[Physics Class Notes] on Propagation Of Electromagnetic Waves Pdf for Exam

Oersted experimentally predicted that the electric current produces a magnetic field. Faraday, from his experiments on electromagnetic induction, found that a varying magnetic field generates an electric current.

Now, the question arises whether the reverse is true? Can a varying electric field produce a magnetic field?

To clear this confusion, Clerk Maxwell performed experiments on capacitors, where he found that the magnetic field is not only produced by electric current; however, it also by a time-varying electric field.

Therefore, he formulated a set of equations involving electric and magnetic fields and their sources; charge and current. These equations are called Maxwell equations. These equations, along with the Lorentz force formula mathematically explain all the laws of electromagnetism. 

Through these equations, Maxwell came out with an important prediction, i.e., Electromagnetic waves.

He stated that electromagnetic waves (em waves) travel with the speed of light, i.e. [3 ? 10^{8}m/s].

It led him to conclude that light is electromagnetic radiation, and it is carried in the electromagnetic waves.

In 1885, Hertz demonstrated experimentally, the existence of em waves.

Later, Marconi, the father of wireless communication, established this communication technology by using em waves.

Nowadays, this technology has revolutionized our life.

Now, let’s understand the em waves.

What are Electromagnetic Waves?

EM waves are the oscillations or vibrations that create electromagnetic radiation.

These waves are produced because of the oscillation of electric and magnetic fields.

The direction of the oscillation of an electric field, magnetic field, and the direction of the propagation of waves are perpendicular.

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These waves travel in a space with speed very close to the speed of light, i.e. [3 ? 10^{8}m/s].

Propagation of Electromagnetic Waves

According to Maxwell, the electromagnetic waves are those waves in which there is a sinusoidal variation of electric and magnetic field vectors are at right angles to each other, and the direction of wave propagation.

The electric field vectors (E) and the magnetic field vectors are vibrating along the Y, and the X-axis respectively, and the direction of propagation of a wave is shown on the Z-axis. This means em waves are transverse in nature.

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If you look at this figure, the em waves are generated by the oscillating molecular dipole or discharging capacitor.

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The spark current oscillates at a frequency (f) and the oscillator determines this frequency, while the wavelength is determined by the oscillation frequency divided by the velocity of the wave, i.e. λ = f/v.

Maxwell found that light travels in free space with a speed given by

                                         c  = 1/√μ0ε0…(1)

 Here,  c = speed of light,

            μ0   =  permeability; its value = [4 ? ? 10^{-7}]Wb[A^{-1}][m^{-1}].

            ε0 = Permittivity of free space; its value = [8.85 ? 10^{-12}][C^{2}][N^{-1}][m^{-2}].

Putting these values in eq(1), we get c =  [3.00 ? 10^{8}m/s].

The velocity of em waves is given by

                      v = 1/√με….(2)

Here, μ and ε are absolute permeability and permittivity, respectively. 

We know that μ = μr μ0  (product of vacuum and the relative permeability), and

                      ε = εrε0 (product of vacuum and the relative permittivity)

So, the formula in eq(2) becomes:

                              v = 1/√ μr μ0εrε0 …(3)

Now, putting the value of eq(3) in eq(3), we get,               

Properties of Electromagnetic Waves

The properties of em waves are like all the waves that exist in nature.

Let’s discuss these properties one by one:

1. These waves have a velocity, frequency, and wavelength.

2. They oscillate periodically.

Here, the properties display electromagnetic waves, characteristics viz amplitude,  frequency, and wavelength that defines the energy, direction, and intensity of the radiation.

Electromagnetic Waves Characteristics

1. In a vacuum,  the average electric energy density (uE) and average magnetic energy (uB) because of static electric field E and magnetic field (B) which remains constant with time and is given by

                       uE  = 1/2ε0[E^{2}]  and uB = [B^{2}]/2μ0

        So, total energy density = uE + uB = 1/2ε0[E^{2}]  + [B^{2}]/2μ0

2. In em waves, the electric and magnetic fields vary sinusoidally with space (s) and time (t).

Now, replacing the above expression with their RMS values, we get,

           uE  = 1/2ε0Erm[s^{2}] and  uB = Brm[s^{2}]/2μ0.    

Since Brms = E rms/c and c =1/√μ0ε0

The total average energy density, uavg  = uE + uB = 2uE = 2uB

= 2 x 1/2ε0Erm[s^{2}] = ε0Erm[s^{2}]= Brm[s^{2}]/μ0.

Therefore, ε0E[0^{2}]=  B[0^{2}]/μ0.

3. The electric vector is responsible for the optical effects of em waves
   and is also called the Light vector.

4. The em waves are uncharged, so they don’t get deflected by electric and magnetic fields.

5. The velocity of the em wave in the dielectric is less than 3 ? [10^{8}] m/s.