â« â«
Transcription
â« â«
3/23/15 Chapter #32 Electromagnetic Waves • 34.1: Displacement Current and the General Form of Ampere's Law • 34.2: Maxwell's Equations and Hertz's Discoveries • 34.3: Plane Electromagnetic Waves • 34.4: Energy Carried by Electromagnetic Waves • 34.5: Momentum and Radiation Pressure • 34.6: Production of Electromagnetic Waves by an Antenna • 34.7: The Spectrum of Electromagnetic Waves Laws of Electromagnetism Gauss’s Law for E Gauss’s Law for B Qnclosed ε0 ∫ B ⋅ dA = 0 € Ampere’s Law ∫ E ⋅ dA = ∫ B ⋅ d l = (µ I) 0 € Faraday’s Law € enclosed dΦ dt ∫ E⋅dl =− • This is what we€ already get in our course Maxwell’s Equation Gauss’s Law for E Gauss’s Law for B € Ampere’s Law ∫ E ⋅ dA = Qnclosed ε0 ∫ B ⋅ dA = 0 & ∫ B ⋅ d l = µ (' I + ε 0 € Faraday’s Law ∫ E⋅dl =− 0 d Φ) + d t * enclosed dΦ dt € • This is Maxwell’s Equations for Free Space! € 1 3/23/15 Ampere’s Law • The line integral: ∫ B ⋅ d l = µ0Ienclosed • around any closed path equals µ0 times the net current through the area enclosed by the path. € & ∫ B ⋅ d l = µ (' I + ε 0 0 d Φ) + d t * enclosed • Solve problem 34.1, page 985 € Definition of EMW • Electromagnetic waves are traveling waves of oscillating electric and magnetic field. • RHR: point the fingers of your right hand in the direction of electric field, curl your fingers in the direction of magnetic field, your thumb will point you the direction of propagation. • Solve problem 34.2, page 991 Transverse waves versus longitudinal waves • In transverse wave the displacement is perpendicular to the direction of propagation. • In longitudinal wave the displacement is in the direction of propagation. 2 3/23/15 The speed of light • Modern experiments: • C = 2.99792458×108 [m/s] ≈ 3.0×108 [m/s] • Ole Romer (1676) observed eclipses of Jupiter’s moon behind the planet. His result was 2.25×108 [m/s] Calculate speed of light yourself • Radius of Sun orbit 150 million kilometers, delay time ~ 1000 sec. • Later it was shown by Maxwell that we can calculate speed of light with a help of two constants ε0 and µ0. c= 1 = 2.99792458 ⋅10 8 [m /s] ε 0 µ0 € Wavelength • Wavelength is a minimum distance over which a wave repeats. • Usual designation is λ [m] • Read all definitions in Chapter 16 in your book 3 3/23/15 Period and Frequency λ = cT • Period (T) is a time required for one wave to pass a given point. • Frequency (f) is a number of crests/ troughs that pass a given point per second f = 1/T [Hz] • Read all definitions in Chapter 16 in your book € Test problems 25-11,38,39 • An electromagnetic wave propagates along the +y direction as shown in Figure 25-1. If the E-field at the origin is along the +z direction, what is the direction of the Bfield? • The frequency of a microwave signal is 9.76 GHz. What is its wavelength in meters? • The wavelength of an electromagnetic wave is 600 nm. What is its frequency? Electromagnetic spectrum • Light spreads out into a rainbow of colors from red to violet. • Visible light is a very small part of electromagne tic spectrum. 4 3/23/15 Boundaries: 106 Hz to 1022 Hz • E = c B The longest part: Radio Waves • Frequency 106 Hz to 109 Hz (1 [km] - 1 [m]) • Used for Radio and TV connection. • Produced by alternating current in metal antennas. Microwaves • Frequency 109 Hz to 1012 Hz (1 m - 1 mm) • Used for long-distance phone calls, for cook food (microwave - 12.2 [cm], 2.4 [GH]). • The highest frequency electromagnetic waves that can be produced by electronic circuitry. 