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Electromagnetic, Waves, Recap Notes, Electromagnetic (E.M.) waves : E.M., waves are those waves in which there is a, sinusoidal variation of electric and magnetic, fields at right angle to each other as well, as at right angle to the direction of wave, propagation., X For a plane progressive electromagnetic, wave propagating along + Z direction,, the electric and magnetic fields can be, written as, E = E0 sin (kz – wt), B = B0 sin (kz – wt), Y, , where m and e are permeability and, permittivity of the medium respectively., c, 1, v=, =, µ 0µ r ε 0 ε r, µr εr, X, , , E, , X, Z, , X, , X, , X, , , B, , In electromagnetic wave, the electric and, magnetic fields vary with space and time, and have the same frequency and are in, the same phase., The amplitudes of electric and magnetic, fields in free space, in electromagnetic, waves are related by, E, E0 = cB0 or B0 = 0, c, The speed of electromagnetic wave in, free space is, E, 1, = 3 × 108 m/s, c= 0 =, B0, µ0ε0, where m0 and e0 are the permeability and, permittivity of free space respectively., , X, , The speed of electromagnetic wave in a, medium is, 1, v=, µε, , X, , X, , Properties of electromagnetic waves, – These waves do not carry any charge., – These waves are not deflected by, electric and magnetic fields., – They travel with the speed of light c, (= 3 ×× 108 m s–1) in vacuum., – The frequency of electromagnetic wave, does not change when it goes from one, medium to another but its wavelength, changes., – These waves are transverse in nature,, hence they can be polarised., Production of electromagnetic waves, – Maxwell showed that an electric, charge oscillating harmonically with, frequency u produces electromagnetic, waves of the same frequency., – An electric dipole is a basic source of, electromagnetic waves., Energy density of electromagnetic, waves, – Electromagnetic waves carry energy, as they travel through space and this, energy is equally shared by electric field, and magnetic field of electromagnetic, wave., – The energy density of the electric field, is, 1, 2, u E = ε 0 Erms, 2, – The energy density of magnetic field is, uB =, , 2, 1 Brms, 2 µ0

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– Average energy density of electromagnetic wave is, 1, 1 2, 2, < u > = ε 0 Erms, +, B, 2, 2µ 0 rms, X, , X, , Intensity of electromagnetic wave, : It is defined as energy crossing per, unit area per unit time perpendicular, to the direction of propagation of, electromagnetic wave. The intensity of, electromagnetic wave is, B2, 1, 2, I = < u > c = ε 0 Erms, c + rms c, 2, 2µ 0, Momentum of electromagnetic wave, – An electromagnetic wave carries linear, momentum., – Electromagnetic wave strikes the, surface at normal incidence and, transports a total energy U to the, surface in a time t , if the surface, absorbs all the incident energy, the, total momentum p transported to the, surface is, p=, , Type, Radio, waves, , U, (complete absorption), c, , Wavelength, range, > 0.1 m, , Microwaves 0.1 m to 1 mm, , Frequency, range (in Hz), < 3 ×× 109, 3 ××× 108 to, 3 ×× 1011, 3 ×× ×1011 to, 4 ×× 1014, , Infra-red, , 1 mm to 700 nm, , Visible, light, , 700 nm to 400 nm 4 ×× 1014 to, 8 ×× ×1014, , – If the surface is a perfect reflector, and incidence is normal then the, momentum transported to the surface, is, 2U, (complete reflection), p=, c, Radiation pressure : It is defined as the, pressure exerted by the electromagnetic wave, on a surface., X If I is the intensity of the incident, electromagnetic radiation, then the, radiation pressure for normal incidence, is, Pradiation =, , I, (perfectly absorbing surface), c, , Pradiation =, , 2I, (perfectly reflecting surface), c, , Electromagnetic spectrum : The orderly, distribution of electromagnetic radiations, according to their wavelength or frequency, is known as electromagnetic spectrum., , Production, , Detection, , Rapid acceleration, and deceleration of, electrons in aerials, Klystron valve or, magnetron valve, Vibration of atoms, and molecules, , Receiver’s aerials, , Electrons in atoms, emit light when they, move from one energy, level to a lower, energy level, Inner shell electrons, in atoms moving from, one energy level to a, lower level, , The eye, Photocells,, Photographic film, , Point contact diodes, Thermopiles, Bolometer,, Infrared photographic, film, , Ultraviolet 400 nm to 1 nm, , 8 ××× 1014 to, 8 ×× 1016, , X-rays, , 1 nm to 10–3 nm, , 1 ××× 1016 to, 3 ×× 1021, , X-ray tubes or inner, shell electrons, , Photographic film,, Geiger tubes, , Gamma, rays, , < 10–3 nm, , > 3 ××× 1021, , Radioactive decay of, the nucleus, , Photographic film, Ioniz, ation chamber, , Photocells, Photographic, film

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Practice Time, OBJECTIVE TYPE QUESTIONS, , Multiple Choice Questions (MCQs), 1. A plane electromagnetic wave travels in, vacuum along z-direction. If the frequency of, the wave is 40 MHz then its wavelength is, (a) 5 m, (b) 7.5 m, (c) 8.5 m, (d) 10 m, 2. An electromagnetic wave of frequency, u = 3 MHz passes from vacuum into a dielectric, medium with permittivity e = 4. Then, (a) wavelength and frequency both become half., (b) wavelength is doubled and frequency, remains unchanged., (c) wavelength and frequency both remain, unchanged., (d) wavelength is halved and frequency remains, unchanged., 3. The ratio of contributions made by the, electric field and magnetic field components to, the intensity of an electromagnetic wave is, (a) c : 1, (b) c2 : 1, (c) 1 : 1, (d) c :1, 4. About 6% of the power of a 100 W light bulb, is converted to visible radiation. The average, intensity of visible radiation at a distance of, 8 m is (Assume that the radiation is emitted, isotropically and neglect reflection)., (a) 3.5 × 10–3 W m–2, (b) 5.1 × 10–3 W m–2, –3, –2, (c) 7.4 × 10 W m, (d) 2.3 × 10–3 W m–2, 5. Which of the following rays is not an, electromagnetic wave?, (a) X-rays, (b) g-rays, (c) b-rays, (d) Heat rays, 6. A radio can tune to any station in 7.5 MHz, to 12 MHz band. The corresponding wavelengthband is, (a) 40 m to 25 m, (b) 30 m to 25 m, (c) 25 m to 10 m, (d) 10 m to 5 m, 7. Which waves are used in sonography ?, (a) Microwaves, (b) Infrared rays, (c) Radio waves, (d) Ultrasonic waves, , 8. Light with an energy flux of 18 W cm–2 falls, on a non-reflecting surface at normal incidence., If the surface has an area of 20 