Electromagnetic Waves PDF - Lect-01

Ch 8- Electromagnetic Waves Lect-01 06-10-2020 Physicswallah Lakshya Batch 2020-21  Today’s Goal Displacement Current Maxwell’s Equation 06-10-2020 Physicswallah Lakshya Batch 2020-21 ...

Ch 8- Electromagnetic Waves Lect-01 06-10-2020 Physicswallah Lakshya Batch 2020-21  Today’s Goal Displacement Current Maxwell’s Equation 06-10-2020 Physicswallah Lakshya Batch 2020-21  MAXWELL’S DISPLACEMENT CURRENT 06-10-2020 Physicswallah Lakshya Batch 2020-21 1. In 1831, Michael Faraday gave Faraday’s Laws of electromagnetic induction , according to which a change in magnetic flux produces an induced emf Changing Magnetic Field Produces an Electric Field 06-10-2020 Physicswallah Lakshya Batch 2020-21 2. So, a “changing Magnetic field produces an Electric Field” 3. Now the Question arises “ Can changing Electric Field produce a Magnetic Field ??” 4. YES BACHOOO!! James Clerk Maxwell 06-10-2020 Physicswallah Lakshya Batch 2020-21 Maxwell’s Experiment to Prove his point Consider a Parallel Plate Capacitor being Charged by a battery 06-10-2020 Physicswallah Lakshya Batch 2020-21 Idea of Displacement Current Maxwell said that not only current produces magnetic field but a changing Electric Field in vacuum/free space also produces magnetic field. 06-10-2020 Physicswallah Lakshya Batch 2020-21 Displacement Current : A current due to changing Electric Field (or electric flux) 06-10-2020 Physicswallah Lakshya Batch 2020-21 Q1) Prove that the conduction current (ic) and displacement current (id) are equal (have property of continuity) 06-10-2020 Physicswallah Lakshya Batch 2020-21 06-10-2020 Physicswallah Lakshya Batch 2020-21 Modification of Ampere’s Circuital Law 06-10-2020 Physicswallah Lakshya Batch 2020-21 Properties of displacement Current 1. It is not conventional current, As it produces Magnetic Field, so it is called a current. 2. It exists only when there is a change in Electric Field (electric Flux) 3. It does not exist under steady conditions 4. Together with the conduction current, displacement current satisfies the property of continuity. 06-10-2020 Physicswallah Lakshya Batch 2020-21 Q2) A parallel plate capacitor with plate area A and separation between the plates d, is charged by a constant current i. Consider a plane surface area A/2 parallel to the plates and drawn simultaneously between the plates. The displacement current through this area is a) i b) i/2 c) i/4 d) i/8 06-10-2020 Physicswallah Lakshya Batch 2020-21 Important Note: Electric Field induced due to changing Magnetic Field is Perpendicular to the Magnetic Field 06-10-2020 Physicswallah Lakshya Batch 2020-21 Magnetic Field induced due to changing Electric Field is Perpendicular to the Electric Field 06-10-2020 Physicswallah Lakshya Batch 2020-21  Maxwell’s equation 06-10-2020 Physicswallah Lakshya Batch 2020-21 Maxwell’s Equation All the basic principles of ElectroMagnetism can be explained in terms of FOUR fundamental equations called Maxwell’s Equation. Maxwell did not discovered FOUR equations, but he worked on them & stated that these FOUR fundamental equations define complete ElectroMagnetism 06-10-2020 Physicswallah Lakshya Batch 2020-21 1. Gauss Law of Electrostatics Ï Electric Flux through a closed surface is times 𝜺𝟎 the total charge ‘q’ enclosed by surface 