Electricity & Magnetism Lecture 23

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Electricity & Magnetism Lecture 23 Electricity & Magne/sm Lecture 23, Slide 1

Transcript of Electricity & Magnetism Lecture 23

Electricity & MagnetismLecture 23

Electricity&Magne/smLecture23,Slide1

1 cycle per second

2 cycles per second

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

No–movingintheminuszdirec/on

No–hasEyratherthanEx

CheckPoint 2

Electricity&Magne/smLecture23,Slide5

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

Waves Carry Energy

Electricity&Magne/smLecture23,Slide14

Intensity

SunlightonEarth: I ∼ 1000 J/s/m2 ∼ 1 kW/m2

Intensity=Averageenergydeliveredperunit/me,perunitarea

Area=ALength=c dt

Electricity&Magne/smLecture23,Slide15

Waves Carry Energy

Electricity&Magne/smLecture23,Slide16

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

ExerciseAnelectromagne/cwaveisdescribedby:

Wavemovesinnega/vez direc/on

WhichofthefollowingplotsrepresentsBx(z)at/met = π/2ω ?

ABCD

Electricity&Magne/smLecture23,Slide23

+ z pointsoutofscreen− z pointsintoscreen

x

y

B

E

Pointsindirec/onofpropaga/on

at ω t = π/2: