ELECTROMAGNETIC WAVES

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1 J-Physics INTRODUCTION LCTROMAGNTIC WAVS A changing electric field produces a changing magnetic field and vice versa which gives rise to a transverse wave known as electromagnetic waves. The time varying electric field and magnetic field mutually perpendicualr to each other are also perpendicualr to the direction of propogation. Thus the electromagnetic waves consist of sinusoidally time varying electric and magnetic field acting at right angles to each other as well as at right angles to the direction of propogation. HISTORY OF LCTROM AGNTIC WAVS In the year 1865, Mawell predicted the electromagnetic waves theoretically. According to him, an accelerated charge sets up a magnetic field in its neighborhood. In 1887, Hertz produced and detected electromagnetic waves eperimentally at wavelength of about 6m. Seven year later, J.C. Bose became successful in producing electromagnetic waves of wavelength in the range 5mm to 5mm. In 1896, Marconi discovered that if one of the spark gap terminals is connected to an antenna and the other terminal is earthed, the electromagnetic waves radiated could go upto several kilometers. The antenna and the earth wires are connected to the two plates of a capacitor which radiates radio frequency waves. These waves could be received at a large distance by making use of an antenna earth system as detector. Using these arrangements; in 1899 Marconi first established wireless communication across the nglish channel i.e., across a distance of about 5 km. CONCPT OF DISPLACMNT CURRNT When a capacitor is allowed to charge in an electric circuit, the current flows through connecting wires. As capacitor charges, charge accumulates on the two plates of capacitor and as a result, a changing electric field is produced across between the two plate of the capacitor. According to mawell changing electric field intensity is equivalent to a current through capacitor known as displacement curent (I d ). If q and q be the charge on the left and right plates of the capacitor respectively at any instant if be the surface charge density of plate of capacitor the electric field between the plate is given by q A Z Y B z y I=I c I=I d c I=I c X Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65 If charge on the plates of the capacitor increases by dq in time dt then dq = I dt change in electric field is d = I = A d dt = d d t d q = A (A) = I dt A d d t d dt = I A d ( = A) I d dt The conduction current is the current due to the flow of charges in a conductor and is denoted as Ic and displacement current is the current due to changing electric field between the plate of the capacitor and denoted as I d so the total current I is sum of I c and I d i.e. I = I c I d Ampere's circuital law can be written as z B. d = (I c I d ) z B. d = (I c d ) dt 19

2 J-Physics MA XWLL' S QUATION There are four mawel' equation given below (1) Gauss law in electrostatics : z. ds q = () Gauss law in magnetism : z B. ds = (3) Faraday's law of electromagnetic induction : emf = (4) Mawell - Ampere's circuital law : z B. d = Ic HRTZ XPRIMNT (Practical production of M waves) In 1888, Hertz demonstrated the production of electromagnetic waves by oscillating charge. His eperimental apparatus is shown schematically in fig. An induction coil is connected to two spherical electrodes with a narrow gap between them. It acts as a transmitter. The coil provides short voltage surges to the spheres making one positive and the other negative. A spark is generated between the spheres when the voltage between them reaches the breakdown voltage for air. As the air in the gap is ionised, it conducts more rapidly and the discharge between the spheres becomes oscillatory. The above eperimental arrangement is equivalent to an LC circuit, where the inductance is that of the loop and the capacitance is due to the spherical electrodes. 11 z. d = d dt L NM d dt O QP B q Input...(i)...(ii)...(iii)... (iv) Induction coil - q Transmitter Receiver lectromagnetic waves are radiated at very high frequency ( 1 MHz) as a result of oscillation of free charges in the loop. Hertz was able to detect these waves using a single loop of wire with its own spark gap (the receiver). Sparks were induced across the gap of the receiving electrodes when the frequency of the receiver was adjusted to match that of the transmitter. PROPRTIS OF LCTROM AGNTIC WAVS The electric and magnetic fields satisfy the following wave equations, which can be obtained from Mawell's third and fourth equations. B B and t t lectromagnetic waves travel through vacuum with the speed of light c, where 1 8 c 3 1 m / s The electric and magnetic fields of an electromagnetic wave are prependicular to each other and also perpendicular to the direction of wave propagation. Hence, these are trnasverse waves. The instantaneous magnitudes of and B in an electromagnetic wave are related by the epression B c lectromagnetic waves carry energy. The rate of flow of energy crossing a unit area is described by the Poynting vector S. Where 1 S B Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65

