In free space, . Obtain H(z,t).

Concept:

Any vector quantity can be represented as the product of magnitude and vector quantity, i.e.

|A| = Magnitude of the vector quantity.

û = Unit direction vector.

Poynting vector:

It states that the cross product of electric field vector (E) and magnetic field vector (H) at any point is a measure of the rate of flow of electromagnetic energy per unit area at that point that is 

Where P = Poynting vector, E = Electric field and H = Magnetic field

The Poynting vector describes the magnitude and direction of the flow of energy in electromagnetic waves.

The unit of the Poynting vector is watt/m2

The ratio  for the wave is equal to the intrinsic impedance of the medium, η.

Analysis:

The direction of propagation = +z direction

Electric field vector = +y direction

The direction of the magnetic field will be such that the Poynting vector theorem is satisfied

i.e. P = E × H

∴ The magnetic field must be along (-a_x) direction.

The magnitude will be:

∴ The magnetic field vector will be:

 (z, t) = |H| sin (ωt – βz) (-a_x)

= -2.65 sin (ωt - βz) a_x