Chapter:   ELECTROMAGNETIC WAVE

What is em wave ? how it is produced ?and all kind of feature are explained here.

The propagating in space through electric and magnetic field varying in space and time simultaneously are called electromagnetic wave .

Origin – The electro magnetic wave are produced by an accelerated and deaccelerated charge or LC circuit . T he frequency of the electromagnetic wave is  ѵ = 1/2Π √LC .

Characteristics of em wave –

1. The electro magnetic waves is produced in free space with speed of light
2. em waves are neutral , so they are not deflected by electric and magnetic field .

• The em waves shows the properties of reflection, refraction , diffraction and polarisation.

1. In em wave the electric and magnetic field are always in the same phase .
2. The ratio of electric field and magnetic field in free space is constant which is equal to velocity of light ( c ) i.e. E₀/B₀ =1/√µ₀ϵ₀ =C=3 X 10⁸ m/s .
3. In an em wave the energy is propagated by means of electric and magnetic field vectors in the direction of propagation of wave .

Maxwell’s modification of Ampere’s law and displacement current –

According to Ampere’s the line integral of magnetic field for a closed path is µ₀ times the total current passes through the closed loop. i.e. ∫B. dl = µ₀ I but Maxwell modified the law and, dc according to him ∫B. dl = µ₀ (I + I_D) Where I_d is the displacement current.

 Displacement current – It is the current which come in the existence due to the rate of change of electric flux with respect to time

As we know I = dQ/dt but between the plates of the capacitor  ,

Electric field E = Q/ A ϵ₀ and hence Q = E A ϵ₀ = ɸ₀ ϵ₀ (WHERE ɸ₀ = electric flux)

But, I = dɸ₀ /dt = ϵ₀ dɸ₀ /dt.

So we can write improved form of Ampere’s law ∫ B. dl = µ₀ ( I + ϵ₀ dɸ₀ /dt ) .

Consequences of displacement current –

(a)with the discovery of displacement current the law of electricity and magnetism become more symmetrical then before .

(b) since the displacement current is produced by time varying electric field , an important link between electric field and magnetic field established .

Hertz’s experiment – Hertz demonstrated the production and detection of electromagnetic wave by electrical means . Experimental arrangement used by Hertz shown in figure :-   S and S’ are the two spheres connected by two large metal plates P and P’ , the spheres are connected to an induction coil . By causing a discharge between the spheres , the current distribution between the plates is such that an electromagnetic wave is generated parallel to the gap SS’ . the radiation thus produced is detected by Hertz by using an open wire loop . the em wave reaches at the gap GG’ of the detector has an electric field is enough the establish a high potential difference between this gap and cause a spark .

When the detector gap GG’ is at right angles to the right gap SS’ , no electromagnetic radiation detected  ,  the sensitivity is maximum  when the gap GG’  is parallel to SS’ . this property explain the transverse nature of the em wave , and em wave propagate perpendicular to the direction of propagation of electric field .

Speed of electromagnetic wave in vacuum –

According to faradays law of electromagnetic induction

∫E. dl = – dɸ_B /dt  ………..eq.1

And according to Ampere-Maxwell’s law , ∫B. dl =µ₀ I + µ₀ ϵ₀ dɸ_E /dt …………………..eq.2

[ ɸ_B Flux for magnetic flux and ɸ_e is the electric flux .]

For a plane polarised em wave travelling in the X- axis eq 1 and 2 gives

dE_y /dx = -dB_Z/dt .

or , dE/dx = – dB/dt ………………………eq. 3

and ,    dB_Z/dx = -µ₀ϵ₀ dE_y/dt .

or ,     dB_x /dx = – µ₀ϵ₀ dE/dt ………………………eq. 4

taking the partial differentiation of eq 3 we get

d(dE/dx)/dx = – d(dB/dt)/dx = – d(dB/dx)/dt .

or d²E/dx² = -d(-µ₀ϵ₀ dE/dt)= µ₀ϵ₀ d² E/dt²……………..eq. 5

similarly ,

d²B/dx² = µ₀ϵ₀ d² B/dt² ………………………………..eq. 5

on comparing eq 5 and 6 we get with the general equation of wave

d²y/dx² = (1/v²) ( d²y/dt²)     where  v is the speed of wave  .

we get 1/v² = µ₀ϵ₀ and hence ,

we can write , v = 1/√ µ₀ϵ₀ or velocity of light in vacuum c = 1/√ µ₀ϵ₀ .

