(pre- and) post tests and surveys - physics.rutgers.educizewski/227_s2018/l24-ch32b-post.pdf ·...
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(Pre-and)PostTestsandSurveysAllengineeringstudentsarebeingtestedintheircorecoursesthisacademicyearatthebeginningofthesemesterandagainattheendofthesemester.Thesedatawillbeusedtoimproveyourlearningexperiences.• Yourresponsestothesetests&surveyswillhavenobearingonyourcoursegrade.• Iwillnotseeyourscores.• Iwillonlytrackwhetherornotyoutookthetestsandsurveys.
• Therearefourcomponentstothepreandposttestrequirements:• Twoin-classexams;Twoon-linesurveys• Anexamandasurveybothatthebeginningandattheendofthesemester.• Ifyouparticipateinall4components,youwillget100%on2%ofyourgrade• Ifyoumissanyofthe4components,youwillgetazerofor2%ofyourgrade.• Secondin-classexamThursday,April26inlecture.
TakesurveyTODAYandsaveconfirmationpage.DeadlineMondayApril3011:59pm.https://rutgers.ca1.qualtrics.com/jfe/form/SV_2lVQrms4jn96hJX
• Taketheexamsandsurveysseriously!Answerallpartstobestofyourabilities.• Ifyoudonottaketheexamsandsurveysseriously,youwillgetazero.• IfyoutaketheexamsorsurveysforsomeoneelseORyouasksomeonetotakethe
examsforyou,youwillnotonlygetazerobutmaybeseparatedfromtheuniversitybecauseyouhaveviolatedacademicintegrity. 1
Summerstudyopportunity:PlasmaphysicsUndergraduatePlasmaPhysicsWorkshop
July18through20,2018atPrincetonPlasmaPhysicsLabThisworkshoptargetsfirstandsecond-yearundergradsandintroducesthemtoplasmaphysicsfromanexperimentalandatheoreticalperspective.Theobjectiveisforparticipantstogainanintroductoryunderstandingofthefieldofplasmaphysicsandopportunitieswithin.Alltravel,boardingandmealswillbecoveredbyPPPL.Underrepresentedstudentsareespeciallyencouragedtoapply.
https://www.pppl.gov/education/science-education/programs/workshop-plasma-physics-undergraduates 2
AnnouncementsThisweek: courseevalhttps://sakai.rutgers.edu/portal/site/sirs• Requiredposttest–ThursdayApril26inlecture
• Ifmisslecture,limitedopportunityformakeup;elsezerofor2%ofgrade
• Homework10dueThursdayApril26:Chapter31+32• RecitationonFridayApril27:Chapter32.• QuizonFridayApril27:Homework10,Lectures22+23+24
Finalexam:Wednesday,May9,20184:00to7:00PMinPhysicsLectureHall.
• 30multiplechoicequestions,≈15fromChapters30-32,≈15cumulativeChapters21-29
• ReviewsessionTuesday,May84to6PM227SerinPhysics&Astro
Allexamsareclosed-book,nocalculatorsorotherelectronicdevicesallowed.
AnnouncementsFinalexam
• Wednesday,May9,2018inlecture:4:00–7:00pm• 30multiplechoicequestions.≈15fromChapters30-32,≈15fromChapters21-29
• ExamreviewTuesday,May8,4:00– 6:00pm227SerinPhysics&Astro
Allexamsareclosed-book,nocalculatorsorotherelectronicdevicesallowed.Allquestionswillbemultiplechoice.Forthefinalexam,youmaybringwithyouthree(3)"formulasheets",on8.5x11inchsheetsofpaper(OKtousebothsides)onwhichyoumayhandwriteanyformulaeordiagramsornotesorproblemsolutionsthatmightbehelpfultoyouduringtheexam.Informationonthesheetsmustbehandwritten,noattachmentsareallowed.Thenumericalvaluesofrelevantconstantswillbeprovidedtoyou.Youshouldbring#2pencilstotheexamsforthecomputerforms.