3 J-Physics lectromagnetic waves carry momentum and hence can eert pressure(p) on surfaces,which is known as radiation pressure. For an electromagnetic wave with Poynting vector S, incident upon a perfectly absorbing surface S P c and if incident upon a perfectly reflecting surface S P c The electric and magnetic fields of a sinusoidal plane electromagnetic wave propagating in the positive -direction can also be written as = m sin(k t) and B = B m sin(k t) where is the angular frequency of the wave and k is wave number which are given by f and k The intensity of a sinusoidal plane electro-magnetic wave is defined as the average value of Poynting vector taken over one cycle. S av mb m m c c B m The fundamental sources of electromagnetic waves are accelerating electric charges. For eamples radio waves emitted by an antenna aries from the continuous oscillations (and hence acceleration) of charges within the antenna structure. lectromagnetic waves obey the principle of superposition. The electric vector of an electromagnetic field is responsible for all optical effects. For this reason electric vector is also called a light vector. TR ANSVRS NATUR OF LCTROM AGNTIC WAVS Mawell showed that a changing electric field produces a changing magnetic field and vice-versa. This alternate production of time 'varying electric and magnetic fields gives rise to the propagation of electromagnetic waves. Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65 The variation of electric field ( ) and magnetic field ( B ) are mutually perpendicular to each other as well as to the direction of the propagation of the wave i.e., the electromagnetic waves are transverse in nature. Proof : Consider a plane electromagnetic wave travelling along X-direction with its wave front in the YZ plane and ABCD is its portion at time t. The values of electric field and magnetic field to the left of ABCD will depend on and t (and not on y and z as the wave under consideration is a plane wave propagating in direction. According to Gauss' law, the total electric flu across the parallelopiped' ABCDOFG is zero because it does not z enclose any charge. i.e.. ds z z z z z z or. ds. ds. ds. ds. ds. ds...(i) ABCD FOG ADG BCOF OCDG FBA 111 Z G Y F O A D B plane wave front C X direction of propagation since electric field does not depend on y and z, so the contribution to the electric flu coming from the faces normal to y and z aes cancel out in pairs. z z i.e.. ds. ds... (ii) OCDG FBA

4 J-Physics z ADG z BCOF and. ds. ds... (iii) Using equation (ii) and (iii) in equation (i), we get z ABCD z FOG. ds. ds...(iv) Now. ds. ds cos ds ds ( is parallel to ds ) z z z z ABCD ABCD ABCD ABCD and FOG = area of face ABCD = S... (v) z z z '. ds ' ds cos 18 ' ds FOG FOG ( ' is antiparallel to ds ) ' = ' area of facefog = S... (vi) where, and ' are the -components of electric field on the faces ABCD and FOG respectively. Substituting the values of equations (v) and (vi) in equation (iv), we get S 'S = or S( ') = S ' = or ' = This equation shows that the value of the -component of electric field does not change with time. In other words, electric field along -ais is static. Since the static electric field cannot propagate the wave, hence the electric field parallel to the direction of the propagation of the wave is zero. i.e. ' = = It means, electric field is perpendicular to the direction of propagation of the wave. similarly, it can be proved that the magnetic field is perpendicular to the direction of the propagationof the wave. Since both electric and magnetic fields are perpendicualr to the direction of the propagation of the wave, so electromagnetic wave is transverse in nature. GOLDN KY POINTS When a capacitor is connected across the battery through the connecting wires there is flow of conduction current, while thorugh the gap between the plates of capacitor,there is flow of displacement current. Mawell's equation are mathematical formulation of Gauss's law in electrostatics (I) Gauss's law in electromagnetism (II) foradays law of electromagnetic induction (III) and Ampere's circuital law (IV) Frequency of electromagnetic waves is its inherent characterstic, when an electromagnetic wave travels from one medium to another, its wavelength changes but frequency remains unchanged. Ozone layer absorbs the ultra-violet rays from the sun and these prevents them from producing harmful effect on living organisms on the earth. Further it traps the infra-red rays and prevents them from escaping the surface of earth. It helps to keeps the earth's at atmosphere warm 11 Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65

