Summary

Maxwell found an inconsistency in the Ampere’s law and suggested the existence of an additional current, called displacement current, to remove this inconsistency. This displacement current is due to time-varying electric field and is given by \[ i_{d}=\varepsilon_{0} \frac{\mathrm{d} \Phi_{\mathrm{E}}}{\mathrm{d} t} \] and acts as a source of magnetic field in exactly the same way as conduction current.
An accelerating charge produces electromagnetic waves. An electric charge oscillating harmonically with frequency ν , produces electromagnetic waves of the same frequency ν . An electric dipole is a basic source of electromagnetic waves.
Electromagnetic waves with wavelength of the order of a few metres were first produced and detected in the laboratory by Hertz in 1887. He thus verified a basic prediction of Maxwell’s equations.
Electric and magnetic fields oscillate sinusoidally in space and time in an electromagnetic wave. The oscillating electric and magnetic fields, E and B are perpendicular to each other, and to the direction of propagation of the electromagnetic wave. For a wave of frequency ν , wavelength λ , propagating along z-direction, we have \[ \begin{aligned} E &=E_{x}(t)=E_{0} \sin (k z-\omega t) \\ &=E_{0} \sin \left[2 \pi\left(\frac{z}{\lambda}-v t\right)\right]=E_{0} \sin \left[2 \pi\left(\frac{z}{\lambda}-\frac{t}{T}\right)\right] \\ B &=B_{y}(t)=B_{0} \sin (k z-\omega t) \\ &=B_{0} \sin \left[2 \pi\left(\frac{z}{\lambda}-v t\right)\right]=B_{0} \sin \left[2 \pi\left(\frac{z}{\lambda}-\frac{t}{T}\right)\right] \end{aligned} \] They are related by \( E_{0} / B_{0} = c \).
The speed c of electromagnetic wave in vacuum is related to µ 0 and ε 0 (the free space permeability and permittivity constants) as follows \(c=1 / \sqrt{\mu_{0} \varepsilon_{0}}\). The value of c equals the speed of light obtained from optical measurements. Light is an electromagnetic wave; c is, therefore, also the speed of light. Electromagnetic waves other than light also have the same velocity c in free space. The speed of light, or of electromagnetic waves in a material medium is given by \[ v=1 / \sqrt{\mu \varepsilon} \] where \(\mu\) is the permeability of the medium and \(\varepsilon \) its permittivity.
Electromagnetic waves carry energy as they travel through space and this energy is shared equally by the electric and magnetic fields. Electromagnetic waves transport momentum as well. When these waves strike a surface, a pressure is exerted on the surface. If total energy transferred to a surface in time t is U, total momentum delivered to this surface is \( p = U/c \)
The spectrum of electromagnetic waves stretches, in principle, over an infinite range of wavelengths. Different regions are known by different names; γ-rays, X-rays, ultraviolet rays, visible rays, infrared rays, microwaves and radio waves in order of increasing wavelength from \( 10^{-2} \) Å or \( 10^{-12} \) m to \( 10^6 \) m. They interact with matter via their electric and magnetic fields which set in oscillation charges present in all matter. The detailed interaction and so the mechanism of absorption, scattering, etc., depend on the wavelength of the electromagnetic wave, and the nature of the atoms and molecules in the medium.