Electromagnetic Waves

Electromagnetic Waves


Displacement Current

Displacement current comes into existence in the region, whenever the electric field or electric flux is changing with respect to time.

The displacement current is defined by the relation

where = absolute permittivity of space and = rate of change of electric flux.

When there is a steady electric flux linked with a region, the displacement current is zero.


Ampere-Maxwell law

The line integral of magnetic field over a closed path in vacuum is equal to ₀ times the sum of the conduction current (I) and displacement current (I_D).



The sum of conduction current and displacement current provides continuity along any closed path although individually they may not be continuous.

Maxwell's Equations

(a) (Gauss's theorem in electrostatics)

The electric lines of force start from positive charge and end on negative charge i.e. the electric lines of force do not form a continuous closed path.

(b) (Gauss's law in magnetism)

The number of magnetic lines of force leaving a closed surface is equal to number of magnetic lines of force entering that same closed surface.

(c) (Faraday's law of electromagnetic induction)

Line integral of electric field is equal to the magnitude of rate of change of magnetic flux.

(d) (Ampere-Maxwell law)

It states that the magnetic field can be produced by a conduction current as well as by a displacement current.



Important features of Electromagnetic waves

E.M. waves are transverse waves in which there are sinusoidal variations of electric and magnetic fields. These two fields exist at right angles to each other as

well as at right angles to the direction of wave propagation.

Both these fields vary with time and space and have the same frequency of variation. These waves can travel through vacuum also.

Velocity of electromagnetic wave in free space (vacuum) is constant and given by



Direction of wave propagation is given by the direction of .

The amplitudes of electric and magnetic fields in free space, in electromagnetic waves are related by E₀= cB₀

NOTE : The velocity of electromagnetic wave does not depend on amplitude of field metros.

Energy Density of Electromagnetic Wave
Consider a plane electromagnetic moving through a medium. The electric and magnetic field in such a plane electromagnetic wave can be given by

and .

The average energy density of electric field is,

The average energy density of magnetic field is,

The average energy density due to either field are equal, i.e. U_E= u_B

Total average energy density


Intensity of Electromagnetic Wave
The intensity of E.M. wave is the energy of electromagnetic wave crossing per unit time per unit area perpendicular to the direction of propagation of wave.

Expression for the intensity of electromagnetic wave is as given below :





Momentum of Electromagnetic Wave

The electromagnetic wave has linear momentum associated with it. The linear momentum p carried by the portion of wave having energy U is given by

If the electromagnetic wave incident on a material surface is completely absorbed, it will deliver energy U and momentum p = U/c to the surface. Due to this

momentum change, there is force exerted on the surface.



Radiant Flux of Electromagnetic Wave
According to Maxwell, the accelerated charged particles produce electromagnetic waves. The total radiant flux emitted at any instant is given by

Here q is the charge carried by the particle and a is its instantaneous acceleration.


Poynting Vector

When an electromagnetic wave advances, the electromagnetic energy flows in the direction of . The total energy flowing per second per unit area perpendicular to the surface in free space (vacuum) is called a Poynting vector , where . The S.I. unit of S is watt/ (metre)².


Radiant Flux Density

Radiant flux density is the average value of poynting vector () over a convenient time interval in the propagation of electromagnetic wave. When the

electromagnetic wave is incident on a surface, the radiant flux density is called intensity of wave (which is denoted by I). Thus I = S.

A harmonic electromagnetic wave travelling along X-axis in free space can be described by periodic variation of electric and magnetic fields along y-axis and z-

axis with the equations.

and

Then radiant flux density is given by

Therefore . The average value of over a single cycle period T is given by



Electromagnetic Spectrum

The orderly distribution of electromagnetic radiations according to their wavelengths or frequency is called the electromagnetic spectrum.

The major components of electromagnetic spectrum with their wavelength ranges in increasing order are

1. Gamma rays [ = 6 × 10^-19m to 10^-11m]

2. X-rays [= 10^-11m to 3 × 10^-8m]

3. Ultraviolet [= 6 × 10^-10m to 4 × 10^-7m]

4. Visible light [= 4 × 10^-7m to 8 × 10^-7m]

5. Infra red [= 8 × 10^-7m to 3 × 10^-5m]

6. Heat radiations [= 10^-5m to 10^-1m]

7. Micro waves [= 10^-3m to 0.03 m]

8. Ultra high frequency [= 10^-1m to 1 m]

9. Very high radio frequency [= 1 m to 10 m]

10. Radio frequencies [ = 10 m to 10⁴m]

11. Power frequencies [ = 5 × 10⁶m to 6 × 10⁶m]


Typical uses of electromagnetic spectrum

1. Radio and Microwave radiations are used in radio and T.V. communication systems. Microwave radiations are also used in Radar communication.

2. Infrared radiations are used (i) in green houses to keep the plants warm (ii) in highlighting the secret writings on ancient walls (iii) for looking through haze, fog

and mist during war time, as these radiations can pass through them.

3. Ultraviolet radiations are used (i) in preserving processed food by killing microorganisms (ii) in the detection of invisible writing, forged documents, finger prints

in forensic laboratory. (iii) For understanding the structure of the molecules and arrangement of electrons in the external shells of atoms.

4. X-rays have wide field of applications. These are used to get valuable information (i) about the structure of atomic nuclei (ii) in the study of crystal structure (iii)

about the fracture of bones and other medical diagnosis etc.