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PHYS219 Fall semester 2014 Lecture 18: Maxwell’s Equations (1864) and EM Radiation Dimitrios Giannios Purdue University Second Midterm (EXAM II) Lecture! Date)) Subject) L01! L02! Chapter) Aug.!25! !course!overview! ! Aug.!27! Charge,! 17.1>2! Coulombs!law! Aug.!29! Electric!Fields! 17.3>4! Sep.!1! Holiday! ! Sep.!3! Electric!Potential! 18.1>2! Sep.!5! Recitation) ! Sep.!8! Equipotential! 18.3>4! surfaces! Sep.!10! Capacitors! 18.4>5! Sep.!12! Recitation! ! Sep.!15! Electric!current,! 19.1>3! resistance! Sep.!17! Kirchoff’s!Rules! 19.4! Sep.!19! Recitation! ! Sep.!22! RC!circuits! 19.5>9! Sep.!24! Magnetic!fields! 20.1>2! Sep.!25! Exam)I:)) Chapters!17>19!! 8pm,)PHYS)112 Sep.!26! Recitation! ! Sep.!29! Lorentz!Force! 20.3! Oct.!1! Magnetic!Force! 20.4>6! on!elec.!currents! Oct.!3! Recitation! ! Oct.!6! Ampere’s!Law! 20.7>9! Oct.!8! Magnetic! 21.1>3! Induction,!Lenz’s! Law!! Oct.!10! Recitation! ! Oct.!15! RL!circuits! 21.4>6! Oct.!17! Recitation! ! Oct.!20! AC!Voltages! 22.1>3! Oct.!22! AC!circuits! 22.4>6! Oct.!24! Recitation! ! Oct.!27! AC!circuits! 22.7>9! Oct.!29! EM!waves! 23.1>4! Oct.!31! Recitation! ! Nov.!3! Generating!EM! 23.5>7! waves! Nov.!5! Gen.!EM!waves! 23.5>7! Nov.!6! Exam)II:)) Chapters!20>22! 8pm,)PHYS)112 Nov.!7! Recitation! ! • Date: November 6 @ 8pm L03! ! L04! R01! L05! • Place: Physics, Room 112 • Duration: 1 hour L06! R02! L07! Homework) ! ! ! ! ! CHIP!1! ! ! CHIP!2! ! • Material: Chapters 20, 21, 22, and 23 L08! R03! L09! L10! EXAM!I! Note: this exam replaces the Wednesday, November 5 lecture NO LECTURE ON November 5 R04! L11! L12! R05! L13! L14! R06! L15! R07! L16! L17! R08! L18! L19! R09! L20! L21! EXAM!II! R10! ! 23 ! CHIP!3! ! ! ! CHIP!4! ! ! CHIP!5! ! ! CHIP!6! ! CHIP!7! ! ! CHIP!8! ! ! CHIP!9!! ! ! ! CHIP!10! 7! Maxwell’s Equations Summarizes All Known Fundamental Properties of Electricity and Magnetism (1864) E + S E diverges from point charge I N Changing B induces current B I B B is continuous in space PLUS Maxwell’s hypothesis that a changing electric field can produce a magnetic field Current produces B Changing B fields Changing E fields Maxwell’s Prediction: an Electromagnetic Wave No fields at all! No fields at all! E=E(x,t) B=B(x,t) Eo Bo c = f λ Relating f and λ: Units: [c] in m/s; [λ] in m; [f] in s-1 = Hz Relating E and B: E/B = c (at any position and at any time) Notation You must be able to distinguish between three closelyrelated concepts Symbol Meaning Comment E,B Instantaneous values Depends on exact location and time Eo , Bo Amplitude, maximum value Characteristic of the EM wave Erms , Brms Time-averaged values Characteristic of the EM wave Maxwell predicts the velocity c of an EM wave c= 1 1 = 2.998 ×108 m s = εoμo (8.85 ×10-12 C 2 N × m2 )(4π ×10-7 T × m A) Date Investigator Technique distance result 1600’s Galileo Lanterns/hills few km (?) ~10x faster than sound 1675 Roemer Eclipse/Jupiter’s moon 600 km 2 x 108 m/s 1728 Bradley Stellar aberration Inter-stellar 3.01 x 108 m/s 1849 Fizeau Rotating toothed wheel 8.6 km 3.13 x 108 m/s 1862 Focault Spinning mirror 35 km 299,790,000 m/s 1926 Michelson Rotating 8-sided mirrored “wheel” 35 km (299,798,000 ± 4000) m/s today International Agreement Defined by length of 1 m - 2.99792458 x 108 m/s Light is an Electromagnetic Wave! The Electromagnetic Spectrum visible light wavelengths from ~4 x 10-7 m to ~7.6 x 10-7 m (c = f λ ) Uses of EM radiation Observing the Cosmos Observing in different wave lengths Different views of the Crab Nebula Important Properties of EM waves • No electric waves; no magnetic waves; ONLY EM waves • Direction of E and B fields are perpendicular to each other AND to the direction of travel – TRANSVERSE WAVE • Strength of E and B fields vary in strength at a given point with time • E and B fields occur simultaneously and have maxima and minima at SAME time and place – they are “IN PHASE” • EM waves can have a fixed POLARIZATION (plane containing E field) • EM waves can travel in a vacuum • Speed of wave depends on properties of medium in which they travel • EM waves can be absorbed, reflected, change direction • EM waves carry energy and momentum • EM waves exhibit INTERFERENCE effects (constructive and destructive) • EM waves have a frequency and wavelength related by c=fλ (ELECTROMAGNETIC SPECTRUM) How to generate an EM wave? http://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html Heinrich Hertz 1888 H. Hertz is first to produce and detect EM radiation at ~100 MHz R L Breakdown switch S “closes” when spark I formation occurs. This event completes an RLC circuit which then produces a rapidly oscillating current. ~ 0.1 μs t Antennas and radio waves Wavelength and frequency 1. Hertz produced EM radiation near 100 MHz. What is the wavelength of this EM wave? c = fλ λ= c = 3×108 m / s =3 m f 100 ×106 s-1 2. WBAA broadcasts at 890 kHz. What is the wavelength of the EM radio waves? c 3 ×108 m / s λ= = = 337 m 3 -1 f 890 ×10 s 3. What is the frequency of a light wave with a wavelength of 5.0 x 10-7 m (green light)? 8 f = c = 3×10 m / s = 4.286 ×10 14 Hz λ 7 ×10-7 m Astrophysical sources send us EM radiation of f = 3x1027 Hz, λ = 10-19 m They oscillate 10 trillion times faster than green light!!! Energy is transported by an EM wave! The Poynting vector S specifies the instantaneous power per unit area transported by an EM wave at a point in space at an instant of time [E(t) and B(t) are instantaneous values]. 1 E(t) B(t) S = E ×B = μo μo E 1 c= = B εoμo 2(t E ) = cεoE 2(t) S= cμo Eo2 S AVERAGE = cεo 2 = cεoE2rms Units: [W/m2] Wave Intensity The time-averaged value of S is called the intensity I of the wave 1 2 I S AVERAGE = cεoEo2 = cεo Erms 2 Eo since c = = 1 Bo εoμo IS = AVERAGE æ B2 1 1 = ceo (c 2B o2 ) = ceo ç o çe m 2 2 è o o ö ÷ = c B2 rms ÷ m ø o The intensity I specifies the power (in Watts per m2) carried by an EM wave in free space averaged over time. The time averaged energy density of an EM wave KEY IDEA: Energy is stored in both E and B fields : Total absorber time aver. power thru hole : P = IA W time aver. energy thru hole : ΔU = PΔt J Hole in mask, area A utot Define time aver. energy density utot é utot u tot = = ΔU (AcΔt) I 1 = PΔt (AcΔt) = u tot = eoE rms = 2 1 mo 2 B rms cΔt (AcΔt ) Energy passing thru hole in time Δt 1 = eoE o = B o2 c 2 2mo 2 IAΔt J ù in êë ú m3 û Units: J/m3 Time aver. radiation, intensity I