# Electromagnetic Waves

### Electromagnetic Oscillations

A time varying electric field produces a magnetic field and a time varying magnetic field produces an electric field. Therefore Maxwell predicted that there exists a wave of electric and magnetic fields, both varying with space and time and acting as sources of each other. Thus an electromagnetic wave is started.

In an electromagnetic wave both electric and magnetic fields are mutually perpendicular and also both perpendicular to the direction of wave propagation.

The widely used source of production of electromagnetic waves is inductance-capacitance circuit (or LC circuit), also called the tank circuit. The frequency of oscillations being given by:

$f = \dfrac{1}{2 \pi \sqrt{LC}}$

### A brief history of electromagnetic waves

(a) In 1865 Maxwell predicted the presence of electromagnetic waves. He formulated the theory in terms of four Maxwell’s equations.

Maxwell’s four equations are mathematical form of the basic laws of electrostatics and magneto statics.

(i) Gauss’s Law of electrostatics:

$\oint_{s} \overrightarrow{E} \, \overrightarrow{ds} = \dfrac{1}{\epsilon _0} Q \cdots Equation \, \, \, 1$

Where Q is total charge enclosed by closed surface S.

(ii) Gauss’s law of magnetism is:

$\oint_{s} \overrightarrow{B} \, \overrightarrow{ds} = 0 \cdots Equation \, \, \, 2$

(iii) Faraday’s law of electromagnetic induction is:

$\oint_{0} \overrightarrow{E} \, \, \overrightarrow{dl} = - \dfrac{d \varphi m}{dt} \cdots Equation \, \, 3$

Where $\overrightarrow{E}$ = electric field strength, $\oint$ represents line integral along closed path and $\emptyset _m$ is the magnetic flux.

(iv) Modified Ampere’s law: Ampere’s law of magnetism was modified by Maxwell.

The modified law is:

$\oint \overrightarrow{B} \, \, \overrightarrow{dl} = \mu _0 ( I + \epsilon _0 \dfrac{d \emptyset E}{Pdt} )$

Where I is the current produced by moving charges and $\epsilon _0 \dfrac{d \emptyset E}{dt}$ is the displacement current, which is caused by varying electric field.

The maxwell’s equations predict that the electromagnetic waves are transverse and the electromagnetic waves of all frequencies propagate with the speed of light.

(b) Hertz in 1888 succeeded in producing and observing electromagnetic waves of wavelength of the order of 6m in the laboratory.

(c) J. C. Bose in 1895 succeeded in producing and observing electromagnetic waves of much shorter wavelength 25 mm -5 mm.

(d) G. Marconi in the same year succeeded in transmitting electromagnetic waves over distances of many kilometers.

### Characteristics of Electromagnetic waves

(i) In electromagnetic waves electric field vector $\overrightarrow{B}$ and propagation vector $\overrightarrow{K}$ are mutually perpendicular. Hence electromagnetic waves are transverse in nature.

(ii) Electromagnetic waves travel with speed in light.

In vaccum their speed is$c = \dfrac{1}{ \sqrt{ \mu _0 \epsilon}}$

In isotropic medium, their speed is:

$v = \dfrac{1}{\sqrt{\mu \epsilon}} = \dfrac{1}{\mu _r \mu _0 \epsilon _r \epsilon _0} = \dfrac{1}{\sqrt{\mu _r \epsilon _r}} \dfrac{1}{\sqrt{\mu _0 \epsilon _0}}$

$= \dfrac{1}{\mu} c = \dfrac{c}{\mu}$

Where $\mu = \dfrac{1}{\sqrt{\mu _r \epsilon _r}}$ = refractive index of medium

$\mu _r$ = relative permeability and

$\epsilon _r$ = relative permittivity or dielectric constant

(iii) The Pointing vector $\overrightarrow{S} = \overrightarrow{E} \times \overrightarrow{H}$ represent the power flow per unit area along the direction of wave propagation. It unit is $Watt / M^2$ .

(iv) Wave Impedance: the medium offers hindrance to the propagation of electromagnetic wave called the wave impedance and its value is given by:

$\dfrac{1}{2} \epsilon E^2 rms = \dfrac{B^2 rms}{2 \mu}$

### Electromagnetic Spectrum

The electromagnetic waves extend from very short gamma rays to long radio waves. The classification of spectrum according to wavelength/frequency range is given below:

 Name Wave length range Frequency range (i) Gamma Rays $10 ^ {-3} A - 1 A$ $10^{21} Hz - 10^{18} hz$ (ii) X –Rays $1 A - 100 A$ $10^{18} Hz - 10^{16} Hz$ (iii) Ultraviolet rays $100 A - 4000 A$ $10^{16} - 8 \times 10^{14} Hz$ (iv) Visible Rays $4000 A - 7800 A$ $8 \times 10^{14} Hz - 4 \times 10^{14} hz$ (v) Infrared rays 7800 A – 1mm $4 \times 10^{14} Hz - 3 \times 10{11} Hz$ (vi) Short Radio waves or Hertzian Waves 1mm – 1m $3 \times 10^{11} Hz - 3 \times 10^9 Hz$ (viii) Long Radio Waves $1 m - 10^4 m$ $10^9 Hz - 10^4 Hz$

Remarks: $\alpha \, \, \, and \, \, \, \beta$ rays are not electromagnetic waves and they are emitted from radioactive substance; out of these only $\gamma$ rays are electromagnetic.

### Properties of Atmosphere w.r. to various parts of electromagnetic spectrum

(i) The atmosphere is transparent to visible radiation.

(ii) The atmosphere absorbs most of infrared radiations.

(iii) Earth is heated by sun’s infrared radiations. The earth also emits radiations most in infrared region. These radiations are reflected back by atmosphere. These back radiations keep the earth’s surface warm at night. This phenomenon is called Greenhouse effect.

(iv) The ozone layer which is some 50-80 km above the ground (mesosphere) absorbs ultraviolet radiations, thus protects us from harmful radiations of sun. Practically all radiations of wavelength less than $3000 A = 3 \times 10^{-7} m$ are absorbed by ozone layer.

(v) The waves of wavelength 1 mm or higher are broadly called radio waves. They include radio, television and microwaves. Waves having wavelength 10 cm or more (frequencies less than 30 MHZ) are termed as amplitude modulated waves. These waves are transmitted in lower atmosphere but reflected by top-most region called ionosphere.

These waves are of two types:-

(a) Ground Waves: These follow surface of earth.

(b) Sky waves: They are reflected back by ionosphere.

The ground waves are attenuated depending on frequency. The communication up to 1500 Kc/s may be via ground waves but above this frequency the communication is via sky waves. These two regions of waves of Amplitude modulated waves are termed as medium waves and short radio waves respectively.

For waves above 40 MHz, the ionosphere behinds incident waves but does not reflect back to earth. T.V. signal waves 100 MHz – 200 MHz called frequency modulated waves neither follow the curvature of earth not get reflected by ionosphere, their reception is possible either by large antenna or by geostationary satellites.

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