cm2, the average, force exerted on the surface during a 30 minute, time span is, (a) 2.1 × 10–6 N, (b) 1.2 × 10–6 N, 6, (c) 1.2 × 10 N, (d) 2.1 × 106 N, 9. T h e p a r t o f t h e s p e c t r u m o f t h e, electromagnetic radiation used to cook food is, (a) ultraviolet rays, (b) cosmic rays, (c) X-rays, (d) microwaves, 10. A plane electromagnetic wave of frequency, 25 MHz travels in free space along x-direction., At a particular point in space and time, electric, field E = 6.3 V m–1. The magnitude of magnetic, field B at this point is, (a) 1.2 × 10–6 T, (b) 1.2 × 10–8 T, –6, (c) 2.1 × 10 T, (d) 2.1 × 10–8 T, 11. A plane electromagnetic wave is incident on a, material surface. The wave delivers momentum, p and energy E. Then, (a) p ≠ 0, E ≠ 0, (b) p = 0, E = 0, (c) p = 0, E ≠ 0, (d) p ≠ 0, E = 0, 12. Radiations of intensity 0.5 W m–2 are striking, a metal plate. The pressure on the plate is, (a) 0.166 × 10–8 N m–2 (b) 0.332 × 10–8 N m–2, (c) 0.111 × 10–8 N m–2 (d) 0.083 × 10–8 N m–2, 13. One requires 11 eV of energy to dissociate, a carbon monoxide molecule into carbon and, oxygen atoms. The minimum frequency of the, appropriate electromagnetic radiation to achieve, the dissociation lies in, (a) visible region., (b) infrared region., (c) ultraviolet region. (d) microwave region., 14. The amplitude of the magnetic field of a, harmonic electromagnetic wave in vacuum is, B0 = 510 nT. The amplitude of the electric field, part of the wave is, (a) 120 N C–1, (b) 134 N C–1, –1, (c) 510 N C, (d) 153 N C–1

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15. The decreasing order of wavelength of, infrared, microwave, ultraviolet and gamma, rays is, (a) microwave, infrared, ultraviolet, gamma rays, (b) infrared, microwave, ultraviolet, gamma rays, (c) gamma rays, ultraviolet, infrared, microwaves, (d) microwaves, gamma rays, infrared, ultraviolet, 16. If µ0 be the permeability and k0 be the dielectric, constant of a medium, then its refractive index is, given by, 1, 1, (a), (b), (c), µ0k0 (d) µ0k0, µ0k0, µ0k0, 17. Which of the following statement is false for, the properties of electromagnetic waves?, (a) Both electric and magnetic field vectors, attain the maxima and minima at the same, place and same time., (b) The energy in electromagnetic wave is, divided equally between electric and, magnetic field vectors., (c) Both electric and magnetic field vectors are, parallel to each other and perpendicular to, the direction of propagation of wave, (d) These waves do not require any material, medium for propagation., 18. The source of electromagnetic waves can be, charge, when, (a) moving with a constant velocity, (b) moving in a circular orbit, (c) falling in an electric field, (d) both (b) and (c), 19. An electromagnetic wave radiates outwards, from a dipole antenna, with the amplitude of its, electric field vector E0. The electric field which, transports significant energy from the source, falls off as, 1, 1, 1, (a) 3, (b) 2, (c), (d) r, r, r, r, 20. The electric field associated with an, electromagnetic wave in vacuum is given by, , ^, E = 40 cos(kz − 6 × 108t) i , where E , z and t are, in volt per meter, meter and second respectively., The value of wave vector k is, (a) 2 m–1, (b) 0.5 m–1 (c) 6 m–1 (d) 3 m–1, 21. A microwave and an ultrasonic sound wave, have the same wavelength. Their frequencies, are in the ratio (approximately), (a) 102, (b) 104, (c) 106, (d) 108, , 22. The photon energy in units of eV for, electromagnetic waves of wavelength 2 cm is, (a) 2.5 × 10–19, (b) 5.2 × 1016, –16, (c) 3.2 × 10, (d) 6.2 × 10–5, 23. Which of the following electromagnetic, wave play an important role in maintaining the, earth’s warmth or average temperature through, the greenhouse effect?, (a) Visible rays, (b) Infrared waves, (c) Gamma rays, (d) Ultraviolet rays, 24. The amplitude of an electromagnetic wave, in vacuum is doubled with no other changes, made to the wave. As a result of this doubling of, the amplitude, which of the following statement, is correct?, (a) The speed of wave propagation changes only, (b) The frequency of the wave changes only, (c) The wavelength of the wave changes only, (d) None of these., 25. The frequency of electromagnetic wave, which is best suitable to observe a particle of, radius 3 × 10–4 cm is of the order of, (a) 1015 Hz, (b) 1011 Hz, 13, (c) 10 Hz, (d) 1012 Hz, 26. Frequency of radiations arising from two, close energy levels in hydrogen, known as lamb, shift is 1057 MHz. This frequency falls in which, range of electromagnetic wave?, (a) Infrared rays, (b) X-rays, (c) g-rays, (d) Radio waves, 27. X-rays, gamma rays and microwaves, travelling in vacuum have, (a) same wavelength but different velocities, (b) same frequency but different velocities, (c) same velocity but different wavelengths, (d) same velocity and same frequency, 28. The electric field part of an electromagnetic, wave in vacuum is E = 3.1 N C−1 cos (1.8 rad m −1 ) y, , 8, −1  ^, + (5.4 × 10 rad s ) t i . The wavelength of this, , part of electromagnetic wave is, (a) 1.5 m, (b) 2 m, (c) 2.5 m (d) 3.5 m, 29. The ratio of amplitude of magnetic field to the, amplitude of electric field for an electromagnetic, wave propagating in vacuum is equal to, (a) the speed of light in vacuum, (b) reciprocal of speed of light in vacuum, (c) the ratio of magnetic permeability to the, electric susceptibility of vacuum, (d) unity

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30. The electric field part of an electromagnetic, wave in a medium is represented by Ex = 0,, E y = 2 .5, , N, rad , , , −2 rad  , cos   2π × 106,  t −  π × 10, x ,, , C, m, s  , , , Ez = 0. The wave is, (a) moving along x direction with frequency, 106 Hz and wavelength 100 m, (b) moving along x direction with frequency, 106 Hz and wavelength 200 m, (c) moving along –x direction with frequency, 106 Hz and wavelength 200 m, (d) moving along y direction with frequency, 2p × 106 Hz and wavelength 200 m, 31. A plane electromagnetic wave of frequency, 25 MHz travels in free space along the, x-direction. At a particular point in space and, , , ^, time, E = 6.3 j V m −1 . At this point B is equal, to, ^, , ^, , (a) 8.33 × 10−8 k T, , (b) 18.9 × 10−8 k T, , (c) 2.1 × 10−8 k T, , (d) 2.1 × 10−8 k T, , ^, , ^, , 34. An electromagnetic wave propagating along, north has its electric field vector upwards. Its, magnetic field vector point towards, (a) north, (b) east, (c) west, (d) downwards, 