Spread the love

Transverse Nature of Electromagnetic Waves | Nature of Electromagnetic Waves

Transverse Nature of Electromagnetic Waves | Nature of Electromagnetic Waves :- Electromagnetic waves are a type of energy that travels through space at the speed of light. They are generated by oscillating electric and magnetic fields and unlike mechanical waves like sound, they do not require any medium for propagation. Radio waves, microwave waves, infrared waves, visible light, ultraviolet rays, X-rays and gamma rays etc. are electromagnetic waves of different wavelengths and frequencies.

Electromagnetic waves arise from oscillating electrical circuits and are transverse waves, which means that the oscillations of the electric and magnetic fields are perpendicular to each other as well as to the direction of wave propagation.

In the above figure, $\displaystyle \overrightarrow{E}$ and $\displaystyle \overrightarrow{B}$ are in the direction of Y-axis and Z-axis respectively and the transmission of electromagnetic wave is along $\displaystyle \overrightarrow{E }\times \overrightarrow{B}$ i.e. along the X-axis. Electromagnetic waves can be expressed like the equation of a plane progressive wave by the following equations :-

$\displaystyle {{E}_{y}}={{E}_{0}}\sin (kx-\omega t)\text{ }.....(1)$

$\displaystyle {{B}_{z}}={{B}_{0}}\sin (kx-\omega t)\text{ }.....(2)$

Here

$\displaystyle {{E}_{0}}$ = Peak value (or amplitude) of electric field

$\displaystyle {{B}_{0}}$ = Peak value (or amplitude) of magnetic field

$\displaystyle {{E}_{y}}$ = instantaneous value of electric field

$\displaystyle {{B}_{z}}$ = instantaneous value of magnetic field

$\displaystyle k=\frac{2\pi }{\lambda }$ = propagation constant

$\displaystyle \omega$ = angular frequency

Maxwell proved mathematically that electromagnetic waves travel in free space (or vacuum) with the following speed :-

$\displaystyle c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\text{ }.....(3)$

Where μ₀= 4π × 10^-7 Weber/ampere meter and ε₀=8.854 × 10^-12 Coulomb²/ Newton meter² are the magnetic permeability of vacuum and the electrical permittivity of vacuum respectively. Substituting these values in equation (3),

$\displaystyle c=\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}=\frac{1}{\sqrt{4\pi \times {{10}^{-7}}\times 8.854\times {{10}^{-12}}}}$

$\displaystyle \Rightarrow c\approx 3\times {{10}^{8}}m/s$

The speed of electromagnetic waves in any medium is given by the following formula :-

$\displaystyle v=\frac{1}{\sqrt{\mu \varepsilon }}\text{ }.....(4)$

Here μ and ε are the magnetic permeability and electrical permittivity of the given medium respectively.

Now we know that μ = μ₀ μ_r and ε = ε₀ ε_r, here μ_r and ε_r are relative permeability and relative permittivity of the medium respectively.

Therefore

$\displaystyle v=\frac{1}{\sqrt{{{\mu }_{0}}{{\mu }_{r}}{{\varepsilon }_{0}}{{\varepsilon }_{r}}}}=\frac{c}{\sqrt{{{\mu }_{r}}{{\varepsilon }_{r}}}}\text{ }.....(5)$

As $\displaystyle \frac{c}{v}=n=Refractive\text{ }Index$ , hence, from equation (5) the refractive index (n) of any medium,

$\displaystyle n=\sqrt{{{\mu }_{r}}{{\varepsilon }_{r}}}\text{ }.....(6)$

During the propagation of an electromagnetic wave, the ratio of the magnitudes of the electric and magnetic field vectors at any point is equal to the speed of light. In vacuum,

$\displaystyle c=\left| \frac{\overrightarrow{E}}{\overrightarrow{B}} \right|\text{ }.....(7)$

When the wavelength of vibrations of electric and magnetic fields is in a certain range from 0.4 µm to 0.7 µm, then the vector $\displaystyle \overrightarrow{E}$ produces a visual effect on the retina of the human eye and these waves become visible to us. Which we call visible light. Due to visible light, we see phenomena of light like reflection, refraction, interference etc. The color of visible light depends on the wavelength (or frequency) of these vibrations, for example, if the wavelength is 450 nm to 495 nm then this light appears blue to us and similarly when the wavelength is 550 nm then this light appears green to us. The electric field $\displaystyle \overrightarrow{E}$ is more effective and important than the magnetic field $\displaystyle \overrightarrow{B}$ .