Electromagnetic Waves PDF

CLASS XII - PHYSICS CHAPTER 8 – ELECTRO MAGNETIC WAVES INTRODUCTION In 1865, James Clerk Maxwell theoretically predicted the existence of electromagnetic waves. As per Faraday’s law, we know that a time-varying magnetic field is a source of changing electric field. Similarly, Ma...

CLASS XII - PHYSICS CHAPTER 8 – ELECTRO MAGNETIC WAVES INTRODUCTION In 1865, James Clerk Maxwell theoretically predicted the existence of electromagnetic waves. As per Faraday’s law, we know that a time-varying magnetic field is a source of changing electric field. Similarly, Maxwell argued that a time-varying electric field is a source of changing magnetic field. He further showed that these variations in electric and magnetic fields occur in mutually perpendicular directions and have wave like properties. SOURCE OF EM WAVES A stationary charge produces electrostatic field which does not vary with time. Also, charges moving at constant velocity (steady current) produce only magnetic field that does not vary with time. Hence, Maxwell predicted that accelerating charges can radiate EM waves. Consider a charge oscillating with some frequency (An oscillating charge is an example of accelerating charge). This produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of oscillating electric field, and so on. The oscillating electric and magnetic fields thus regenerate each other as the wave propagates through the space. The frequency of the electromagnetic wave naturally equals the frequency of oscillation of the charge. The energy associated with the propagating wave comes from the energy of the source – the accelerated charge. The existence of EM waves was experimentally proved first by Heinrich Hertz. Later, Indian scientist, Jagdish Chandra Bose, succeeded in producing and observing electromagnetic waves. At around the same time, Guglielmo Marconi in Italy followed Hertz’s work and succeeded in transmitting electromagnetic waves over distances of many kilometres. Marconi’s experiment marks the beginning of the field of communication using electromagnetic waves. An electromagnetic wave is a wave radiated by an accelerating charge and which propagates through space as coupled electric and magnetic fields, oscillating perpendicular to each other and to the direction of propagation of the wave. MATHEMATICAL EXPRESSION OF EM WAVES In the figure, we show a typical example of a plane electromagnetic wave propagating along the z direction. The electric field Ex is along the x-axis, and varies sinusoidally with z, at a given time. The magnetic field By is along the y-axis, and again varies sinusoidally with z. The electric and magnetic fields Ex and By are perpendicular to each other, and to the direction z of propagation. The mathematical expressions of the electric and magnetic fields in an EM wave are as follows: Ex = E0 sin (kz – ωt) in Newton/Coulomb By = B0 sin (kz – ωt) in Tesla Where, E0 and B0 are the amplitudes of electric and magnetic fields respectively, k is the propagation constant and is given by k = 2π/λ λ is the wave length of the EM wave. ω is the angular frequency and is given by ω = 2πυ υ is the frequency of EM wave. 𝜔 2𝜋 𝜔 The speed of propagation of EM wave, v = υ λ = ( )( ) = 2𝜋 𝑘 𝑘 𝜔 In vacuum all EM waves travel at the speed of light, c = = 3 x 108 m/s 𝑘 The amplitudes of electric and magnetic fields of an EM wave are related by the equation, 𝐸0 =𝑐 𝐵0 Alternate expressions for E and B: 2𝜋 𝑧 Ex = E0 sin ( 𝜆 z – 2πυt) = E0 sin [2π (𝜆 – υt)] 2𝜋 𝑧 By = B0 sin ( 𝜆 z – 2πυt) = E0 sin [2π (𝜆 – υt)] PROPERTIES OF EM WAVES 1. EM waves are produced by accelerating charges. 2. EM wave is transverse in nature. The directions of oscillations of electric and magnetic fields are perpendicular to each other, as well as perpendicular to the direction of propagation of wave. 3. EM waves do not require any material medium for propagation. They can propagate in vacuum. 4. All EM waves travel in vacuum with the same speed c = 3 x 108 m/s. 𝑐 In any other material medium, the speed of EM wave = v = 𝑛, where n is the refractive index of the medium. 5. The oscillations of electric and magnetic fields in an EM wave are in same phase. 𝐸0 6. The amplitude ratio of electric and magnetic fields of an EM wave is = 𝑐. 𝐵0 7. The electromagnetic waves carry energy as they travel through space. This energy is equally shared by the electric and magnetic fields. 8. Electromagnetic waves transport linear momentum as they through space. 9. Electromagnetic waves are not deflected by electric or magnetic fields. 