35. The waves used by artificial satellites for, communication is, (a) microwaves, (b) infrared waves, (c) radio waves, (d) X-rays, 36. Assume a bulb of efficiency 2.5% as a point, source. The peak values of electric and magnetic, fields produced by the radiation coming from a, 100 W bulb at a distance of 3 m is respectively, (a) 2.5 V m–1, 3.6 × 10–8 T, (b) 4.2 V m–1, 2.8 × 10–8 T, (c) 4.08 V m–1, 1.36 × 10–8 T, (d) 3.6 V m–1, 4.2 × 10–8 T, 37. An electromagnetic radiation has an energy, of 13.2 keV. Then the radiation belongs to the, region of, (a) visible light, (b) ultraviolet, (c) infrared, (d) X-ray, , 32. Which one of the following is the property, of a monochromatic, plane electromagnetic wave, in free space?, (a) Electric and magnetic fields have a phase, π, difference of ., 2, (b) The energy contribution of both electric and, magnetic fields are equal., (c) The direction of propagation is in the,  , direction of B × E ., (d) The pressure exerted by the wave is the, product of its speed and energy density., , 38. The magnetic field of a beam emerging, from a filter facing a flood light as given by, B = 12 × 10–8 sin (1.20 × 107 z – 3.60 × 1015 t) T., The average intensity of the beam is, (a) 1.71 W m–2, (b) 2.1 W m–2, –2, (c) 3.2 W m, (d) 2.9 W m–2, , 33. An electromagnetic wave is propagating, along x-axis., At x = 1 m and t = 10 s, its electric, , vector |E | = 6 V/ m then the magnitude of its, magnetic vector is, (a) 2 × 10–8 T, (b) 3 × 10–7 T, (c) 6 × 10–8 T, (d) 5 × 10–7 T, , 40. Radio waves diffract around buildings,, although light waves do not. The reason is that, radio waves, (a) travel with speed larger than c, (b) have much larger wavelength than light, (c) are not electromagnetic waves, (d) none of these, , 39. The electric field of a plane electromagnetic, wave varies with time of amplitude 2 Vm –1, propagating along z-axis. The average energy, density of the magnetic field is (in J m–3), (a) 13.29 × 10–12, (b) 8.85 × 10–12, –12, (c) 17.72 × 10, (d) 4.43 × 10–12, , Case Based MCQs, Case I : Read the passage given below and answer, the following questions from 41 to 44., Directions of Electromagnetic Waves, In an electromagnetic wave both the electric and, magnetic fields are perpendicular to the direction, of propagation, that is why electromagnetic, , waves are transverse in nature. Electromagnetic, waves carry energy as they travel through, space and this energy is shared equally by the, electric and magnetic fields. Energy density of, an electromagnetic waves is the energy in unit, volume of the space through which the wave, travels.

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41. The electromagnetic waves propagated, , , perpendicular to both E and B. The electromagnetic, waves travel in the direction of,  ,  , (a) E ⋅ B , (b) E × B,  ,  , (c) B ⋅ E , (d) B × E, , (a) 500, (b) 100, 250, 500, (c), (d), 3, 3, Case III : Read the passage given below and, answer the following questions from 48 to 50., , 42. Fundamental particle in an electromagnetic, wave is, (a) photon, (b) electron, (c) phonon, (d) proton, , Oscillating Charge, A stationary charge produces only an electrostatic, field while a charge in uniform motion produces, a magnetic field, that does not change with time., An oscillating charge is an example of accelerating, charge. It produces an oscillating magnetic field,, which in turn produces an oscillating electric, fields and so on. The oscillating electric and, magnetic fields regenerate each other as a wave, which propagates through space., , 43. For a wave propagating in a medium, identify, the property that is independent of the others., (a) velocity, (b) wavelength, (c) frequency, (d) all these depend on each other, 44. The electric and magnetic fields of an, electromagnetic waves are, (a) in opposite phase and perpendicular to each, other, (b) in opposite phase and parallel to each other, (c) in phase and perpendicular to each other, (d) in phase and parallel to each other., Case II : Read the passage given below and, answer the following questions from 45 to 47., Momentum and Pressure of an Electromagnetic Wave, An electromagnetic wave transports linear, momentum as it travels through space. If, an electromagnetic wave transfers a total, energy U to a surface in time t, then total linear, U, momentum delivered to the surface is p = ., c, When an electromagnetic wave falls on a surface,, it exerts pressure on the surface. In 1903, the, American scientists Nichols and Hull succeeded, in measuring radiation pressures of visible light, where other had failed, by making a detailed, empirical analysis of the ubiquitous gas heating, and ballistic effects., 45. The pressure exerted by an electromagnetic, wave of intensity I(W m–2) on a non-reflecting, surface is (c is the velocity of light), (a) Ic, (b) Ic2, (c) I/c, (d) I/c2, 46. Light with an energy flux of 18 W/cm2 falls, on a non-reflecting surface at normal incidence., The pressure exerted on the surface is, (a) 2 N/m2, (b) 2 × 10–4 N/m2, 2, (c) 6 N/m, (d) 6 × 10–4 N/m2, , 47 A point source of electromagnetic radiation, has an average power output of 1500 W. The, maximum value of electric field at a distance of, 3 m from this source (in V m–1) is, , x, E, , E, , B, , B, , O, , y, , z, B, , E, , B, Direction of, propagation, , E, , 48 Magnetic field in a plane electromagnetic, , ^, wave is given by B = B0 sin(kx + ωt) j T ., Expression for corresponding electric field will, be (Where c is speed of light.), , ^, (a) E = − B0c sin(kx + ωt) k V/m, , ^, (b) E = B0c sin(kx − ωt) k V/m, , ^, (c) E = B0 sin(kx + ωt) k, V/m, c, , ^, (d) E = B0c sin(kx + ωt) k V/m, 49 The electric field component of a monochromatic, , ^, radiation is given by E = 2E0 i cos kz cos ωt. Its, , magnetic field B is then given by, 2E0, c, 2E0, (c), c, (a), , ^, , j cos kz cos ωt, , ^, , j sin kz sin ωt, , 2E0 ^, j sin kz cos ωt, c, 2E ^, (d) − 0 j sin kz sin ωt, c, (b), , 50. A plane em wave of frequency 25 MHz, travels in a free space along x-direction. At a, ^, , particular point in space and time, E = (6.3 j ) V/m., What is magnetic field at that time?, (a) 0.095 mT, (b) 0.124 mT, (c) 0.089 mT, (d) 0.021 mT

