is the direction of propagation of these fields as shown in fig. 2.4.

Substituting eqn (7) in eqn (3) and eqn (8) in eqn (4) we have

Solutions of the plane Wave Equations 

The plane wave equations for electric field and magnetic field are given by

c- speed of EM wave

The solutions of the above wave equations of progressive wave are given by

where, ω - angular frequency

k - wave vector

Here E0 and H0 are the maximum values (amplitudes) of the electric and magnetic vectors respectively.

The general solution of the wave equation is written as

where c is the wave velocity.