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Q.1 Ans. Q.2 Ans. Q.3 Ans. Q.4 Ans. Q.5 Ans. Q.6 Ans. Q.7 Ans. Q.8 Ans. Q.9 Ans. CLUSTER LEVEL PHYSICS WORKSHOP CLASS-XII ELECTROMAGNETIC WAVES One marks questions The charging current for a capacitor is 0.25 A. what is the displacement current across its plates? Displacement current = charging current = 0.25 A. A variable frequency a.c. source is connected to a capacitor. Will the displacement current increase or decrease with increase in frequency? Increase in frequency causes decrease in impedance of the capacitor and consequent increase in the current. Hence displacement current which equals conduction current increases with increase in frequency of a.c. What is the ratio of velocities of light rays of wavelengths 4000 Å and 8000 Å in vacuum? Ratio = 1, because light rays of both wavelengths travel with the same velocity of 3x108ms-1 in vacuum. Name the electromagnetic radiation to which the following wavelengths belong: (a) 10-2m (b) 1 Å (a) Microwaves (b) X-rays. Arrange the following in the descending order of wavelengths: -rays, infrared rays, microwaves, yellow light, radio waves. Radio waves ˃ infrared rays ˃ red light ˃ yellow light ˃ -rays. If the wavelength of an electromagnetic radiation is doubled, what will happen to the energy of photons? hc Energy of a photon, E hv When the wavelength of an electromagnetic radiation is doubled, the energy of the photons is halved. How does a charge q oscillating at certain frequency produce electromagnetic waves? Oscillating charge produces sinusoidal variation of electric and magnetic field, which in turn produces electromagnetic wave. Identify the following electromagnetic radiation as per the wavelength given below. (i) 10-12m (ii) 10-4m (iii) 106m (i) Gamma rays, (ii) Infrared rays, (iii) Radio wave. Express velocity of propagation of e.m. waves in terms of the peak value of electric & magnetic fields. 𝐸0 𝐸 = 𝑐 or 𝐵 = 𝑐 𝐵 0 Q.10 Ans. Q.1 Ans. What is the relation between conduction current and displacement current. IC = ID Two marks questions What is displacement current? Why was this concept introduced? Displacement current - It is that current which comes into existence, whenever the electric field and hence the electric flux changes with time. It is equal to 0 times the rate of change of electric flux through a given surface d dE Id 0 E 0 A dt dt Q.2 Ans. Q.3 Ans. Q.4 Ans. Q.5 Ans. Maxwell introduced the concept of displacement current for the following reasons: (i) To make the Ampere's circuital law logically consistent. (ii) To satisfy the property of continuity of electric current along any closed path. A parallel plate capacitor is being charged. Show that the displacement current across an area in the region between the plates and parallel to it is equal to the conduction current in the connecting wires. dq The conduction current I c is not continuous across the capacitor gap as no charge dt is transported across this gap. The displacement current I d is zero outside the capacitor plates and in the gap, it has the value d d d q dq I d 0 E 0 EA 0 dt dt dt 0 dt It is exactly the value of the conduction current in the lead wires. Thus the displacement current satisfies the basic condition that the current is continuous. The sum I c I d has the same value along the entire path (both inside and outside the capacitor plates), although individually the two currents are discontinuous. What is an electromagnetic wave? Express it graphically It is the wave radiated by an accelerated charge and which propagates through space as coupled electric and magnetic fields, oscillating perpendicular to each other and to the direction of propagation of wave. The graph showing e m wave is drawn below A plane electromagnetic wave travels, in vacuum, along the y-direction. Write (i) the ratio of the magnitudes, and (ii) the directions of its electric and magnetic field vectors. E (i) c , speed of light. B (ii) For an electromagnetic wave travelling along y-direction, its electric and magnetic field vectors are along z-axis and x-axis respectively. The direction of E B is same as that of direction of wave propagation and kˆ iˆ ˆj. Name the following constituent radiations of electromagnetic spectrum which : (i) Produce intense heating effect. (ii) Is absorbed by the ozone layer in the atmosphere. (iii) Is used for studying crystal structure. (iv) Produced during nuclear reactions (i) Infrared waves. Q.6 Ans. Q.7 Ans. (ii) Ultraviolet radiations. (iii) X-rays. (iv) Gamma rays A parallel plate capacitor has circular plates, each of radius 5.0 cm. It is being charged so that electric field in the gap between its plates rises steadily at the rate of 1012 Vm1 s 1 . What is the displacement current? d dE dE Displaceme nt current , I d 0 E 0 A 0 . r 2 dt dt dt 12 2 8.85 10 5 10 1012 0.07 A Electromagnetic waves travel in a medium at a speed of 2.0 108 ms 1 . The relative permeability of the medium is 1.0. Find the relative permittivity. Speed of an e. m.wave in a medium is given by 1 1 v r 0 r 0 1 1 0 0 r r 2 c r r c2 r r hence relative permittivity, (3 108 ) 2 r 2.25 r 2 1.0 (2 108 ) 2 To which regions of the electromagnetic spectrum the following wavelengths belong? 2000 Ǻ,5000 Ǻ’ 10000 Ǻ and 1.0Ǻ 2000 Ǻ - ultraviolet rays 5000 Ǻ - visible light 10000 Ǻ - infrared rays and 1.0Ǻ - X rays Which constituent radiations of electromagnetic spectrum is used (i) In radar, (ii) To photograph internal parts of a human body (iii) For taking photographs during nights and foggy conditions (iv) In water purification (i) Microwaves, (ii) X rays, (iii)Infrared rays and (iv) UV rays Find the wavelength of electromagnetic wave of frequency 4X109Hz in free space. Give its two applications. 𝑐 3 𝜆 = 𝜈 =3X108/ 4X109 = 40 = 0.075m This wavelength corresponds to microwaves and is used (i) microwave oven and (ii) radar Three marks questions Mention the various properties of electromagnetic waves. c2 Q.8 Ans. Q.9 Ans. Q.10 Ans. Q.1 Ans. These are as follows: 1. The electromagnetic waves are produced by accelerated charges and do not require any material medium for their propagation. 2. The directions of oscillations of E and B fields are perpendicular to each other as well as perpendicular to the direction of propagation of the wave. So the electromagnetic waves are transverse in nature. 3. The oscillations of E and B fields are in same phase. 4. All electromagnetic waves travel in free space with the same speed, 1 c 3 10 8 ms 1 0 0 In a material medium, the electromagnetic waves travel with the speed, 1 c c v , where n is the refractive index of the medium. r r n E0 c B0 6. The electromagnetic waves carry energy as they travel through space and this energy is shared equally by the electric and magnetic fields. The average energy density of an e.m. wave is B2 1 u u E u B 0 E02 0 2 0 7. Electromagnetic waves are not deflected by electric and magnetic fields. 8. Electromagnetic waves show the properties of reflection, refraction, interference, diffraction and polarization. 5. The amplitude ratio of the electric and magnetic fields is Q.2 Ans. Mention the wavelength range, frequency range and source of production of Radio Wave, Microwave, Infrared Rays and Visible light, give the important properties and uses of each part. Radio waves – These are the e. m. waves of longest wavelength and minimum frequency. Wavelength range - 600m to 0.1 m Frequency range 500 KHz to 100 MHz. Source Accelerated motion of charges in conducting wires or oscillating circuits. Uses: (i) In radio and television communication systems. (ii) In radioastronomy. Microwaves - They are the e. m. waves having wavelength next smaller to radiowaves. Due to their shorter wavelength, they can travel as a beam. Wavelength range 0.3 m to 10 3 m 10 9 Hz to1012 Hz Frequency range Source Oscillating currents in special vacuum tubes like Klystrons and Magnetrons. Uses: (i) In radar systems for aircraft navigation. (ii)In long-distance communication systems via geostationary satellites. (iii) In microwave ovens. Infrared rays – These rays produce heating effect, so they are also known as heat waves or thermal radiation. 