06-10-2020 Physicswallah Lakshya Batch 2020-21 2. Gauss Law of Magnetism Magnetic Flux through any closed surface is always ZERO 06-10-2020 Physicswallah Lakshya Batch 2020-21 3. Faraday’s Law of Electromagnetic Induction Charge in Magnetic Flux induces an emf OR Changing Magnetic Field induces an Electric Field 06-10-2020 Physicswallah Lakshya Batch 2020-21 4. Ampere-Maxwell Law Changing Electric Field induces a Magnetic Field 06-10-2020 Physicswallah Lakshya Batch 2020-21 06-10-2020 Physicswallah Lakshya Batch 2020-21  Ch 8- Electromagnetic Waves Lect-02 07-10-2020 Physicswallah Lakshya Batch 2020-21  Today’s Goal Source of Electromagnetic Waves Equation of Oscillating Electric & Magnetic Field 07-10-2020 Physicswallah Lakshya Batch 2020-21 We have studied 1. A changing Magnetic Field induces an Electric Filed 2. The induced Electric Field is perpendicular to Magnetic Field 07-10-2020 Physicswallah Lakshya Batch 2020-21 1. A changing Electric Field induces a Magnetic Field. 2. The induced Magnetic Field is perpendicular to Magnetic Field 07-10-2020 Physicswallah Lakshya Batch 2020-21 Electric & Magnetic Field due to a charge Case I: Charge at Rest Case II: Charge in Motion with Uniform Velocity 07-10-2020 Physicswallah Lakshya Batch 2020-21 Case III : accelerated charged particle 07-10-2020 Physicswallah Lakshya Batch 2020-21 Accelerated charge - oscillating charge Charge kaha oscillate Karta Hai? 07-10-2020 Physicswallah Lakshya Batch 2020-21 07-10-2020 Physicswallah Lakshya Batch 2020-21 07-10-2020 Physicswallah Lakshya Batch 2020-21 Oscillating Electric Field Produces an Oscillating Magnetic Field E and B are in same phase 07-10-2020 Physicswallah Lakshya Batch 2020-21  Transverse nature of Electromagnetic Wave 07-10-2020 Physicswallah Lakshya Batch 2020-21  Ch 8- Electromagnetic Waves Lect-03 08-10-2020 Physicswallah Lakshya Batch 2020-21  Today’s Goal Equation of Electric Field & Magnetic Field in an Electromagnetic Wave 08-10-2020 Physicswallah Lakshya Batch 2020-21 Electromagnetic Wave 1. Electromagnetic Wave is radiated(produced) by an accelerated (or oscillating) charge particle. 2. Electromagnetic Wave propagates in space through Oscillations of Electric and Magnetic Field , perpendicular to each other and also perpendicular to the direction of wave propagation. 3. Since the oscillation of Electric Field and Magnetic Field occur perpendicular to direction of wave propagation, EMW is a Transverse Wave 08-10-2020 Physicswallah Lakshya Batch 2020-21 08-10-2020 Physicswallah Lakshya Batch 2020-21  Equation of Electric Field & Equation of Magnetic Field 08-10-2020 Physicswallah Lakshya Batch 2020-21 Brief Introduction to Travelling Wave 08-10-2020 Physicswallah Lakshya Batch 2020-21 Displacement of particle(y) 08-10-2020 Physicswallah Lakshya Batch 2020-21 Equation of Electromagnetic Waves 1. Electric Field 𝑬 08-10-2020 Physicswallah Lakshya Batch 2020-21 2. Magnetic Field 𝑩 08-10-2020 Physicswallah Lakshya Batch 2020-21 08-10-2020 Physicswallah Lakshya Batch 2020-21 Q1) The electric field in a plane electromagnetic wave is 3 11 𝑵 given by Ey=2sin(0.5x 10 𝒙+1.5x10 t) j a) What is the direction of propagation b) Speed of wave 08-10-2020 Physicswallah Lakshya Batch 2020-21 Peak Value of 𝑬 (𝑬𝒐) and 𝑩 (𝑩𝒐) 08-10-2020 Physicswallah Lakshya Batch 2020-21 Q2) The magnetic field in the plane electromagnetic wave is given by Bz=2x10-7 sin(0.5 x 103x +1.5 x 1011 t)tesla. The expression for electric field will be a) Ez=30 Ðsin(0.5 x 103𝒙 + 1.5 x1011 t)V/m b) Ez=60sin(0.5 x 103𝒙 + 0.5 x1011 t)V/m c) Ey= 30 Ð sin(0.5 x 1011𝒙 + 0.5 x103 t)V/m d) Ey= 60 sin(0.5 x 103𝒙 + 1.5 x1011 t)V/m 08-10-2020 Physicswallah Lakshya Batch 2020-21 Permeability & Permittivity of Medium 1. In air/vacuum/free space 2. In any other medium 08-10-2020 Physicswallah Lakshya Batch 2020-21 Q4) If c is the speed of electromagnetic waves in vacuum ,its speed in a medium of dielectric constant K and relative permeability μr is Ï a) 𝒗 = 𝝁𝒓𝑲 b) 𝒗 = 𝒄 𝝁𝒓𝑲 𝒄 c) 𝒗 = 𝝁𝒓𝑲 𝑲 d) 𝒗 = 𝝁𝒓 j 08-10-2020 Physicswallah Lakshya Batch 2020-21 Q5) A plane electromagnetic wave Ez=100cos(6x108t +4x) V/m propagates in a non magnetic medium of dielectric constant a) 1.5 b) 2.0 c) 2.4 d) 4.0 08-10-2020 Physicswallah Lakshya Batch 2020-21  Ch 8- Electromagnetic Waves Lect-04 09-10-2020 Physicswallah Lakshya Batch 2020-21  Today’s Goal Electromagnetic Wave 1. Energy Density 2. Intensity 3. Momentum 09-10-2020 Physicswallah Lakshya Batch 2020-21  Energy Density of ElectroMagnetic Waves 1. Electromagnetic Waves carry energy as they travel through space. Thus Energy is contained in oscillating Electric and Magnetic Field. 2. Equal amount of Energy is contributed by Electric and Magnetic Field. 3. By now, we know that EMW are produced by oscillating charge in L-C circuit. The energy of Electric Field is from Capacitor(C) while Energy of Magnetic Field is from Inductor (L) 09-10-2020 Physicswallah Lakshya Batch 2020-21 Energy density of Electric Field (𝝁𝑬) 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 Energy density of Magnetic Field (𝝁𝑩) 𝒏 = 𝒏𝒐. 𝒐𝒇 𝒕𝒖𝒓𝒏𝒔 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕 𝒍𝒆𝒏𝒈𝒕𝒉 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 Show that (𝝁𝑩) = (𝝁𝑬) 09-10-2020 Physicswallah Lakshya Batch 2020-21 Total Energy density in Electromagnetic Wave 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 Summary 𝟏 𝟏 𝝁𝒂𝒗𝒈 = 𝜺𝒐𝑬𝒐𝟐 = 𝑩𝒐𝟐 𝟐 𝟐𝝁𝒐 𝟏 𝟏 (𝝁𝑬)𝒂𝒗𝒈 = 𝝁𝒂𝒗𝒈 = 𝜺𝒐𝑬𝒐𝟐 𝟐 𝟒 𝟏 𝟏 (𝝁𝑩)𝒂𝒗𝒈 = 𝝁𝒂𝒗𝒈 = 𝜺𝒐𝑩𝒐𝟐 𝟐 𝟒 09-10-2020 Physicswallah Lakshya Batch 2020-21 Intensity of an Electromagnetic Wave The energy crossing per unit time in a direction perpendicular to the direction of propagation is called intensity of the wave. 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21 Relation between Power & Intensity 09-10-2020 Physicswallah Lakshya Batch 2020-21 Momentum of Electromagnetic Wave De-Broglie hypothesis 09-10-2020 Physicswallah Lakshya Batch 2020-21 Pointing Vector (𝑺) 𝑺 represents the direction of energy flow per unit area per unit time along the direction of wave propagation 09-10-2020 Physicswallah Lakshya Batch 2020-21 09-10-2020 Physicswallah Lakshya Batch 2020-21  Ch 8- Electromagnetic Waves Lect-05 10-10-2020 Physicswallah Lakshya Batch 2020-21  Today’s Goal Properties of Electromagnetic Wave Electromagnetic Spectrum 10-10-2020 Physicswallah Lakshya Batch 2020-21 Properties of Electromagnetic Waves The electromagnetic waves are produced by accelerated charges and do not require any material medium for their propagation. The direction of oscillations of 𝑬 and 𝑩 fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves so the electromagnetic waves are transverse in nature. The oscillations of 𝑬 and 𝑩 fields are in same phase. 