5 J-Physics Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65 Various parts of electromagnetic spectrum S. Radiation Discover How Wavelength Range Frequency range nergy Properties Application No. produced range 1. -Rays Henry Due to decay 1 14 m to 1 1 m 3 1 Hz to 1 7 ev-1 4 ev (a) High (a)gives Becquerel of radioactive penetrating Information on and nuclei. power nuclear structure Madam (b) Uncharged (b) Medical trea- Cuire (c) Low ionising tment etc. power. X-Ray Roentgen Due to collisions m to 1 9 m Hz to ev to (a)low Penetrating (a) Medical of high energy Hz ev power diagnosis and electrons with (b) other properties treatment heavy targets similar to -rays (b) Study of ecept wavelength crystal structure (c) Industrial radiography 3. Ultraviolet Ritter By ionised gases, m to Hz to 1 3 ev to 3eV (a) All properties (a) To detect Rays sun lamp m Hz of light adulteration, spark etc. (b) Photoelectric writing and effect signature (b) Sterilization of water due to its destructive action on bacteria 4. Visible light Newton Outer orbit electron m to Hz to 3. ev to 1.6 ev (a) Sensitive to (a)to see objects transitions in atoms, m Hz human eye (b) To study gas discharge tube, molecular Subparts of incandescent solids structure visible and liquids. spectrum (a) Violet m to m Hz to Hz (b) Blue m to m Hz to Hz (c) Green m to m Hz to Hz (d) Yellow m to m Hz to Hz (e) Orange m to m Hz to Hz (f) Red m to m Hz to Hz 113

6 J-Physics S. Radiation Discover How Wavelength Range Frequency range nergy Properties Application No. producted range 5. Infra-Red Willam (a) Rearrangement m to 1 3 m Hz to Hz 1.6eV to 1 3 ev (a) Thermal effect (a) Used in induwaves Herschell of outer orbital (b) All properties stry, medicine electrons in atoms simillar to those of and astronomy and molecules. light ecept (b) Used for fog (b) Change of or haze photography molecular vibrational (c) lucidating and rotational energies molecular structure. (c) By bodies at high temperature. 6. Microwaves Hertz Special electronic 1 3 to.3m Hz to 1 9 Hz 1 3 ev to 1 5 ev (a) Phenomena of (a) Radar and telecodevices such as reflection, mmunication. klystron tube refraction and (b) Analysis of fine diffraction details of molecular structure 7. Radio waves Marconi Oscillating circuits.3 to few kms. 1 9 Hz to few Hz 1 3 ev to (a) hibit waves (a) Radio like properties communication more than particle like properties. Subparts of Radiospectrum (A) Super High Frequency.1m to.1m Hz to Hz Radar, Radio and satelite communication (a) SHF (Microwaves), Radar and Television Ultra High Frequency.1 m to 1m Hz to Hz broadcast short distance communication, (b) UHF Television communication. Very High Frequency 1 m to 1 m Hz to Hz (c) VHF (B) High Frequency 1m to 1 m Hz to Hz Medium distance communication (HF) Telephone communication, Marine and Medium Frequency 1 m to 1 m Hz to Hz navigation use, long range communi- (MF) cation. Long distance communication. Low Frequency (LF) 1 m to 1 m Hz to Hz Very Low Frequency 1 m to 3 m Hz to 1 4 Hz (VLF) 114 Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65

7 J-Physics SOM WORKD OUT XAMPLS a m p l e # 1 In a plane electomagnetic wave, the electric field oscillates sinusoidally at a frequency of 1 1 Hz and amplitude 48 V/m. The amplitude of oscillating magnetic field will be 8 Oscillating magnetic field 48 B c 3 1 a m p l e # Wb/m In the above problem, the wavelength of the wave will be Wavelength of electromagnetic wave 8 c cm a m p l e # 3 A point source of electromagnetic radiation has an average power output of 8W. The maimum value of electric field at a distance 3.5 m from the source will be Pav m Intensity of electromagnetic wave given is by I 4 r c o cp o av m r = 7 8 (4 1 ) (3 1 ) = 6.6 V/m Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65 a m p l e # 4 In the above problem, the maimum value of magnetic field will be a m p l e # 5 The maimum value of the magnetic field is given by 115 B 6.6 = T c 3 1 m m 8 What should be the height of transmitting antenna if the T.V. telecast is to cover a radius of 18 km? d Height of transmitting antenna h R 3 e ( 18 1 ) m

