Module 4 : Uniform Plane Wave Lecture 30 : Phase Velocity of a Wave

Objectives

In this course you will learn the following

Velocity of a wave (phase velocity).

Phase velocity in different media.

Dispersion in a medium having finite conductivity.

Module 4 : Uniform Plane Wave Lecture 30 : Phase Velocity of a Wave

Phase Velocity of a Wave

The electric field of a plane wave travelling in direction is written as

The phase of this wave is

The phase velocity is the velocity of a constant phase point of the wave.

Said differently, it is the velocity of an observer to whom the phase appears constant as a function of time.

Differentiating with respect to time we get

Phase velocities of a wave in different media

Free Space : For free space (or vacuum) we have

. We therefore have

This is the velocity of light in the free-space and is normally denoted by letter ` '. Module 4 : Uniform Plane Wave Lecture 30 : Phase Velocity of a Wave

Phase velocities of a wave in different media (contd.)

Pure Dielectric : For a pure dielectric = 0, = =

The above eqn. gives the velocity of light in a medium with dielectric constant .We note that the velocity of an electromagnetic wave in a dielectric medium is always less than that in the vacuum and is independent of the frequency of the wave.

The refractive index of a medium is defined as

Therefore, we get

The refractive index of a dielectric material is the square root of its dielectric constant.

Good conductor: For a good conductor and the phase constant is

Multiplying numerator and denominator within the square root sign by and re-arranging we get

For a good conductor and therefore . The electromagnetic wave therefore slows down considerably in a conductor. As can be seen from the example, the phase velocity of an electromagnetic wave inside copper is few hundred meter/s which is of the order of the velocity of sound in copper. Module 4 : Uniform Plane Wave Lecture 30 : Phase Velocity of a Wave

Recap

In this course you have learnt the following

Velocity of a wave (phase velocity).

Phase velocity in different media.

Dispersion in a medium having finite conductivity.