10-10-2020 Physicswallah Lakshya Batch 2020-21  All Electromagnetic waves travel in free space with the same speed, Ï c= ≈ 3 × Ï𝟎𝟖 m/s. √𝝁∘𝟄∘ In material medium, the electromagnetic waves travel with a speed, Ï 𝒄 𝒄 v= = = √𝝁𝝐 √𝝁𝒓 𝝐𝒓 𝒏 where n is the refractive index of the medium. 10-10-2020 Physicswallah Lakshya Batch 2020-21  The amplitude ratio of electric and magnetic field is 𝑬∘ Ï =c=. 𝑩∘ √𝝁∘𝟄∘ The electromagnetic waves carry energy as they travel through space and this energy is shared equally by electric and magnetic field. The average energy density of an e.m. wave is u= 10-10-2020 Physicswallah Lakshya Batch 2020-21  Electromagnetic waves transport linear momentum as they travel through space. 𝑼 p= 𝒄 Electromagnetic Waves obey the principle of superposition. They show the properties of reflection,refraction, interference, diffraction and polarisation. 10-10-2020 Physicswallah Lakshya Batch 2020-21  The electric field of an electromagnetic waves is responsible for its optical effects, because 𝑬𝟎 >> 𝑩𝟎 10-10-2020 Physicswallah Lakshya Batch 2020-21 Electromagnetic Spectrum The orderly distribution of the electromagnetic waves in accordance with their wavelength or frequency into distinct groups having widely differing properties is called ELECTROMAGETIC SPECTRUM. 10-10-2020 Physicswallah Lakshya Batch 2020-21 1. Gamma Waves: Wavelength Range: less than 10-3 nm Production/Service: Radioactive decay of nucleus Main Uses: Due to their high energy, they 1. Have strong penetrating power & hence are used to kill Cancerous cells. 2. To preserve food stuffs for a long time because soft Gamma rays can kill micro organism. 10-10-2020 Physicswallah Lakshya Batch 2020-21 2. X-Rays: Wavelength Range: 10-3 to 1nm Production/Service: X-ray tubes or inner electrons Main Uses: Medical diagnosis 1. Because X-rays can pass through flesh but not through bones. 2. In the study of crystal structure. 10-10-2020 Physicswallah Lakshya Batch 2020-21 3. Ultraviolet light (U.V. Waves) Wavelength Range: 1nm to 400 nm Production/Service: inner shell e- in atoms moving from one energy level to a lower energy level. Main Uses: 1. In food preservation as it has lethal effect on micro- organism. 2. To detect alteration ghee because of its property of florescence 10-10-2020 Physicswallah Lakshya Batch 2020-21 4. Visible light Wavelength Range: 400 nm to 700 nm Production/Service: e- in an atoms emit light when they move from one energy level to a lower energy level Main Use: Stimulates nerve ending of human eye. 10-10-2020 Physicswallah Lakshya Batch 2020-21 5. Infrared Waves Wavelength Range: 700 nm to 1mm Production/Service: Vibration of atoms & molecules Main Uses: 1. They are not scattered in fog or smoke, useful for infra-red photographs or haze photography. 2. Used for therapeutic purposes. 10-10-2020 Physicswallah Lakshya Batch 2020-21 6. Microwaves Wavelength Range: 1mm to 0.1 m Production/Service: Magnetron valve Main Use: 1. Radar Communication. 10-10-2020 Physicswallah Lakshya Batch 2020-21 7. Radiowaves Wavelength Range: > 0.1 m Production/Service: Rapid acceleration & deaccelerations of e- in aerials. Main Use: 1. Radio Communication. 10-10-2020 Physicswallah Lakshya Batch 2020-21