# Electromagnetic Waves , Equations of Electromagnetic Waves

Electromagnetic Waves :

The idea of electromagnetic waves was given by Maxwell and experimental verification was provided by Hertz and other scientists.
On the basis of experimental study of electromagnetic induction, Faraday concluded that a magnetic field changing with time at a point produces a time varying electric field at that point.
Maxwell in 1864 pointed out an electric field changing with time at a point also produces a time varying magnetic field. The two fields are mutually perpendicular to each other.
This idea led Maxwell to conclude that the mutually perpendicular time varying electric and magnetic fields produce electromagnetic disturbances in space. These disturbances have the properties of wave which are called as electromagnetic waves.

According to Maxwell:

Electromagnetic waves are those waves in which there are sinusoidal variation of electric and magnetic field vectors at right angle to each other as well as right angles to the direction of wave propagation. The velocity of electromagentic waves in free space is equal to the velocity of light. Therefore, light is electromagnetic waves. The electromagnetic waves are transverse in nature

Transverse nature of electromagnetic waves:

We have seen that electromagnetic waves consists of a sinusoidally verying electric and magnetic field. These fields act right angles to each other as well as right angles to the direction of propagation of waves. These fields are represented by

E = E0 sin(ω t – kx)

and B = B0 sin(ωt – kx) ; Where k = 2π/λ is wave no.

respectively. The two fields combine to constitute electromagnetic wave. The electromagnetic wave propagates in space in a direction perpendicular to the directions of both fields as shown . The electric field vectors (E) is along Y-axis and magnetic field vector (B) along Z-axis while the wave propagation direction is along X-axis. As both the fields are perpendicular to the direction of propagation of electromagnetic wave and hence the electromagnetic waves are transverse in nature.

Some important points:

(1)  Electromagnetic waves can travel through vacuum.

(2)  These waves are produced by accelerated or oscillating electric charge.

(3) The sinusoidal variations of and occur with the same frequency and hence they attain the maxima and minima at the same time .

(4)  The amplitudes of electric and magnetic fields bear a constant ratio of the speed of light i.e. $\displaystyle \frac{E_0}{B_0} = c$

(5)  The speed of electromagnetic waves is a function of the electric and magnetic properties of the medium in which these waves travel and is independent of the amplitude of the field vectors.

(6)  The velocity of light in free space is given by

$\displaystyle c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$

### Poynting vector

Poynting vector is a vector that describes the magnitude and direction of energy flow rate .

$\displaystyle \vec{S} = \frac{\vec{E}\times \vec{B}}{\mu_0}$

Where $\vec{S}$ = Poynting vector
The magnitude of poynting vector represents the rate at which energy flows through a unit surface area perpendicular to the direction of wave propogation SI unit J/sm2 or w/m2

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