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©2014JohnWiley&Sons,Inc.Allrightsreserved.
Waterwaves
©2014JohnWiley&Sons,Inc.Allrightsreserved.
Waterwaves
Waterwaves
Waterwaves
Waterwaves
Electromagne,cWaves
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Chapter33
33-1ElectromagneDcWaves
©2014JohnWiley&Sons,Inc.Allrightsreserved.
Maxwell’sRainbow
InMaxwell’sDme(themid1800s),thevisible,infrared,andultravioletformsoflightweretheonlyelectromagneDcwavesknown.SpurredonbyMaxwell’swork,however,HeinrichHertzdiscoveredwhatwenowcallradiowavesandverifiedthattheymovethroughthelaboratoryatthesamespeedasvisiblelight,indicaDngthattheyhavethesamebasicnatureasvisiblelight.Asthefigureshows,wenowknowawidespectrum(orrange)ofelectromagneDcwaves:Maxwell’srainbow.
33-1ElectromagneDcWaves
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TravellingElectromagne,cWave
AnarrangementforgeneraDngatravelingelectromagneDcwaveintheshortwaveradioregionofthespectrum:anLCoscillatorproducesasinusoidalcurrentintheantenna,whichgeneratesthewave.Pisadistantpointatwhichadetectorcanmonitorthewavetravelingpastit.
33-1ElectromagneDcWaves
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TravellingElectromagne,cWave
Electromagne,cWave.Figure1showshowtheelectricfieldEandthemagneDcfieldBchangewithDmeasonewavelengthofthewavesweepspastthedistantpointPofFig.2;ineachpartofFig.1,thewaveistravelingdirectlyoutofthepage.(WechooseadistantpointsothatthecurvatureofthewavessuggestedinFig.2issmallenoughtoneglect.Atsuchpoints,thewaveissaidtobeaplanewave,anddiscussionofthewaveismuchsimplified.)NoteseveralkeyfeaturesinFig.2;theyarepresentregardlessofhowthewaveiscreated:
Figure2
Figure1
33-1ElectromagneDcWaves
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TravellingElectromagne,cWave
1. TheelectricandmagneDcfieldsEandBarealwaysperpendiculartothedirecDoninwhichthewaveistraveling.Thus,thewaveisatransversewave,asdiscussedinChapter16.
2. TheelectricfieldisalwaysperpendiculartothemagneDcfield.
3. ThecrossproductE×BalwaysgivesthedirecDoninwhichthewavetravels.
4. Thefieldsalwaysvarysinusoidally,justlikethetransversewavesdiscussedinChapter16.Moreover,thefieldsvarywiththesamefrequencyandinphase(instep)witheachother.
Figure2
Figure1
33-1ElectromagneDcWaves
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TravellingElectromagne,cWave
Inkeepingwiththesefeatures,wecandeducethatanelectromagneDcwavetravelingalonganxaxishasanelectricfieldEandamagneDcfieldBwithmagnitudesthatdependonxandt:
whereEmandBmaretheamplitudesofEandB.TheelectricfieldinducesthemagneDcfieldandviceversa.
Figure2
Figure1
33-1ElectromagneDcWaves
TravellingElectromagne,cWave
WaveSpeed.Fromchapter16(Eq.16-13),weknowthatthespeedofthewaveisω/k.However,becausethisisanelectromagneDcwave,itsspeed(invacuum)isgiventhesymbolcratherthanvandthatchasthevaluegivenby
whichisabout3.0×108m/s.Inotherwords,
Figure2
Figure1
33-2EnergyTransportandThePoynDngVector
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ThePoyn,ngVector:TherateperunitareaatwhichenergyistransportedviaanelectromagneDcwaveisgivenbythePoynDngvector
TheDme-averagedrateperunitareaatwhichenergyistransportedisSavg,whichiscalledtheintensityIofthewave:inwhichErms=Em/√2.
ApointsourceofelectromagneDcwavesemitsthewavesisotropically—thatis,withequalintensityinalldirecDons.TheintensityofthewavesatdistancerfromapointsourceofpowerPsis
33-2EnergyTransportandThePoynDngVector
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33-3RadiaDonPressure
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WhenasurfaceinterceptselectromagneDcradiaDon,aforceandapressureareexertedonthesurface.IftheradiaDonistotallyabsorbedbythesurface,theforceisinwhichIistheintensityoftheradiaDonandAistheareaofthesurfaceperpendiculartothepathoftheradiaDon.IftheradiaDonistotallyreflectedbackalongitsoriginalpath,theforceisTheradia,onpressurepristheforceperunitarea:and
TotalAbsorp:on
TotalReflec:onbackalongpath
TotalAbsorp:on
TotalReflec:onbackalongpath
33-3RadiaDonPressure
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