Electricity & Magnetism Lecture 23
Transcript of Electricity & Magnetism Lecture 23
Plane Waves from Last Time
EandBareperpendicularandinphase
Oscillatein/meandspace
Direc/onofpropaga/ongivenbyE ×B
B0 = E0/c
Argumentofsin/cosgivesdirec/onofpropaga/on
Electricity&Magne/smLecture23,Slide3
Understanding the speed and direction of the wave
Ex
z t = 0
Ex = Eosin(kz − ωt)
Whathashappenedtothewaveforminthis/meinterval?
IthasMOVEDTOTHERIGHTbyλ/4
t = π/2ω
Ex
z
Electricity&Magne/smLecture23,Slide4
From the prelecture
Theequa/onforthex-componentoftheelectricfieldofaplaneelectromagne/cwaveisgivenby:Ex=Eosin(kz−ωt)
Whichofthefollowingequa/onsdescribestheassociatedmagne/cfield?
A)By=Eocsin(kz−ωt)
B)By=(Eo/c)sin(kz−ωt)
C)By=Eoccos(kz−ωt)
D)By=(Eo/c)cos(kz−ωt)
Prelecture question
Whichofthefollowingstatementsdoesnotcorrectlydescribeaharmonicplanewavetravelinginsomemedium.
A)The/metakenbyanypointofthewavetomakeonecompleteoscilla/ondoesnotdependontheamplitude.
B)Doublingthewavelengthofthewavewillhalveitsfrequency.
C)Doublingtheamplitudehasnoeffectonthewavelength.
D)Doublingthefrequencyofthewavewilldoubleitsspeed.
Prelecture
Anelectromagne/cwaveistravelingthroughfreespaceandthemagnitudesofitselectricandmagne/cfieldsareEoandBorespec/vely.Itthenpassesthroughafilterthatcutsthemagnitudeoftheelectricfieldbyaquarter(E=Eo/4).Whathappenstothemagnitudeofthemagne/cfield?
A. B=Bo/4
B. B=Bo/2
C. B=Bo
Prelecture Question
Thecolorofthestarsweobserveingalaxiescanbeusedtodeducethevelocityofthegalaxyrela/vetoEarth.
Supposetheaveragecolorofthestarsinanewlydiscoveredgalaxyisbluerthantheaveragecolorofstarsinourowngalaxy.Whatwouldbeasensibleconclusionaboutthemo/onofthenewgalaxyrela/vetoourown?
A. Thatitismovingtowardus.
B. Thatitismovingawayfromus.
CheckPoint 6
Wavelengthisequaltothespeedoflightdividedbythefrequency.
C = 3.0 x 108 m/s
Check:Lookatsizeofantennaonbaseunit
Electricity&Magne/smLecture23,Slide6
Doppler Shift
TheBigIdeaAssourceapproaches:WavelengthdecreasesFrequencyIncreases
Electricity&Magne/smLecture23,Slide7
BigBang
Paris Ambulance
Dr Chai Demo
f 0 = f
s1 + �1 � �
What’sDifferentfromSoundorWaterWaves?
Sound/WaterWaves:Youcancalculate(norela/vityneeded)
BUTResultissomewhatcomplicated:issourceorobservermovingwrtmedium?
Electromagne/cWaves:Youneedrela/vity(/medila/on)tocalculate
BUTResultissimple:onlydependsonrela/vemo/onofsource&observer
β > 0 ifsource&observerareapproaching
β < 0 ifsource&observeraresepara/ng
β = v/c
Doppler Shift for E-M Waves
Electricity&Magne/smLecture23,Slide8
v
or f’f
v
ff’
Doppler Shift for E-M Waves
Electricity&Magne/smLecture23,Slide9
f 0 = f
s1 + �1 � �
TheDopplerShijistheSAMEforbothcases!f ʹ/f onlydependsontherela/vevelocity
f 0 = f
s1 + �1 � �
ANoteonApproxima/ons
why?
Doppler Shift for E-M Waves
Electricity&Magne/smLecture23,Slide10
β << 1
Evaluate:NOTE:
TaylorSeries:Expand around β = 0F(�) =
1 + �1 � �
!1/2
OurSun Starinadistantgalaxy
wavelen
gth
Wavelengthsshijedhigher
Red Shift of Stellar Spectra
Frequenciesshijedlower
Starsepara/ngfromus(ExpandingUniverse)
Electricity&Magne/smLecture23,Slide11
PoliceradarsgettwicetheeffectsincetheEMwavesmakearoundtrip:
v β f’ f’-f30 m/s (108 km/h) 1.000 x 10-7 24,000,004,800 4800 Hz
31 m/s (112 km/h) 1.033 x 10-7 24,000,004,959 4959 Hz
If f = 24,000,000,000 Hz (k-bandradargun)c = 300,000,000 m/s
Example
Electricity&Magne/smLecture23,Slide12
Intensity
SunlightonEarth: I ∼ 1000 J/s/m2 ∼ 1 kW/m2
Intensity=Averageenergydeliveredperunit/me,perunitarea
Area=ALength=c dt
Electricity&Magne/smLecture23,Slide15
Justanotherwaytokeeptrackofallthis:ItsmagnitudeisequaltoI Itsdirec/onisthedirec/onofpropaga/onofthewave
Comment on Poynting Vector
Electricity&Magne/smLecture23,Slide17
ABCD
Whichofthefollowinggraphsrepresentsthez−dependenceofBxatt =0?
ExerciseAnelectromagne/cwaveisdescribedby:whereistheunitvectorinthe+ydirec/on.
X
EandB are“inphase”(or180ooutofphase)
X
x
y
z
E
B
xy
z
Wavemovesin+z direc/on
Electricity&Magne/smLecture23,Slide21
Pointsindirec/onofpropaga/on
dEdt! dU
dt= IA v! c
Light has Momentum!
Ifithasenergyanditsmoving,thenitalsohasmomentum:
Analogyfrommechanics:
pressure
Electricity&Magne/smLecture23,Slide18
ForE − M waves:
Radia/onpressure
Butthenagain,whatarewekeepingconstanthere?
WHATABOUTPHOTONS?
CheckPoint 4
Electricity&Magne/smLecture23,Slide19
A) B) C)
Webelievetheenergyinane-mwaveiscarriedbyphotons
Ques/on:WhatarePhotons?Answer:PhotonsarePhotons.
Photonspossessbothwaveandpar/cleproper/esPar/cle: EnergyandMomentumlocalizedWave: Theyhavedefinitefrequency&wavelength ( fλ = c)
Ques/on:Howcansomethingbebothapar/cleandawave?Answer:Itcan’t(whenweobserveit)Whatweseedependsonhowwechoosetomeasureit!Themysteryofquantummechanics:MoreonthisinPHYS285
h = 6.63×10−34 J⋅s Planck’sconstant
Connec/onsseeninequa/ons: E = hf p = h/λ
Photons
Electricity&Magne/smLecture23,Slide20
Exercise
Anelectromagne/cwaveisdescribedby:
+z pointsoutofscreen−zpointsintoscreen
x
y
WhatistheformofBforthiswave?
A)
B)
C)
D)
B
E
xy
z
Wavemovesin−zdirec/on
Electricity&Magne/smLecture23,Slide22
Pointsindirec/onofpropaga/on