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Assertion & Reasoning Based MCQs, For question numbers 51-60, two statements are given-one labelled Assertion (A) and the other labelled Reason (R)., Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below., (a) Both A and R are true and R is the correct explanation of A, (b) Both A and R are true but R is NOT the correct explanation of A, (c) A is true but R is false, (d) A is false and R is also false, 51. Assertion (A) : Radio waves cannot be, diffracted by the buildings., Reason (R) : The wavelength of radio waves is, very small., , 56. Assertion (A) : Velocity of light is constant, in all media., Reason (R) : Light is an electromagnetic wave, which has constant velocity in all media., , 52. Assertion : Only microwaves are used in radar., Reason : Because microwaves have very small, wavelength., , 57. Assertion (A) : X-rays in vacuum travel, faster than light waves in vacuum., Reason (R) : The energy of X-rays photon is, less than that of light photon., , 53. Assertion (A) : The electric field and, magnetic field have equal average values in, linearly polarised plane em wave., Reason (R) : The electric energy and magnetic, energy have equal average values in linearly, polarised plane em wave., , 58. Assertion (A) : Electromagnetic waves, exert pressure called radiation pressure., Reason (R) : Electromagnetic waves carries, energy., , 54. Assertion (A) : Light can travel in vacuum, whereas sound cannot do so., Reason (R) : Light has an electromagnetic wave, nature whereas sound is mechanical wave., , 59. Assertion (A) : Infrared waves sometimes, referred as heat waves., Reason (R) : Infrared waves heat up the earth, surface., , 55. Assertion (A) : The microwaves are better, carriers of signals than radio waves., Reason (R) : The electromagnetic waves do not, required any material medium for propagation., , 60. Assertion (A) : X-ray astronomy is possible, only from satellites orbiting the earth., Reason (R) : Efficiency of X-rays telescope is, large as compared to any other telescope., , SUBJECTIVE TYPE QUESTIONS, , Very Short Answer Type Questions (VSA), 1. To which part of the electromagnetic, spectrum does a wave of frequency 5 × 1019 Hz, belong?, 2., , How are radio waves produced?, , 3. Welders wear special goggles or face masks, with glass windows to protect their eyes from, electromagnetic radiations. Name the radiations, and write the range of their frequency., 4. The small ozone layer on top of the stratosphere, is crucial for human survival. Why ?, 5., , Write two uses of microwaves., , 6., , If the Earth did not have atmosphere, would, , its average surface temperature be higher or, lower than what it is now? Explain., 7. An e.m. wave exerts pressure on the surface, on which it is incident. Justify., 8. Do electromagnetic waves carry energy and, momentum?, 9. How is the speed of em-waves in vacuum, determined by the electric and magnetic fields?, 10. In which directions do the electric and magnetic, field vectors oscillate in an electromagnetic wave, propagating along the x-axis ?

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Short Answer Type Questions (SA-I), 11. Illustrate by giving suitable examples, how, you can show that electromagnetic waves carry, both energy and momentum., 12. A plane electromagnetic wave travels in, vacuum along z-direction. What can you say, about the direction of electric and magnetic field, vectors?, 13. An e.m. wave is travelling in a medium, , ^, with a velocity v = v i . Draw a sketch showing, the propagation of the e.m. wave, indicating the, direction of the oscillating electric and magnetic, fields., , 16. The electric field intensity produced by the, radiations coming from 100 W bulb at a 3 m, distance is E. Find the electric field intensity, produced by the radiations coming from 50 W, bulb at the same distance., 17. The electric field in an electromagnetic wave, is given by E = (50 N C–1)sin w(t – x/c). Find the, energy contained in a cylinder of cross-section, 10 cm2 and length 50 cm along the x-axis., 18. How are infrared waves produced? Why are, these referred as heat waves? Write their one, important use?, , 14. Name the physical quantity which remains, same for microwaves of wavelength 1 mm and, UV radiations of 1600 Å in vacuum., , 19. Explain briefly how electromagnetic waves, are produced by an oscillating charge. How is, the frequency of the e.m. waves produced related, to that of the oscillating charge?, , 15. One requires 11 eV of energy to dissociate, a carbon monoxide molecule into carbon and, oxygen atoms. The minimum frequency of the, appropriate electromagnetic radiation to achieve, the dissociation lies in which region?, , 20. Identify the electromagnetic waves whose, wavelengths vary as, (a) 10–11 m < l < 10–14 m, (b) 10–4 m < l < 10–6 m, Write one use of each., , Short Answer Type Questions (SA-II), 21. Name the constituent radiation of electromagnetic spectrum which is used for, (i) aircraft navigation., (ii) studying crystal structure., Write the frequency range for each., 22. Gamma rays and radio waves travel with, the same velocity in free space. Distinguish, between them in terms of their origin and the, main application., 23. Identify the part of the electromagnetic, spectrum used in (i) radar and (ii) eye surgery., Write their frequency range., 24. (i) Which segment of electromagnetic, waves has highest frequency? How are these, waves produced? Give one use of these waves., (ii) Which e.m. waves lie near the high frequency, end of visible part of e.m. spectrum? Give its one, use. In what way this component of light has, harmful effects on humans?, 25. Name the parts of the electromagnetic, spectrum which is, (a) suitable for radar systems used in aircraft, navigation., , (b) used to treat muscular strain., (c) used as a diagnostic tool in medicine., Write in brief, how these waves can be produced., 26. Prove that the average energy density of the, oscillating electric field is equal to that of the, oscillating magnetic field., 27. Name the types of em radiations which, (i) are used in destroying cancer cells,, (ii) cause tanning of the skin and (iii) maintain, the earth’s warmth., Write briefly a method of producing any one of, these waves., 28. (a) Arrange the following electromagnetic, waves in the descending order of their, wavelengths :, (i) Microwaves, (ii) Infra-red rays, (iii) Ultra-violet-radiation, (iv) Gamma rays, (b) Write one use each of any two of them., 29. (a) Optical and radio telescopes are built on, the ground but X-ray astronomy is possible only, from satellites orbiting the earth. Why?

