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 \(\nu\), produces electromagnetic waves of the same frequency \(\nu\). 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, \(\mathbf{E}\) and \(\mathbf{B}\) are perpendicular to each other, and to the direction of propagation of the electromagnetic wave. For a wave of frequency \(\nu\), wavelength \(\lambda\), propagating along \(z\)-direction, we have \( \begin{aligned} E & =E_x(t)=E_0 \sin (k z-\omega t) \\ & =E_0 \sin \left[2 \pi\left(\frac{z}{\lambda}-\nu t\right)\right]=E_0 \sin \left[2 \pi\left(\frac{z}{\lambda}-\frac{t}{T}\right)\right] \\ B & =B_y(t)=B_0 \sin (k z-\omega t) \\ & =B_0 \sin \left[2 \pi\left(\frac{z}{\lambda}-\nu t\right)\right]=B_0 \sin \left[2 \pi\left(\frac{z}{\lambda}-\frac{t}{T}\right)\right] \end{aligned} \) They are related by \(E_0 / B_0=c\).
The speed \(c\) of electromagnetic wave in vacuum is related to \(\mu_0\) and \(\varepsilon_0\) (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.
The spectrum of electromagnetic waves stretches, in principle, over an infintte range of wavelengths. Different regions are known by different names; \(\gamma\)-rays, X-rays, ultraviolet rays, visible rays, infrared rays, microwaves and radio waves in order of increasing wavelength from \(10^{-2} Å\) or \(10^{-12} \mathrm{~m}\) to \(10^6 \mathrm{~m}\). 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.
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The basic difference between various types of electromagnetic waves lies in their wavelengths or frequencies since all of them travel through vacuum with the same speed. Consequently, the waves differ considerably in their mode of interaction with matter.
Accelerated charged particles radiate electromagnetic waves. The wavelength of the electromagnetic wave is often correlated with the characteristic size of the system that radiates. Thus, gamma radiation, having wavelength of \(10^{-14} \mathrm{~m}\) to \(10^{-15} \mathrm{~m}\), typically originate from an atomic nucleus. X-rays are emitted from heavy atoms. Radio waves are produced by accelerating electrons in a circuit. A transmitting antenna can most efficiently radiate waves having a wavelength of about the same size as the antenna. Visible radiation emitted by atoms is, however, much longer in wavelength than atomic size.
Infrared waves, with frequencies lower than those of visible light, vibrate not only the electrons, but entire atoms or molecules of a substance. This vibration increases the internal energy and consequently, the temperature of the substance. This is why infrared waves are often called heat waves.
The centre of sensitivity of our eyes coincides with the centre of the wavelength distribution of the sun. It is because humans have evolved with visions most sensitive to the strongest wavelengths from the sun.