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MIT 8 02X - Electricity and Magnetism

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Electricity and MagnetismPoynting VectorPolarizationPolarizationSuperposition of WavesSuperposition of WavesSuperposition of WavesStanding WaveDouble Slit ExperimentInterference with MatterScattering of LightMay 15 2002Electricity and Magnetism•Today– More on wave phenomena• Polarization•Superposition–Standing waves– Interference (proof that light is a wave)• Scattering of light (why is the sky blue)May 15 2002Poynting Vector• Not a typo: John Henry Poynting (1852-1914)• Wave: Direction + Magnitude• Summarize using vector: Poynting VectorS = 1/µ0E x BDirection: S B, S EMagnitude: S = 1/µ0EBPower/Unit AreaMay 15 2002PolarizationMay 15 2002Polarization• Polarization:– Oscillation of fields has well defined direction• Polarization only possible for transverse waves• In general, light (sun, lightbulb) is unpolarized– Superposition of waves with many different orientations• Can be polarized using e.g. polarizer foilsMay 15 2002Superposition of Waves• We saw many examples of superposition principle• Not only true for static fields, but also for time-dependent fields-> Superposition of wavesMay 15 2002Superposition of Waves• Example: Standing wavesReflecting SurfaceIncoming waveE(z,t) = E0sin(kz+ωt)ConductorzE(z,t) = E0sin(kz-ωt)Reflected waveMay 15 2002Superposition of WavesSuperposition of Incoming wave and Reflected waveEtotal= E0sin(kz+ωt) + E0sin(kz+ωt)= 2 E0sin(kz) cos(ωt) Standing wavezEt = 00 < t < Tλλ/2NodeMay 15 2002Standing WaveL = M λ/2; M = 1,2,3... Eλλ/23/2λE = 0 E = 0 Microwave oven:λ ~ 10cmMay 15 2002Double Slit Experimentdαr1r2Etot= E0sin(kr1-ωt) + E0sin(kr2-ωt)Max. if “constructive interference”kr1-ωt = kr2-ωt + M 2πyRyMax= M λ/d R yMin= (M+1/2) λ/d RMay 15 2002Interference with MatterInterference can also happen for “matter waves”Bose-Einstein condensate of atoms(Ketterle et al, Nobel Prize ’01)May 15 2002Scattering of LightWhy is the sky blue during the day and red at sunset?Molecules, dust (size << λ)Red Light (λ ~ 700 nm)Lord Rayleigh: Scattering probability ~ 1/λ4scattering (blue)/scattering(red): -> 7004/4004~ 10 Blue Light (λ ~ 400


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