Class 32: OutlineRecall: Electromagnetic RadiationRecall Electromagnetic Radiation: Plane WavesProperties of EM WavesGenerating Plane Electromagnetic RadiationShake A Sheet of Charge Up and DownJava Applet for Generation of Plane WavesFirst Pull The Sheet of Charge Down At Speed vRate of Work Done?What About B Field?Rate Energy Carried Away?To generate plane wave, move sheet up and down sinusoidallyGenerating Plane Wave AppletPRS Question:Generating A Plane WaveGenerating Electric Dipole Electromagnetic WavesGenerating Electric Dipole Radiation AppletQuarter-Wavelength AntennaWhy are Radio Towers Tall?Quarter-Wavelength AntennaQuarter-Wavelength AntennaSpark Gap TransmitterSpark Gap Generator:An LC OscillatorFirst: Example of “lumped” LC Oscillator (Capacitor & Inductor together as one)Group Problem: Lumped LC CircuitOur spark gap antennaSpark Gap TransmitterPRS Question:Spark Gap AntennaSpark Gap AntennaSpark Gap AntennaPRS Questions:Angular Distribution & Polarization of RadiationDemonstration:AntennaPolarizationPolarization of TV EM WavesDemonstration:Microwave PolarizationExperiment 12:Measure Wavelength by Setting Up Standing WaveExperiment 12:MicrowavesExam 3 Results1P32-Class 32: OutlineHour 1:Generating Electromagnetic WavesPlane EM WavesElectric Dipole EM WavesHour 2:Experiment 12: MicrowavesReview Exam 3 Results2P32-Recall:Electromagnetic Radiation3P32-Recall Electromagnetic Radiation: Plane Waveshttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/07-EBlight/07-EB_Light_320.html4P32-Properties of EM Waves8001310mvcsµε== =×00EEcBB==Travel (through vacuum) with speed of lightAt every point in the wave and any instant of time, E and B are in phase with one another, withE and B fields perpendicular to one another, and to the direction of propagation (they are transverse):Direction of propagation = Direction of ×EBGG5P32-Generating Plane Electromagnetic Radiation6P32-Shake A Sheet of Charge Up and Down7P32-Java Applet for Generation of Plane Waves http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/09-planewaveapp/09-planewaveapp320.html8P32-First Pull The Sheet of Charge Down At Speed v10tanEvT vEcTcθ===100ˆˆ2vvEccσε⎛⎞⎛⎞==⎜⎟⎜⎟⎝⎠⎝⎠EjjGWhen you pull down, there is a back force up!9P32-Rate of Work Done?2100ˆˆ()22evvdAddq dAccσσσεε⎛⎞⎛ ⎞== =⎜⎟⎜ ⎟⎝⎠⎝ ⎠FE j jGG2ext0ˆ2evdAddcσε⎛⎞=− =−⎜⎟⎝⎠FF jGG()2222ext ext00ˆˆ22dW ddv vvdAdt dA dt c cσσεε⎛⎞=⋅=− ⋅−=⎜⎟⎝⎠FsjjGG10P32-What About B Field?010ˆ(2), 0 ˆ(2), 0vxvxµσµσ⎧+>⎪=⎨−<⎪⎩kBkG100ˆˆ2vvEccσε⎛⎞⎛⎞==⎜⎟⎜⎟⎝⎠⎝⎠EjjG11P32-Rate Energy Carried Away?22011000 011ˆˆˆ224vvvccµσσσµµε ε⎛⎞ ⎛⎞⎛⎞=×= × =⎜⎟ ⎜⎟⎜⎟⎝⎠⎝⎠ ⎝⎠SEB j k iGGGEnergy radiated to left and right is exactly equal to the rate of work required to move sheet down12P32-To generate plane wave, move sheet up and down sinusoidallyThe work you do in moving the sheet is carried away as electromagnetic radiation, with 100% efficiency.13P32-Generating Plane Wave Applet14P32-PRS Question:Generating A Plane Wave15P32-Generating Electric Dipole Electromagnetic Waves16P32-Generating Electric Dipole Radiation Applet17P32-Quarter-Wavelength AntennaAccelerated charges are the source of EM waves. Most common example: Electric Dipole Radiation.4λ4λt = 0 t = T/4 t = T/2 t = T18P32-Why are Radio Towers Tall?AM Radio stations have frequencies 535 – 1605 kHz. WLW 700 Cincinnati is at 700 kHz. 83310m/s429m700 10 Hz/ 4 107m 350ftcfλλ×== =×≈≈The WLW 700 Cincinnati Tower is 747 ft tall19P32-Quarter-Wavelength Antenna20P32-Quarter-Wavelength Antennahttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/04-QuarterWaveAntenna/04-MicrowaveDLICS_320.html21P32-Spark Gap Transmitter22P32-Spark Gap Generator:An LC OscillatorFirst: Example of “lumped” LC Oscillator (Capacitor & Inductor together as one)23P32-Group Problem: Lumped LC CircuitHeight (into page): hParallel Plate CapacitorCylindrical InductorQuestion: What is the resonance frequency?Recall:01LCω=0ACdε=LIΦ=[]solenoidcurrent per unit lengthoBµ=24P32-Our spark gap antenna612 4(4.5 10 )(33 10 F) 1.5 10 sτ RC−−==×Ω× =×rad14cfTl==10310cm/s12.4cm×=92.4 10 Hz 2.4GHz=× =1) Charge gap (RC)2) Breakdown! (LC)3) Repeat25P32-Spark Gap Transmitter26P32-PRS Question:Spark Gap Antenna27P32-Spark Gap Antennahttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/03-AntennaPattern/03-MicrowaveAntenna_320.html28P32-Spark Gap Antenna29P32-PRS Questions:Angular Distribution & Polarization of Radiation30P32-Demonstration:Antenna31P32-Polarization32P32-Polarization of TV EM WavesWhy oriented as shown?Why different lengths?33P32-Demonstration:Microwave Polarization34P32-Experiment 12:Measure Wavelength by Setting Up Standing Wave35P32-Experiment 12:Microwaves36P32-Exam 3
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