Lecture 33: FRI 03 APRLecture 33: FRI 03 APR Ch.33.1 Ch.33.1––3,5: E&M Waves3,5: E&M WavesJames Clerk Maxwell (1831-1879) Physics 2102Jonathan DowlingA solution to the Maxwell equations in empty space isa “traveling wave”…c =1µ0!0= 3 " 108m/sThe “electric” waves travelat the speed of light!Light itself is a wave of electricity and magnetism!Maxwell, Waves and LightMaxwell, Waves and Lightd2Edx2= !µ0"0d2Edt2# E = E0sin k(x ! ct)electric and magnetic “forces” can travel! !!•=•SCdAEdtddsB00"µ!!•"=•SCdABdtddsEA solution to Maxwell’s equations in free space:)sin( txkEEm!"=)sin( txkBBm!"=n.propagatio of speed ,ck=!c =EmBm=1µ0!0=299,462,954 ms!=!187,163 miles/secVisible light, infrared, ultraviolet,radio waves, X rays, Gammarays are all electromagnetic waves.Electromagnetic WavesElectromagnetic WavesRadio waves are reflected by the layer of the Earth’satmosphere called the ionosphere.This allows for transmission between two points which arefar from each other on the globe, despite the curvatureof the earth.Marconi’s experiment discovered the ionosphere! Expertsthought he was crazy and this would never work.Fig. 33-1The wavelength/frequency range in which electromagnetic (EM) waves(light) are visible is only a tiny fraction of the entire electromagneticspectrum.Maxwell’s RainbowFig. 33-2(33-2)An LC oscillator causes currents to flow sinusoidally, which in turn producesoscillating electric and magnetic fields, which then propagate through space asEM waves.Fig.%33-3Oscillation Frequency:1LC!=Next slideThe Traveling Electromagnetic (EM) Wave, Qualitatively(33-3)Fig. 33-5Mathematical Description of Traveling EM WavesElectric Field:( )sinmE E kx t!= "Magnetic Field:( )sinmB B kx t!= "Wave Speed:0 01cµ !=Wavenumber:2k!"=Angular frequency:2!"#=Vacuum Permittivity:0!Vacuum Permeability:0µAll EM waves travel a c in vacuumAmplitude Ratio:mmEcB=Magnitude Ratio:( )( )E tcB t=EM Wave Simulation(33-5)Electromagnetic waves are able to transport energy from transmitterto receiver (example: from the Sun to our skin).The power transported by the wave and itsdirection is quantified by the Poynting vector.John Henry Poynting (1852-1914) 211|| EcEBS00==µµThe The Poynting Poynting Vector:Vector:Points in Direction of Power FlowPoints in Direction of Power FlowEBSUnits: Watt/m2For a wave, sinceE is perpendicular to B: BES!!!!=0µ1In a wave, the fieldschange with time.Therefore the Poyntingvector changes too!!The direction is constant,but the magnitude changesfrom 0 to a maximumvalue.____________222___)(sin11tkxEcEcSIm!µµ"===00The average of sin2 overone cycle is ½:221mEcI0=µ21rmsEcI0=µBoth fields have the same energy density. 2 22 201 1 1 1( )2 2 2 2E BB Bu E cB u! ! !! µ µ0 00 0 0= = = = =or, EM Wave Intensity, Energy DensityEM Wave Intensity, Energy DensityA better measure of the amount of energy in an EM wave is obtainedby averaging the Poynting vector over one wave cycle.The resulting quantity is called intensity. Units are also Watts/m2.The total EM energy density is then0220/µ!BEu ==Solar EnergySolar EnergyThe light from the sun has an intensity of about 1kW/m2.What would be the total power incident on a roof ofdimensions 8m!x!20m!?I!=!1kW/m2 is power per unit area.P=IA=(103 W/m2) x 8m x 20m=0.16 MegaWatt!!The solar panel shown (BP-275) has dimensions 47in x29in. The incident power isthen 880 W. The actualsolar panel delivers 75W(4.45A at 17V): less than10% efficiency….The electric meter on a solar homeruns backwards — Entergy Pays YOU!The intensity of a wave is power per unit area. If one has asource that emits isotropically (equally in all directions) thepower emitted by the source pierces a larger and largersphere as the wave travels outwards: 1/r2 Law!24 rPIs!=So the power perunit area decreasesas the inverse ofdistance squared.EM Spherical WavesEM Spherical WavesExampleExampleA radio station transmits a 10 kW signal at a frequencyof 100 MHz. At a distance of 1km from the antenna, findthe amplitude of the electric and magnetic fieldstrengths, and the energy incident normally on a squareplate of side 10cm in 5 minutes.222/8.0)1(4104mmWkmkWrPIs===!!mVIcEEcImm/775.02212==!=00µµnTcEBmm58.2/ ==mJSAtUAtUAPS
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