5 10 3 m to 10 6 m Wavelength range 1011 Hz to 5 1014 Hz Frequency range Source Hot bodies and molecules. Uses: (i) In the remote control of a TV or VCR. (ii) In green houses to keep the plants warm. (iii) In haze photography because infrared waves are less scattered than visible light by atmospheric particles. (iv) Infrared lamps in the treatment of muscular complaints. (v) In reading the secret writings on the ancient walls (vi) In knowing the molecular structure. Visible light - It is very small part of the e.m. spectrum towards which the human retina is sensitive. 8 10 7 m to 4 10 7 m Wavelength range 4 1014 Hz to 7 1014 Hz Frequency range Source Radiated by excited atoms in ionized gas and incandescent bodies. Uses: (i) It provides us the sensation of vision. (ii) It can cause photo-chemical reactions. Q.3 Ans. Giving the wavelength range, frequency range and source of production of Ultra violet Rays, X-Rays and Gamma Rays, give the important properties and uses of each part. Ultraviolet rays - This region of the e.m. spectrum has wavelengths just shorter than visible light. 3.5 10 7 m to 1.5 10 7 m Wavelength range 1016 Hz to 1017 Hz Frequency range Source High voltage gas discharge tubes Uses: (i) In food preservation. (ii) In the study of invisible writings, forged documents and finger prints. (iii) In the study of molecular structure. X-rays - These e.m. waves have wavelengths just shorter than ultraviolet light. As X-rays can pass through many forms of matter, so they have many useful medical and industrial applications. Wavelength range 10-8m to 10-11m 1018 Hz to 10 20 Hz Frequency range Source Sudden deceleration of fast moving electrons by a metal target. Uses: (i) In medical diagnosis because X-rays can pass through flesh but not through bones. (ii)In the study of crystals structure. (iii) In engineering for detecting faults, cracks, flaws and holes in the finished metal products. (iv) In detective departments to detect explosives, diamond, gold etc. (v) In radiotherapy to cure untraceable skin diseases and malignant growths. Gamma rays - These are e.m. radiations of highest frequency range and lowest wavelength range. These are most penetrating e.m. waves. 10 14 m to 1010 m Wavelength range - Frequency range 1018 Hz to 10 22 Hz Source Radioactive nuclei and nuclear reactions. Uses: (i) In radiotherapy for the treatment of malignant tumours. (ii) In the manufacture of polyethylene from ethylene. (iii) To preserve food stuffs for a long time. (iv) To study the structure of atomic nuclei. Q.4 Electromagnetic waves with wavelength (i) 1 are used to treat muscular strain. (ii) 2 are used by a FM radio station for broadcasting. 3 are used to detect fracture in bones. (iii) (iv) 4 areabsorbed by the ozone layer of the atmosphere. Identify and name the part of electromagnetic spectrum to which these radiations belong. Arrange these wavelengths in decreasing order of magnitude. Ans. (i ) 1 Infra red radiations ii 2 radiwaves iii 3 X rays iv 4 Ultraviolet rays The wavelengths in decreasing order of magnitude are: 2 1 4 3 . Q.5 Ans. When can a charge act as a source of electromagnetic waves? How are the directions, of the electric and magnetic field vectors, in an electromagnetic wave, related to each other and to the direction of propagation of the wave? Which physical quantity, if any, has the same value for waves belonging to the different parts of the electromagnetic spectrum? Only an accelerated charge can act as a source of electromagnetic waves. The directions of electric and magnetic field vectors are perpendicular to each other as well as to direction of propagation of the wave. The wave speed in vacuum has the same value for all the waves. Q.6 The Ans. Given magnetic field in a plane electromagnetic wave By 2 10 7 sin 0.5 103 x 1.5 1011 t tesla. (a) What is the wavelength and frequency of the wave? (b) Write an expression for the electric field. is By 2 10 7 sin 0.5 103 x 1.5 1011 t tesla x On comparing with the standard equation, BY B0 sin 2 vt 2 We get , 0.5 103 2 2 3.14 1.26 10 2 m 3 0.5 10 0.5 103 given by Also, 2 v 1.5 1011 1.5 1011 1.5 1011 v 23.9 10 9 Hz 23.9 GHz. 2 2 3.14 8 (b) E0 cB0 3 10 2 10 7 60 Vm 1 . The electric field is perpendicular to the direction of propagation (x-axis) and the direction of magnetic field (y-axis). So the expression for electric field is E z E 0 sin 0.5 10 3 x 1.5 1011 t Vm 1