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(b) The small ozone layer on top of the stratosphere, is crucial for human survival. Why?, 30. Suppose that the electric field part of an, electromagnetic wave in vacuum is, , E = (3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 108 rad/s)t]t, , (a) What is the direction of propagation?, (b) What is the wavelength l?, (c) What is the frequency n?, , 31. (a) When the oscillating electric and, magnetic fields are along the x-and y-direction, respectively., (i) point out the direction of propagation of, electromagnetic wave., (ii) express the velocity of propagation in terms, of the amplitudes of the oscillating electric, and magnetic fields., (b) How do you show that the e.m. wave carries, energy and momentum?, , Long Answer Type Questions (LA), 32. Answer the following questions:, (a) Show, by giving a simple example, how e.m., waves carry energy and momentum., (b) How are microwaves produced? Why is, it necessary in microwave ovens to select the, frequency of microwaves to match the resonant, frequency of water molecules?, (c) Write two important uses of infrared, waves., 33. State clearly how a microwave oven works to, heat up a food item containing water molecules., Why are microwaves found useful for the radar, systems in aircraft navigation?, 34. The intensity of light ranges from about, , 1W, , m2, for a candle to about 30 mW/m for a modest size, laser. A particular laser produces a power 4 W, in a beam 0.4 mm in diameter., 2, , (a) What is its average intensity?, (b) Find the peak electric field of the laser light., (c) Find the peak magnetic field of the laser, light., (d) If the laser beam is aimed upward to levitate, a 20 mm diameter sphere, what is the, maximum mass of this sphere. Assume the, sphere is perfectly reflecting., 35. A p l a n e E M w a v e t r a v e l l i n g a l o n g, , z-direction is described by E = E0 sin(kz − ωt)i, and B = B sin(kz − ωt) j . Show that, 0, , (a) The average energy density of the wave is, , 1, 1 B02, ε0 E02 +, ., 4, 4 µ0, (b) The time averaged intensity of the wave is, 1, given by I av = cε0 E02 ., 2, given by uav =, , OBJECTIVE TYPE QUESTIONS, 1., , (b) : Wavelength, λ =, , c 3 × 108 m s−1, =, = 7.5 m, υ 40 × 106 s−1, , 2. (d) : The frequency of electromagnetic wave remains, unchanged but the wavelength of electromagnetic wave, changes when it passes from one medium to another., 1, c=, µ0 ε0, 1, ε0, , ∴, , c∝, , ∴, , c, ε, 4, =, =, =2, v, ε0, 1, , and v ∝, , 1, ε, , c, υλ, λ, λ, =, =, = 2 or λ ′ =, v, 2, υλ ′ λ ′, 3., , (c) : Intensity of electromagnetic wave, I = Uav c, 1, In terms of electric field, Uav = ε0 E02, 2, 1 B02, In terms of magnetic field, Uav =, 2 µ0, 1, Now Uav electric field = ε0 E02, 2, 1, 1, 1 2, E0, , , = ε0 ( cB0 )2 = ε0 ×, B0 , ∵ B = c, 2, 2, µ0 ε0, 0, 1 B02, =, = Uav , (due to magnetic field), 2 µ0

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Thus the energy in electromagnetic wave is divided equally, between electric field vector and magnetic field vector. Therefore,, the ratio of contributions by the electric field and magnetic field, components to the intensity of electromagnetic wave is 1 : 1., 4. (c) : Here, power of bulb = 100 W, Power of visible light, As intensity, I =, area, 100 × 6 / 100, =, = 7.4 × 10–3 W m–2, 4 π (8)2, 5., 6., , (c), (a) : Here, u1 = 7.5 MHz, u2 = 12 MHz, , ∴ λ1 =, , 3 × 108, c, =, = 40 m, υ1 7.5 × 106, , 3 × 108, c, and λ2 =, =, = 25 m, υ2 12 × 106, 7. (d), 8. (b) : The total energy falling on the surface is, U = 18 × 20 × (30 × 60) = 6.48 × 105 J, Therefore, the total momentum delivered (for complete, absorption is), U 6.48 × 105, p= =, = 2.16 × 10–3 kg m s–1, c, 3 × 108, The average force exerted on the surface is, p 2.16 × 10 −3, F= =, = 1.2 × 10–6 N, t 0.18 × 104, 9. (d) : Microwaves are used to cook food. Microwave oven, is a domestic application of these waves., E, 6.3, 10. (d) : As, B = =, = 2.1 × 10 −8 T, c 3 × 108, 11. (a) : When plane electromagnetic wave is incident on, a material surface, the wave delivers some momentum and, energy to the surface and hence p ≠ 0 and E ≠ 0., 0.5, I, 12. (a) : P = =, c 3 × 108, = 0.166 × 10–8 N m–2, 13. (c) : Here, E = 11 eV = 11 × 1.6 × 10–19 J = hu, 11 × 1.6 × 10 −19, \ υ=, h, =, , 11 × 1.6 × 10 −19, = 2.6 × 1015 Hz, 6.62 × 10 −34, , This frequency radiation belongs to ultraviolet region., 14. (d) : Here, B0 = 510 nT = 510 × 10–9 T, E0 = cB0 = 3 × 108 × 510 × 10–9 = 153 N C–1, 15. (a), , 16. (c) : Refractive index of medium is, c, 1, µ = ,where c =, υ, µ 0 k0, and, , ∴, , υ=, , µ=, , 1, µ 0 k0 µ r k r, 1 / µ 0 k0, , 1 / µ 0 k0 µ r k r, , = µ r kr, , Given µr = µ0 and kr = k0 then µ =, , µ 0 k0, , 17. (c) : In an electromagnetic wave both electric and, magnetic vectors are perpendicular to each other as well as, perpendicular to the direction of propagation of wave., 18. (d) : An electromagnetic wave can be produced by, accelerated or oscillating charge., In options (b) and (c), the charge is in accelerated state, hence, will be a source of electromagnetic waves., 19. (c) : From a dipole antenna, the electromagnetic waves, are radiated outwards. The amplitude of electric field vector, E0 which transports significant energy from the source falls, off intensity inversely as the distance r from the antenna, 1, i.e., E0 ∝ ., r, 20. (a) : Compare the given equation with, E = E0cos(kz – wt), We get, w = 6 × 108 s–1, 6 × 108 s −1, ω, = 2 m−1, Wave vector, k = =, c 3 × 108 m s −1, 21. (c) : Frequency of microwaves, um ≈ 1011 Hz, Frequency of ultrasonic sound waves, uu ≈ 105 Hz, υ m 1011, ∴, =, = 106, υ u 105, 22. (d) : As E =, , hc, λ, , =, , 6.6 × 10 −34 × 3 × 108, = 9.9 ×10–24 J, 2 × 10 −2, , =, , 9.9 × 10 −24, eV = 6.2 × 10 −5 eV, 1.6 × 10 −19, , 23. (b) : Infrared radiation plays an important role in, maintaining the earth’s warmth through greenhouse effect., Incoming visible light when passes relatively easily through the, atmosphere is absorbed by the earth’s surface and radiated as, infrared (longer wavelength) radiation. This radiation is trapped, by greenhouse gases such as carbon dioxide and water vapour., In this way an average temperature is maintained.