8 J-Physics a m p l e # 6 The area to be covered for T.V. telecast is doubled, then the height of transmitting antenna (T.V. tower) will have to be The area of transmission of surrounding the T.V. tower A = d = (hre) a m p l e # 7 In an electomagnetic wave, the amplitude of electric field is I V/m. The frequency of wave is Hz. The wave is propagating along z-ais. The average energy density of electric field, in Joule/m 3, will be Average energy dendity is given by u 4 o o o o o (1) 4 1 =. 1 1 J/m a m p l e # 8 A T.V. tower has a height of 1 m. How much population is covered by T.V. broadcast, if the average population density around the tower is 1/km? Radius of the area coved by T.V. telecast d hr Total population covered = d population density = hr e polulation density 1 = = a m p l e # 9 An electomagnetic radiation has an energy 14.4 KeV. To which region of electromagnetic spectum does it belong? e A h hc = m =.8Å This wavelength belongs to Xray region 116 Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65

9 J-Physics XRCIS 1 CHCK YOUR GRASP 1. If and B are the electric and magnetic field vectors of electromagnetic waves then the direction of propagation of electromagnetic wave is along the direction of (1) () B (3) B (4) none of these. The electromagnetic waves do not transport - (1) energy () charge (3) momentum (4) information 3. In an electromagnetic wave the average energy density is associated with (1) electric field only () magnetic field only (3) equally with electric and magnetic fields (4) average energy density is zero 4. In an electromagnetic wave the average energy density associated with magnetic field will be (1) 1 L I () B (3) 1 B 1 (4) B 5. In the above problem, the energy density associated with the electric field will be (1) 1 CV () 1 q C (3) 1 (4) 1 6. In which part of earth's atmosphere is the ozone layer present? (1) troposphere () stratosphere (3) ionosphere (4) meosphere 7. The ozone layer is earth's atmosphere is crucial for human survival because it (1) has ions () reflects radio signals (3) reflects ultraviolet rays (4) reflects infra red rays Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65 8. The frequency from Hz to Hz is (1) high frequency band () super high frequency band (3) ultra high frequency band (4) very high frequency band 9. The frequency from 3 to 3 MHz is known as (1) audio band () medium frequency band (3) very high frequency band (4) high frequency band 1. The AM range of radiowaves have frequency (1) less than 3 MHz () more than 3 MHz (3) less than Hz (4) more than Hz 1 1. Select wrong statement from the following for MW - (1) are transverse () travel with same speed in all medium (3) travel with the speed of light (4) are produced by accelerating charge 117

10 J-Physics 1. The nature of electromagnetic wave is (1) longitudinal () longitudinal stationary (3) transverse (4) transverse stationary 1 3. Which of the following are not electromagnetic waves? [AI] (1) Cosmic-rays () -rays (3) -rays (4) X-rays 1 4. The rms value of the electric field of the light coming from the sun is 7 N/C. The average total energy density of the electromagnetic wave is- [ A I 6] (1) J/m 3 () J/m 3 (3) J/m 3 (4) J/m An electromagnetic wave in vacuum has the electric and magnetic fields and B, which are always perpendicular to each other. The direction of polarizaiton is given by X and that of wave propagation by k. Then :- (1) X and k B (3) X and k B () X B and k B (4) X B and k B [AI - 1] 1 6. An electromagnetic wave with frequency and wavelength travels in the y direction. Its magnetic field is along _ ais. The vector equation for the associated electric field (of amplitude ) is :- [ AI 1 (Online)] (1) ˆ cos t y (3) ˆ cos t y z () ˆ cos t y (4) ˆ cos t y z ANSWR KY XRCIS Q A , Node-6\:\Data\14\Kota\J-Advanced\SMP\Phy\Unit No.-1\MI & AC\nglish\4 MW Theory.p65

ELECTROMAGNETIC WAVES MARKS WEIGHTAGE 3 marks

ELECTROMAGNETIC WAVES MARKS WEIGHTAGE 3 marks QUICK REVISION (Important Concepts & Formulas) Electromagnetic radiation is the radiation in which associated electric and magnetic field oscillations are