10. An electromagnetic wave also exerts pressure, called radiation pressure. RELATION BETWEEN c, ε0 and µ0 µ 1 1 1 1 µ0 ε0 = 4𝜋0 x 4π𝜀0 = 10-7 x 9 𝑥 109 = 9 𝑥 1016 = (3 𝑥 108 )2 = 𝑐2 1 Or, c = √µ0 𝜀0 1 1 𝑐 In any other material medium, speed of EM wave = v = = = √µ𝜀 √µ𝑟 µ0 𝜀0 𝜀𝑟 √µ𝑟 𝜀𝑟 𝑐 Since v = 𝑛 , we can also write that refractive index n = √µ𝑟 𝜀𝑟 ENERGY AND MOMENTUM OF EM WAVE Consider a plane perpendicular to the direction of propagation of the electromagnetic wave. If there are electric charges on this plane, they will be set and sustained in motion by the electric and magnetic fields of the electromagnetic wave. The charges thus acquire energy and momentum from the waves. This illustrates the fact that an electromagnetic wave carries energy and momentum. Energy density (u): The energy density is the energy in unit volume of space through which the wave travels. 1 1 The average energy density of an EM wave, u = uE + uB = 2 𝜀0 𝐸0 2 + µ0 𝐵0 2 2 The energy is equally shared by the electric and magnetic fields. (uE = uB) Average energy density of an EM wave, u = 2uE = 𝜀0 𝐸0 2 Or u = 2uB = µ0 𝐵0 2 Momentum (p): Let U be the total energy of an EM wave. The momentum carried by the wave is U/c. If it falls on a perfectly absorbing surface, the linear momentum delivered to the surface in time t is same as that of the EM wave, p = U/c If it falls on a perfectly reflecting surface, the wave re-bounces with equal and opposite momentum (p to -p). By conservation of linear momentum, the momentum delivered to the surface in time t is 2p = 2U/c Intensity (I): It is the energy crossing per unit area per unit time in a direction perpendicular to the direction of propagation. 𝐸𝑛𝑒𝑟𝑔𝑦 𝑈 I= = = 𝑢𝑐 𝐴𝑟𝑒𝑎 x 𝑡𝑖𝑚𝑒 𝐴𝑡 Radiation Pressure (Pr) It is the pressure exerted by an EM wave, when it falls on a surface. 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝐼 Pr = = =𝑢 𝑠𝑝𝑒𝑒𝑑 𝑐 ELECTROMAGNETIC SPECTRUM The orderly distribution of EM waves in accordance to their wavelengths or frequencies into distinct groups of widely varying properties is called EM spectrum. The main parts of the spectrum and their corresponding wavelengths along with the methods of production and detection are given in the table below. APPLICATIONS OF EM SPECTRUM RADIOWAVES In radio and television broadcasting In radio astronomy MICROWAVES In RADAR systems for air craft navigation. Communication via geostationary satellites In microwave ovens  Note: How does microwave oven work? All food items contain water molecules in them. When these molecules vibrate more with higher energies, the temperature of the food increases and it gets cooked. In ovens, the frequency of the microwave is adjusted such that it is equal to the resonant frequency of vibration of water molecules. Thus, the food molecules vibrate with maximum amplitude and the food gets cooked fast. The containers to be used in oven are usually porcelain as their molecules are large and vibrate with much smaller frequencies. So, it does not absorb microwaves much. Why are microwaves better suited for long range communication than radiowaves? Since microwave wavelength is only few millimetres, they are not bent by objects of normal dimensions. Thus, they travel undeviated through long distances in a specific direction. But radiowaves have a wavelength of the order of the size of buildings and trees around us. So, they get bent easily. INFRA RED Produce intense heating effects Remote sensing In green houses to keep plants warm. In haze photography or fog vision cameras. Infrared lamps in treatment of muscular pains In reading secret writings on ancient walls In maintaining earth’s temperature. VISIBLE LIGHT To see and understand the world around us. It can cause chemical reactions like photosynthesis in plants. ULTRA VIOLET Food preservation Water purifiers Study of invisible writings, forged documents and finger prints. Identification of forfeit currencies. Sterilization of surgical instruments. Killing of germs and insects. Note: UV is the most harmful part of EM spectrum. It can cause skin cancer. UV is present in sunlight. But most of it get absorbed by the ozone layer in the atmosphere. Hence, they don’t reach the earth’s surface in high intensities. X RAYS Medical diagnosis Study of crystal structures In engineering to find faults, cracks etc in finished metal products. X ray astronomy.  Note: Optical and radio telescopes can be built on the ground level but X ray telescopes are placed on satellites orbiting the earth. This is because the earth’s atmosphere allows visible and radiowaves to pass through but absorbs X rays. GAMMA RAYS Cancer treatment To initiate nuclear reactions. Study of atomic nuclei