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24. (d) : Velocity of electromagnetic wave, 1, c=, = 3 × 108 m s −1, µ0 ε0, It is independent of amplitude, frequency and wavelength of, electromagnetic wave., 25. (a) : Let l be the radius of the particle then, l = 3 × 10–4 × 10–2 m = 3 × 10–6 m, Frequency of electromagnetic wave, υ =, , c 3 × 108, =, = 1014, λ 3 × 10 −6, , Thus to observe the particle, the frequency of wave should be, more than 1014 i.e 1015 Hz or smaller value of wavelength., 26. (d) : This given frequency corresponds to the radio waves, i.e short wavelength or high frequency., 27. (c) : In vacuum X-rays, gamma rays and microwaves, travel with same velocity, i.e., with the velocity of light, c (= 3 × 108 m s–1) but have different wavelengths., 28. (d) : Given, ^, E = 3.1 N C–1 cos [(1.8 radm−1 ) y + (5.4 × 108 rad s −1 ) t ] i ...(i), Camparing (i) with the equation, E = E0 cos (ky + wt)...(ii), We get, k = 1.8 rad m–1,, E0 = 3.1 N C–1, c = 3 × 108 m s–1, w = 5.4 × 108 rad s–1, 2π 2 × 22, Now, λ =, =, = 3.5 m, k 1.8 × 7, 29. (b) : The amplitudes of electric field and magnetic field, for an electromagnetic wave propagating in vacuum are, related as E0 = B0c, where c is the speed of light in vacuum., B0 1, ∴, =, E0 c, N , rad  , rad , 30. (b) : E y = 2.5 cos  2π × 106  t −  π × 10 −2 , C , m , s , Ez = 0, Ex = 0, The wave is moving in the positive direction of x., This is in the form Ey = E0(wt – kx), w = 2p × 106, 2pu = 2p × 106 ⇒ u = 106 Hz, 2π, 2π, =k ⇒, = π × 10 −2, λ, λ, 2π, ⇒ λ=, = 2 × 102 = 200 m, π × 10 −2, , ^, 31. (c) : Here, E = 6.3 j V m−1, , The magnitude of B is, 6.3 V m−1, E, B= =, = 2.1 × 10 −8 T, c 3 × 108 m s −1, , , x, , , , E is along y-direction and the wave propagates along x-axis., , Therefore, B should be in a direction perpendicular to both,  , x and y-axis. Using vector algebra E × B should be along, x-direction., ^, ^ , ^, Since ( + j ) × ( + k ) = i , B is along z-direction., , ^, Thus, B = 2.1 × 10 −8 k T, 32. (b) : In electromagnetic wave, electric and magnetic, fields are in phase., Electromagnetic wave carry energy as they travel through, space and this energy is shared equally by electric and, magnetic fields., The direction of the propagation of electromagnetic wave is,  , the direction of E × B ., The pressure exerted by the wave is equal to its energy density., , 33. (a) : Here, | E | = 6 V/m, The magnitude of magnetic vector is, , , |E|, 6 V/ m, |B| =, =, = 2 × 10 −8 T, c, 3 × 108 m/ s, 34. (b), 35. (a) : In artificial satellite microwaves are used for, communication., 36. (c) : Here intensity, I =, =, , power, area, , 100 × 2.5, 2.5, =, W m−2, 2, 4 π (3) × 100 36π, , Half of this intensity belongs to electric field and half of that, to magnetic field., I 1, ∴, = ε0 E02 c, 2 4, 2.5, 2×, 2I, 36, π, or E0 =, =, = 4.08 V m–1, 1, ε0 c, 8, 3, 10, ×, ×, 4 π × 9 × 109, ∴, , B0 =, , E0, 4.08, = 1.36 × 10–8 T, =, c 3 × 108, , 37. (d) : Given : E = 13.2 keV, λ(in Å) =, , 12400, hc, =, = 0.939 Å ≈ 1 Å, E (in eV) 13.2 × 103, , X-rays cover wavelengths ranging from about 10 –8 m, (10 nm) to 10–13 m (10–4 nm)., An electromagnetic radiation of energy 13.2 keV belongs to, X-ray region of electromagnetic spectrum.

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38. (a) : Here, B = 12 × 10–8 sin, (1.20 × 107 z –3.6 × 1015 t) T, Comparing it with, B = B0 sin (kz – wt),, we have B0 = 12 × 10–8 T, Iav =, , 1 B02 c, 2 µ0, , 39. (b) : Amplitude of electric field and magnetic field are, related by the relation, E0, =c, B0, Average energy density of the magnetic field is, 1 B02, uB =, 4 µ0, , 1, = ε0 E02, 4, 1, = × 8.854 × 10 −12 × (2)2, 4, , , ∵, , B0 =, , E0 , , c, , 1 , , ∵ c=, , µ 0 ε0 , , = 8.854 × 10–12 J m–3, ≈ 8.85 × 10–12 J m–3, 40. (b) : The wavelength of radiowaves being much larger, than light, has a size comparable to those of buildings, hence, diffract from them., 41. (b) : Electromagnetic waves propagate in the direction,  , of E × B., 42. (a) : Photon is the fundamental particle in an, electromagnetic wave., 43. (c) : Frequency u remains unchanged when a wave, propagates from one medium to another. Both wavelength, and velocity get changed., 44. (c) : The electric and magnetic fields of an electromagnetic, wave are in phase and perpendicular to each other., 45. (c) : Pressure exerted by an electromagnetic radiation,, I, P=, c, 18 W/cm2, Energy flux, 46. (d) : Prad =, =, Speed of light 3 × 108 m/s, =, , 18 × 104 W/m2, = 6 × 10 −4 N/m2, 3 × 108 m/s, , Vav =, , 1, e E2 × c, 2 0 0, , ⇒ E0 =, , 1 (12 × 10 −8 )2 × 3 × 108, = ×, 2, 4 π × 10 −7, –2, = 1.71 W m, , 1 E02, =, 4 µ 0 c2, , 47. (b) : Intensity of EM wave is given by I =, , P, 4 πR2, , P, 1500, =, 2πR2 ε0 c, 2 × 3.14(3)2 × 8.85 × 10 −12 × 3 × 108, , = 10, 000 = 100 V m−1, , 48. (d) : Given : B = B0 sin( kx + ωt )j T, The relation between electric and magnetic field is,, E, c = or E = cB, B, The electric field component is perpendicular to the direction, of propagation and the direction of magnetic field. Therefore,, the electric field component along z-axis is obtained as, , ^, E = cB0 sin (kx + wt) k V/m, 49. (c) :, , dE, dB, =−, dz, dt, , dE, dB, = –2E0k sinkz coswt = −, dz, dt, dB = + 2 E0k sinkz coswtdt, B = +2E0k sin kz, E0 ω, = =c, B0 k, , ∫ cos ωt dt, , = +2E0, , k, sinkz sinwt, ω, ,  2E, 2E0, sin kz sinωt ∴ B = 0 sin kz sinωt j, c, c, E is along y-direction and the wave propagates along x-axis., \ B should be in a direction perpendicular to both x-and, y-axis., 50. (d) : Here, E = 6.3j ; c = 3 × 108 m/s, B=, , The magnitude of B is, E, 6.3, Bz = =, = 2.1 × 10 −8 T = 0.021 µT, c 3 × 108, 51. (d) : For wave to suffer diffraction, the wavelength, should be of the order of size of the obstacle. The wavelength, of radio waves (short radio waves) is order of the size of the, building and the other obstacles coming in their path and, hence they easily get diffracted., 52. (a) : In a radar, a beam signal is needed in particular, direction which is possible if wavelength of wave is very small., Since the wavelength of microwaves is a few millimeter, hence, they are used in radar., 53. (b) : In case of a linearly polarised plane electromagnetic, wave, the average values of electric field and magnetic field, are equal and average values of electric energy and magnetic, energy are also equal.

