Phase and Orientation of Electromagnetic wave in matter

PHASE AND ORIENTATION OF EM WAVE IN MATTER

From the equations (13) and (14), it is clear that the phases of electric and magnetic fields are same (ie., ωt - kx). Thus, both fields are in phase with each other.

Relation between electric and magnetic field vectors

We know for electromagnetic waves in free space

The relation between their time and space variations is given from Maxwell's equation

We know that

Substituting Ey and Hz from the equations (1) & (2) in eqn. (3), we get

This is the relation between the electric field vector and magnetic field vector. I is determined by the μ0 and ε0. 

This ratio of the electric and magnetic vectors is directly professional to the square root of the ratio of  μ0 and ε0.

It shows that the value of electric field at any instant is about 377 times the value of magnetic vector in electromagnetic wave.

The ratio E/H is having the unit of impedance (Resistance)

ie., ohm. Therefore, the quantity has the dimensions of impedance.

It is known as intrinsic or characteristic impedance of free space, denoted by Z0. It is a constant quantity for free space and having value = 377Ω.

The above discussion shows that the vector and the vector are at right angle to each other and the wave propagates in the direction of (Fig. 2.5)

Thus if is parallel to Y . axis. The vector is known as Poynting vector after J.S. Poynting who first investigated its properties.

Further, and  are always in the same phase, i.e., their relative magnitudes are the same at all points and at all times.

Poynting Vector

The cross product of electric field vector and the magnetic field vector is called poynting vector. It is denoted by

An electro-magnetic wave has electric and magnetic field vectors oscillating perpendicular to each other. The electric and magnetic disturbance travels in a same direction perpendicular to both the electric and magnetic vectors.

Let a plane polarized electromagnetic wave be propagating along the x-axis. The electric vector is directed along the y-axis, then the magnetic vector is directed along the z-axis. Hence,

But Ey Hz measures the energy per second (ie power) per unit area. Hence represents the energy propagating along the x-axis in Js-1m-2 or Wm-2.

In other words, Poynting vector gives the time rate of flow of electromagnetic wave energy per unit area of the medium.

Further the average Poynting vector for one complete cycle of electromagnetic wave is given by

Maxwell's findings is summarised as below. 

1. If there is a varying electric field in vacuum, there is also a varying magnetic field and vice versa. The electric and magnetic fields are perpendicular to each other and also perpendicular to the direction of propagation of the wave. 

2. The electric and magnetic fields obey wave equation with identical propagation speeds.

3. The speed of propagation given by c = is the same as the measured speed of light. 

4. The light waves can, therefore, be identified as electromagnetic waves. 

5. The electric and magnetic fields in electromagnetic waves oscillate in phase with each other.