5 3/23/15 Infrared Waves • Frequency 1012 Hz to 4.3×1014 Hz (1mm - 1µm) • “Heat on the skin”. Invisible. • Some creatures (e.g. snakes) have special infrared receptors that allow them to “see” the infrared waves. • All warm-blooded creatures produce infrared waves. • Use in remote control in home electronics. Infrared Radiation • If the object is at room temperature, the wavelength of thermal radiation are mainly in the infrared region, and hence is not visible for our eye. But if the temperature is sufficiently high the radiation is in the visible part of the electromagnetic spectrum like a hot tungsten filament of a light-bulb. Visible Light • Frequency 4.3×1014 Hz to 7.5×1014 Hz (700nm - 400nm or 7000 Å - 4000 Å) • Produced by electrons changing their positions within the atoms. 6 3/23/15 Ultraviolet Light • Frequency 7.5×1014 Hz to 1017 Hz (400nm 3nm or 4000 Å - 30 Å) • Sun tam on our skin. Invisible. • Can be seen by some bees and butterflies. X-Rays 1017 • Frequency Hz to 1020 Hz (10nm - 1 nm or 100 Å - 1 Å) • Generated by the rapid deceleration of highspeed electrons (TV monitor). • Freely path through our bodies (X-ray or MRI diagnostics). • Not safe! Damage or destroy living tissues. Gamma Rays • Frequency 1020 Hz and higher (less than 1 Å and shorter). • Produced in nuclear reactions. • They are highly penetrating and destructive for living cell. • Usual component of nuclear explosion. 7 3/23/15 Energy of Electromagnetic waves • Electric energy density: • Magnetic energy density: 1 2 B 2 µ0 uE = ε0 2 E 2 u= ε0 2 1 2 1 2 E + B = ε0 E 2 = B 2 2€µ0 µ0 € uB = • Solve problem 34.3, page 994 E =c B € € The Intensity • The intensity is the amount of energy a wave delivers to a unit area in a unit time. I= u ( Ac Δ t ) ΔU c = = uc = c ε0 E 2 = B 2 AΔ t AΔ t µ0 € Momentum of Electromagnetic wave Energy absorbed c U uav Ac Δ t Iav AΔ t Δp= = = c c c Δ p Iav A Fav = = Δt c • Solve problem 34.5, page 996 Iav pressure = av • c Momentum = € 8 3/23/15 Questions • Which of the following statements are true? • a) An electromagnetic wave is a result of electric and magnetic fields acting together. • b) The speed of electromagnetic waves through a vacuum is ten times the speed of sound in air. • c) Electromagnetic waves are longitudinal. • d) Electromagnetic waves in a vacuum travel with the speed of light. • e) Electromagnetic waves do not require a medium to be transmitted. Test Problem 25-2 • The orientation of the electric and magnetic fields in electromagnetic waves is • A) perpendicular to the direction of waves and parallel to each other. • B) parallel to the direction of the waves and parallel to each other. • C) parallel to the direction of the waves and perpendicular to each other. • D) perpendicular to the direction of the waves and perpendicular to each other. Test problem 25-10 • • • • • Electromagnetic waves are A) transverse. B) longitudinal. C) longitudinal and transverse. D) None of the other answers given is correct. 9 3/23/15 Test problem 25-16 • 16) Which of the following expressions is the correct representation for the speed of light? • A) (ε µ ) • B) (ε / µ ) • C) (µ / ε ) • D) 1/ (ε µ ) o o o o o o o o Test problem 25-29 • How far does a beam of light travel in one full year? • The value of the electric field for a certain type of electromagnetic wave is 660 N/C. What is the value of the magnetic field for that wave? Test problem 25-35 • 35) Which one of the following is the correct order of the electromagnetic spectrum from low to high frequencies? • A) radio waves, infrared, microwaves, UV, visible, X-rays, gamma rays • B) radio waves, UV, X-rays, microwaves, infrared, visible, gamma rays • C) radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays • D) radio waves, microwaves, visible, X-rays, infrared, UV, gamma rays 10 3/23/15 Test problem 25-48, 53, 54 • A 60.0 W light bulb radiates light uniformly in all different directions. What is the average intensity of the light bulb at a distance of 0.400 m from the bulb? • The electric field component of an electromagnetic wave is 34.4 N/C. What is the electric energy density of the wave? • The magnetic field component of the electromagnetic wave is 15.0 µT. What is the magnetic energy density of the wave? 11