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54. (a) : Light being electromagnetic wave do not require, any material medium for its propagation. Hence light can, travel in vacuum. On the other hand sound is a mechanical, wave and requires a material medium for its propagation., Hence sound cannot travel in vacuum., , 4. , The small ozone layer on the top of the atmosphere, is crucial for human survival because it absorbs harmful, ultraviolet radiations present in sunlight and prevents it from, reaching the earth’s surface. These radiations can penetrate, our skin and can cause harmful diseases like skin cancer etc., , 55. (b) : Microwaves are the electromagnetic waves of, wavelength of the order of a few millimetres, which is less, than those of T.V. signals. On account of smaller wavelength,, the microwaves can be transmitted as beam signals in a, particular direction and are much better than radiowaves, because microwaves do not spread or bend around the, corners of any obstacle coming in their way. Therefore, microwaves are better carriers of signals than radiowaves., , 5. , Uses of microwaves :, (i) In long distance communication, (ii) In radar systems used in aircraft navigation, , 56. (d) : Velocity of light has different values in different, media., It depends on the refractive index of the medium. Related, by formula, velocity in vacuum, vmedium =, refractive index of medium, , 7. , An e.m. wave carries momentum with itself and given by, Energy of wave (U ), p=, Speed of the wave (c), , 57. (d) : All electromagnetic waves including X-rays travels, with same velocity in vacuum. The energy of X-rays is, greater than energy of the light because energy is inversely, proportional to wavelength (E = hc/l) and wavelength of, X-rays are smaller than light waves., 58. (b) : Electromagnetic waves transport linear momentum, as well as energy. When electromagnetic waves strike a, surface, a pressure is exerted on the surface. If the intensity, of wave is I, the radiation pressure P (force per unit area), exerted on the perfectly absorbing surface is P = I/c., 59. (b) : Infrared waves are sometimes called heat waves., This is because water molecules present in most materials, readily absorb infrared waves. After absorption, their thermal, motion increases, that is, they heat up and heat their, surroundings., 60. (c) : The earth’s atmosphere is transparent to visible, light and radio waves, but absorbs X-rays. Therefore X-rays, telescope cannot be used on earth surface., , SUBJECTIVE TYPE QUESTIONS, 1., , X-rays., , 2. , Radio waves are the electromagnetic waves of frequency, ranging from 500 KHz to about 1000 MHz. These waves are, produced by oscillating electric circuits having inductor and, capacitor., 3. , U ltraviolet radiations produced during welding are, harmful to eyes. Special goggles or face masks are used to, protect eyes from UV radiations. UV radiations have a range, of frequency between 1014 Hz – 1016 Hz., , 6. , If the Earth did not have atmosphere, then there would, be absence of green house effect of the atmosphere. Due, to this reason, the temperature of the earth would be lower, than what it is now., , When it is incident upon a surface it exerts pressure on it., 8. , Yes, electromagnetic waves carry energy and momentum., 9. , The speed of em-waves in vacuum determined by the, E, electric (E0) and magnetic fields (B0) is, c = 0 ., B0, 10. , When an electromagnetic wave is propagating along the, x-axis then, electric field vector oscillates in y-axis and magnetic, field vector oscillates in z-axis., 11. , Electromagnetic waves like other waves carry energy and, momentum as they travel through empty space. If light didn’t, carry energy and momentum, it wouldn’t be able to heat stuff, up or generate photocurrent in photocells., , , 12. , The electric and magnetic field vectors E and B are, perpendicular to each other and also perpendicular to the, direction of propagation of the electromagnetic wave. If, a plane electromagnetic wave is propagating along the, z-direction, then the electric field is along x-axis, and magnetic, field is along y-axis., 13. , In figure the velocity of propagation of e.m. wave is along, , , X-axis v = vi and electric field E along Y-axis and magnetic, , field B along Z-axis., Y, , , E, , X, Z, , , B, , 14. , The speed in vacuum (i.e., c = 3 × 108 m s–1) remains, same for both the given wavelengths. It is because both, microwaves and UV rays are electromagnetic waves.

