Electromagnetic Waves

1. A time-varying magnetic field gives rise to an electric field. Maxwell argued that a time-varying electric field should also give rise to a magnetic field. Maxwell thus tried to apply Ampere’s circuital law to find magnetic field outside a capacitor connected to a time-varying current. However, he noticed an inconsistency in Ampere’s circuital law.

2. To remove the inconsistency of Ampere’s circuital law, Maxwell suggested the existence of  "Displacement current”.

3. Displacement current ($ I_d$) is currents which come into play whenever the electric field and, consequently, the electric flux is changing with time. Mathematically, \[I_d = \epsilon_0 \frac{d\phi_E}{dt}\]

4. The sum of conduction current (I) and displacement current ($ I_d $) has the property of continuity along any closed path, although individually they may not be continuous. Thus, Maxwell modified Ampere’s circuital law as \[\oint \vec{B}.\vec{dl} = \mu_0 (I+I_d)\]With this modification the problem of inconsistency observed by Maxwell was rectified.

5. Maxwell was the first person who theoretically predicted the existence of electromagnetic waves, which are coupled with time-varying electric and magnetic fields propagating in space. The speed of these waves in free space is the same as that of light i.e. $ 3 \times 10^8 $ m/s.

6. Electromagnetic waves are produced by accelerated charges (or oscillating charge). An oscillating charge, which is an example of accelerating charge produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn is a source of oscillating electric field and so on. The oscillating electric filed and magnetic fields, thus, regenerate each other i.e., electromagnetic wave propagates through the space.

7. The frequency of the electromagnetic wave is same as the frequency of oscillation of the charge (electric field E) or the frequency of oscillating magnetic field (B).

8. Hertz was the first scientist to experimentally demonstrate the production of electromagnetic waves employing a crude form of an oscillatory LC circuit arrangement. Later on, Jagdish Chandra Bose produced electromagnetic waves of much shorter wavelengths. Marconi succeeded in transmitting electromagnetic waves over a distance of many kilometers.

9. Electromagnetic waves do not require any material medium for their propagation. In free space, their speed is given by \[c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8\]In a medium of absolute permittivity (), the speed of electromagnetic waves is given by \[c = \frac{1}{\sqrt{\mu \epsilon}} = \frac{c}{\sqrt{K\mu_r}}\]

10. In an electromagnetic wave and electric and magnetic fields are in phase with each other. They attain their peak values at the same instant.

11. Electromagnetic waves are transverse in nature. The oscillating electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of the wave. In fact, the direction of ($ \vec{E}\times \vec{B} $) gives the direction of propagation of e.m. waves.

12. If we consider an electromagnetic wave propagating along positive x-axis then oscillating electric and magnetic fields may be represented as:\[\vec{E_y} = E_0sin(kx-\omega t)\hat{j}\] and \[\vec{B_z} = B_0sin(kx-\omega t)\hat{k}\]Here $\omega = 2\pi \nu $ is the angular frequency and $k = (\frac{2\pi}{\lambda})$ propagation constant of given electromagnetic wave.

13. In an electromagnetic wave, Amplitudes $E_0$ and $B_0$ of electric and magnetic fields in free space are related as: \[\frac{E_0}{B_0} = c\]

14. The energy density i.e., energy per unit volume of an electromagnetic wave consists of electric and magnetic contributions. Thus, The mean energy density \[U_m = U_E + U_B = \frac{1}{2}\epsilon_0 E^2_{rms} + \frac{1}{2\mu_0}B^2_{rms}\] It is found that average values of $ U_E $ and $ U_B $ are equal. 