Relation between electric and magnetic field with the speed of electromagnetic wave -the varying electric and magnetic field of a plane electromagnetic wave travelling along X- axis is given as ,

E_y = E₀ sin (kx-ωt) ………………………………………eq. 1

B_z= B₀(kx-ωt) ………………………………………………..eq.2

Here , k = 2Π/λ

ω =2Πѵ ,

Clearly , ω/k = 2Πѵ/ (2Π/λ) = ѵλ = c .

dE/dx = kE₀ cos(kx-ωt)

dB/dt = – ωB₀ cos (kx-ωt)

dE/dx = -dB/dt

kE₀ cos(kx-ωt) = ωB₀ cos(kx-ωt)

KE₀ = ω B₀ .

E₀/B₀ = ω/K = c     ……………….this is the req. relation

Intensity of electromagnetic wave – it is the amount of energy crossing per unit time per unit area perpendicular to the direction of propagation of electromagnetic wave .

Let us consider there is a cylindrical region through which electromagnetic wave passing as wave is perpendicular to its area of cross-action , A is the area of cross-action and l is the length of the cylinder  , then volume of cylinder V = Al

Total energy of the cylinder ; E= U_.x Volume = U Al

Intensity  I = total energy / (time x area) = U Al/ [(l/c) x A]= U X c

Since U = ½ ϵ₀E₀² , therefore  intensity I = ½ ϵ₀E₀² c = ½ ϵ₀E_rms² (√2)² c = I = ϵ₀ E_rms² c .

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Electromagnetic spectrum –

Maxwell predicted the existence of em wave  .

“ The orderly distribution of electromagnetic  radiation according to there frequency / wavelength is called electromagnetic spectrum .”

• Radio wave – It is produced by the accelerated motion of charges in conducting wire or we can say by oscillating electric circuit .

Its frequency range is 500kHz – 1000MHz , wavelength range is 10^-2m – 10⁴m. it reflects , refract and diffract . it is used in radio and t.v. communication.

• Microwave – It is produced by special vacuum tube known as klystrons ,magnetrons . its frequency range is 1GHz – 300GHz . It is used as radar system for aircraft navigation , detect the speed of cricket ball, automobile etc. its another use is in microwave oven .
• Infrared waves – it is produced by hot bodies i.e. vibration of atoms and molecules . Human eye can’t detect it but snake can detect it . These wave is absorbed by water , co₂ and NH₃ . Its frequency range is 10¹¹Hz-10¹⁴Hz and its wavelength is                      between ,  1mm-700nm   . It  can be detected by infrared photographic film . it is used to treat muscle strain  (physical therapy), green house effect, satellite for military purpose and to observe growth of crops, to provide electrical energy in the satellite by using solar cell , to take the photograph during fog and smoke and it is used to study molecular structure.
• Visible light – It is produced by atomic excitation . Its frequency range is 4x 10¹⁴Hz -7x 10¹⁴Hz. , its wavelength lies between 700 nm – 400 nm . It makes the thing visible .
• Ultraviolet ray – It produced by sun , special lamp and very hot bodies . Its frequency lies between 8 x 10¹⁴ Hz – 5 x 10¹⁶ Hz. Its wavelength lies between 400 nm – 0.6 nm . it is detected by photocell and photographic film . It causes the harmful effect on human being. It is used in eye surgery , kill germs in water purifier , to kill the bacteria , in finger print technology.
• X- ray – It is produced in a tube called modern X-ray tube . its frequency range is between 10¹⁶ Hz – 10²¹Hz . its wavelength lies between 10nm – 10^-4nm. It is used as a diagnostic tool in medicine and treatment of certain forms of cancer , in engineering it is used to detect cracks and holes , defect in rubber tyre and gold .
• Gamma rays – it is produced in nuclear reaction they are emitted by radioactive nuclei , its frequency range is 10¹⁸-10²²Hz . its wavelength is less than 10^-3nm. It is detected by photographic film , Geiger tube , ionisation chamber. They shows phosphorescence , fluorescence ,polarisation , diffraction. It has very high penetrating power . it is used for cancer therapy, and it provide important information regarding nuclear structure.

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