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15. , Here, E = 11 eV = 11 × 1.6 × 10–19 J = hu, \, , υ=, , 11 × 1.6 × 10 −19 11 × 1.6 × 10 −19, =, = 2.6 × 1015 Hz, h, 6.62 × 10 −34, , This frequency belongs to ultraviolet region., 16. , Electric field intensity on a surface due to the incident, radiation is, U P, ,  U, E= =, ∵ = P , At A , t, As, E ∝ P, (for the given area of the surface), E ′ P ′ 50 1, = =, =, \, E P 100 2, E, E′ =, 2, 17. The energy density is, 1, 1, –8, –3, uav = ε0 E02 = × (8.85 × 10 −12 ) × (50)2 = 1.1 × 10 J m, 2, 2, The volume of the cylinder is V = 5 × 10–4 m3, The energy contained in cylinder is, U = (1.1 × 10–8 J m–3) × (5 × 10–4 m3) = 5.5 × 10–12 J., 18. , Infra red waves are produced by hot bodies and molecules., They are produced due to the de-excitation of atoms., Infrared waves incident on a substance increase the internal, energy and hence the temperature of the substance. That is, why they are called heat waves., Infra red radiations play an important role in maintaining, the earth’s warmth or average temperature through the, greenhouse effect., 19. , A n oscillating or accelerated charge is supposed, to be source of an electromagnetic wave. An oscillating, charge produces an oscillating electric field in space which, further produces an oscillating magnetic field which in turn, is a source of electric field. These oscillating electric and, magnetic field hence, keep on regenerating each other and, an electromagnetic wave is produced., The frequency of e.m. wave = Frequency of oscillating charge., 20. , (a) Gamma rays lie between 10–11 m to 10–14 m., These rays are used in radiotherapy to treat certain cancers, and tumors., (b) Infrared waves lie between 10–4 m to 10–6 m. These waves, are used in taking photographs during conditions of fog, smoke, etc., as these waves are scattered less than visible rays., 21. (i) Microwaves are used in radar system for aircraft, navigation. The frequency range is 3 × 108 Hz to 3 × 1011 Hz., (ii) X-rays are used for studying crystals structure of solids., Their frequency range is 3 × 1016 Hz to 3 × 1021 Hz., , 22.  Gamma rays : These rays are of nuclear origin and are, produced in the disintegration of radioactive atomic nuclei, and in the decay of certain subatomic particles. They are used, in the treatment of cancer and tumours., Radio waves : These waves are produced by the accelerated, motion of charges in conducting wires or oscillating electric, circuits having inductor and capacitor. These are used in, satellite, radio and television communication, 23., Uses, , Part of, electromagnetic, spectrum, , (i), , In radar, system, , Microwaves, , (ii), , In eye surgery Ultraviolet, , Frequency, range, 3 × 108 Hz to, 3 × 1011 Hz, 8 × 1014 Hz to, 8 × 1016 Hz, , 24.  (i) Gamma rays has the highest frequency in, the electromagnetic waves. These rays are of the nuclear, origin and are produced in the disintegration of radioactive, atomic nuclei and in the decay of certain subatomic particles., They are used in the treatment of cancer and tumours., (ii) Ultraviolet rays lie near the high-frequency end of visible, part of e.m. spectrum. These rays are used to preserve food, stuff. The harmful effect from exposure to ultraviolet (UV), radiation can be life threatening, and include premature aging, of the skin, suppression of the immune systems, damage to, the eyes and skin cancer., 25.  (a) Microwaves are suitable for radar systems used in, aircraft navigation., These waves are produced by special vacuum tubes, namely, klystrons, magnetrons and Gunn diodes., (b) Infra-red waves are used to treat muscular pain. These, waves are produced by hot bodies and molecules., (c) X-rays are used as a diagnostic tool in medicine. These, are produced when high energy electrons are stopped, suddenly on a metal of high atomic number., 26.  In an electromagnetic wave, both E and B fields vary, sinusoidally in space and time. The average energy density, u of an e.m. wave can be obtained by replacing E and B by, their rms value, 1, 1 2, 1, 1 2, 2, u = ε0 Erms, +, Brms or u = ε0 E02 +, B0, 2, 2µ 0, 4, 4µ 0, E0, B0 , , ∵ Erms = 2 , Brms = 2 , , , , 1, 2, , therefore, Moreover, E0 = cB0 and c =, µ0 ε0, 1, 1, uE = ε0 E02 = ε0 ( cB0 )2, 4, 4, B02, 1, 1 2, uE = ε0 ⋅, =, B0 = uB, µ 0 ε0 4µ 0, 4

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27.  (i) Gamma rays, (ii) UV rays, (iii) Infra-red radiations, Infra-red waves are produced by hot bodies and molecules., Infra-red waves are referred to as heat waves, because, water molecules present in most materials readily absorb, infra-red waves (many other molecules, for example, CO 2,, NH3 also absorb infra-red waves). After absorption, their, thermal motion increases, that is they heat up and heat their, surroundings., , 31. , (a) (i) The e.m. wave propagates along z-axis., , 28. , (a) Descending order of wavelengths for given, electromagnetic waves is:, Microwaves (10–3 – 10–1) m, Infra-red rays (7.5 × 10–7 – 10–3) m, Ultra-violet radiation (10–9 – 4 × 10–7) m, Gamma rays (< 10–12) m, , (b) Electromagnetic waves or photons transport energy and, momentum. When an electromagnetic wave interacts with a, small particle, it can exchange energy and momentum with, the particle. The force exerted on the particle is equal to the, momentum transferred per unit time. Optical tweezers use this, force to provide a non-invasive technique for manipulating, microscopic-sized particles with light., , (b) Microwaves :, Frequency range → 3 × 108 Hz –3 × 1011 Hz. These are, suitable for the radar system, used in aircraft navigation., Gamma rays :, Frequency range → > 3 × 1021 Hz., These wave are used for the treatment of cancer cells., , 32. (a) Consider a plane perpendicular to the direction of, propagation of the wave. An electric charge, on the plane will, be set in motion by the electric and magnetic fields of e.m., wave, incident on this plane. This illustrates that e.m. waves, carry energy and momentum., (b) Microwaves are produced by special vacuum tube like, the klystron, magnetron and Gunn diode., The frequency of microwaves is selected to match the resonant, frequency of water molecules, so that energy is transformed, efficiently to the kinetic energy of the molecules., (c) Uses of infra-red waves :, (i) They are used in night vision devices during warfare., This is because they can pass through haze, fog and mist., (ii) Infra-red waves are used in remote switches of household, electrical appliances., , 29. , (a) The earth’s atmosphere is transparent to visible light, and radiowaves but it absorbs X-rays. X-ray astronomy is, possible only from satellites orbiting the earth. These satellites, orbit at a height of 36,000 km, where the atmosphere is very, thin and X-rays are not absorbed., (b) Ozone layer absorbs ultraviolet radiation from the sun, and prevents it from reaching the earth and causing damage, to life., 30. , (a) The waves is propagating along negative y-direction, of its direction is – j ., (b) Comparing the given equation with the standard, equation., ,  y, , E = E0 cos 2π  + νt  , , , λ, , We get,, \, , 2π, = 1.8, λ, , Wavelength, λ =, , 2π 2 × 3.14, ×, = 3.5 m., 1.8, 1.8, , (c) Also, 2pn = 5.4 × 106, ∴ ν=, , 5.4 × 106 5.4 × 108, =, = 85.9 × 106 Hz., 2π, 2 × 3.14, ,  86 MHz, , x, E, , E0, , z, B0, y, , B, , (ii) The speed of em-waves in vacuum determined by the, E, electric (E0) and magnetic fields (B0) is, c = 0, B0, , 33. In microwave oven, the frequency of the microwaves is, selected to match the resonant frequency of water molecules, so that energy from the waves get transferred efficiently to, the kinetic energy of the molecules. This kinetic energy raises, the temperature of any food containing water., Microwaves are short wavelength radio waves, with frequency, of order of GHz. Due to short wavelength, they have high, penetrating power with respect to atmosphere and less, diffraction in the atmospheric layers. So these waves are, suitable for the radar systems used in aircraft navigation., 33. , (a) Intensity equals power per unit area carried by the wave., P, ⇒ Power per unit area = 2, πr, 4W, =, 3.14 × (0.2 × 10 −3 m)2, = 32 × 106 W/m2