15. Intensity of the electromagnetic wave is defined as the mean amount of energy passing through a unit area normally in unit time. It can be shown that Intensity \[I = U_m c = \frac{1}{2}\epsilon_0 c E^2_0 = \frac{c}{2\mu_0}B^2_0\]

16. The electromagnetic wave carries momentum too. If U be the total energy transferred to a surface by an electromagnetic wave in time t, then momentum delivered to this surface, assuming the surface to be completely absorbent, is \[p = \frac{U}{c}\]The average force exerted by e.m. wave on the surface will be \[F= \frac{p}{t} = \frac{U}{ct}\]

17. The classification of electromagnetic radiation waves according to frequency is known as “electromagnetic spectrum”. There is no sharp division between one kind of wave and the next and the classification is based roughly on how the waves are produced/ detected.

18. Complete electromagnetic spectrum in ascending order of frequency (or in decreasing order of wavelength) broadly consists of seven parts namely 

(i) Radio waves, (ii) Microwaves (iii) Infrared waves, (iv) Visible light rays, (v) Ultraviolet rays, (vi) X-rays, and (vii) Gamma rays.

19. Radio waves are produced by accelerated motion of charges in conducting wires and are used in radio and TV communication. They are in the frequency range of 500kHz to about 1000 MHz (or 1 GHz). These are further subdivided as a medium band, short band, HF band, VHF band, UHF band, etc.

20. Microwaves are extremely short-wavelength radio waves having a frequency range of $ 10^9 $ Hz to about 10 11 Hz and are produced by special vacuum tubes e.g., klystrons, magnetrons, and Gunn diodes. These are used in radar, microwave telecommunication, microwave oven, etc.

21. Inferred waves are produced by hot bodies and molecules and are characterized by their heating property. Inferred radiation plays an important role in maintaining the earth’s warmth by the greenhouse effect. Inferred rays are widely used in the remote switches of household electronic systems such as TV sets, video recorders, hi-fi systems, etc.

22. Visible parts are that part of the electromagnetic spectrum which is detected by the human eye. It runs from about $ 4 \times 10^{14} $ Hz to $ 7 \times 10^{14} $ Hz. Visible light emitted or reflected from objects around us provides us information about the world.

23. Ultraviolet rays consist of radiation in the frequency range $ 7 \times 10^{14} $Hz to $ 5 \times  10^{17} $ Hz (or wavelength range from 400 nm to 0.6 nm). These are produced by the sun, special lamps like mercury lamp, hydrogen tube etc, and very hot bodies. Ultraviolet rays have various uses such as in  LASIK eye surgery, to kill germs in water purifiers, as a disinfectant in hospitals, etc. however, ultraviolet light in large quantities has harmful effects on humans.

24. Ozone layer present in the atmosphere at an altitude of about 40 – 50 km absorbs most of the ultraviolet rays coming from the sun and thus, form a protective ring around the earth.

25. X-rays cover wavelengths from about 1 nm to $10^{-3} $ nm. These are produced by bombarding high energy electrons on a metal target. X-rays are used as a diagnostic tool in medicine, as a treatment for certain forms of cancer, and for scientific research.

26. Gamma rays are the hardest electromagnetic waves having wavelengths even less than $ 10^{-3} $ nm. These are produced in nuclear reactions and are also emitted during radioactive decay of the nuclei. These are used in medicine for destroying cancer cells.

Electromagnetic Spectrum

Type	Wavelength range	Production	Detection
Radio	> 0.1 m	Rapid acceleration and decelerations of electrons in aerials	Reciever's aerial
Microwave	0.1 m to 1 mm	Klystron valve or magnetron valve	Point contact diode
Infrared	1 mm to 700 nm	Vibration of atoms and molecules	Thermopiles, Bolometer, Infrared photographic film
Light	700 nm to 400 nm	Electrons in atom emit light when they move from one energy level to a lower energy level	The eye Photocells, Photographic film
Ultraviolet	400 nm to 1 nm	Inner shell electrons in atoms moving from one energy level to lower level	Photocells, Photographic film
X-ray	1 nm to $10^{-3}$ nm	X-ray tubes or inner shell electrons	Photographic film, Geiger tubes, Ionisation chamber
Gamma Ray	< $ 10^{-3} $ nm	Radioactive decay of the nucleus	- do -