Typesofquestions:LikeI-clickers,simplenumbers,formulaeStudy:Homework,Iclickers,examplesintextbook,collaborative+pre-RECOldexams:http://www.physics.rutgers.edu/~cizewski/227_s2018/Physics-227-s2018-old-exams.htm
FreetutoringviaMSLC:https://rlc.rutgers.edu/services/peer-tutoring
Lecture24TuesdayApril24,2018
Chap32continued:ElectromagneticWavesEnergy,momentumRadiationpressureStandingwaves
5
SummaryChapter32E-MwavesMaxwell’sequations=>electromagneticwaves• Travelingatspeedoflightinvacuum
• Transverse;directionofpropagation
• Sinusoidal
7
c = 1ε0µ0
= 3×108 m/s
!E ×!B
!E(x,t) �= y
∧
Emax cos(kx −ωt)!B(x,t) �= z
∧
Bmax cos(kx −ωt)
Emax = cBmax
• Wavemotionisfunctionofposition(x)andtime(t)
Wherev=phasevelocityofthewaveX
y
Z
SinusoidalWaves
8
MechanicalWaves-review
y(x,t)= Acos(kx −ωt)
k =2πλ
ω = vk
E-MWavespropagatingin+xdirection!E(x,t) �= y
∧
Emax cos(kx −ωt)!B(x,t) �= z
∧
Bmax cos(kx −ωt)
Emax = cBmax
IclickerquestionTheelectricpartofanelectromagneticwavemovinginthe+zdirectionisgivenby
WhichofthefollowingstatementsabouttheycomponentofthemagneticfieldpartisCORRECT?
9
Ex = Asin(kz −ωt), Ey = Ez = 0
(A) By ∝ cos(ky−ωt)
(B) By ∝ cos(kz −ωt)
(C) By ∝ sin(kz −ωt)
(D) By = 0
(E) By isgiven bysomeother expression.
IclickeranswerTheelectricpartofanelectromagneticwavemovinginthe+zdirectionisgivenby
WhichofthefollowingstatementsabouttheycomponentofthemagneticfieldpartisCORRECT?
10
Ex = Asin(kz −ωt), Ey = Ez = 0
(A) By ∝ cos(ky−ωt)
(B) By ∝ cos(kz −ωt)
(C) By ∝ sin(kz −ωt)
(D) By = 0
(E) By isgiven bysomeother expression.
SummaryChapter32E-MwavesMaxwell’sequations=>electromagneticwaves• Travelingatspeedoflightinvacuum
• Transverse;directionofpropagation
• Sinusoidal
Next:EnergyandmomentumofE-Mwaves
11
c = 1ε0µ0
= 3×108 m/s
!E ×!B
!E(x,t) �= y
∧
Emax cos(kx −ωt)!B(x,t) �= z
∧
Bmax cos(kx −ωt)
Emax = cBmax
EMEnergy(flow)inEMwaveEMwavescarryenergy,intheelectricandmagneticfields• Recallenergydensities
12
u = uE +uB =12ε0E
2 +1
2µ0
B2
B =Ec= ε0µ0E
EnergydensityofB-field=EnergydensityofE-fieldButE(position,time)=>u(position,time)
u =12ε0E
2 +1
2µ0
ε0µ0E( )2= ε0E
2 = u
c = 1ε0µ0
EMEnergy(flow)inEMwave• EnergyinvolumedV=areaxdistancetraveledintimedt
• Energyflowperunittimeperunitarea(invacuum)=S
• S“points”indirectionofenergyflow=directionofpropagationoftheEMwave
Ø ThePoyntingvector• Units:power/unitarea• BecauseE,B(position,time)=>S(position,time)
13
dU = udV = ε0E2(Acdt)
S =1AdUdt
= ε0cE2 = ε0cE(cB)=
EBµ0
!S =
1µ0
!E ×!B
c = 1ε0µ0
EMEnergyflow/intensityinEMwaveAssumesinusoidalwavetravelingin+xdirection
• Direction=+xdirection• Magnitude
• TimeaverageofS:• Timeaverageofcos=0• IntensityI=Sav
14
!S(x,t)=
1µ0
y∧
Emax cos(kx −ωt)× z∧
Bmax cos(kx −ωt)⎡⎣⎢
⎤⎦⎥
!E(x,t) �= y
∧
Emax cos(kx −ωt)!B(x,t) �= z
∧
Bmax cos(kx −ωt)
S =1µ0
EmaxBmax cos2(kx −ωt)=
1µ0
EmaxBmax 1+ cos2(kx −ωt)[ ]
I = Sav =EmaxBmax
µ0
=E2
max
2µ0c=12ε0cE
2max
!S =
1µ0
!E ×!B
c = 1ε0µ0
Imaginethatwhenyouswitchonyourlamp,youincreasetheintensityoflightshiningonyourtextbookbyafactorof16.Bywhatfactordoestheaverageelectricfieldstrengthinthislightincrease?
Iclickerquestion
15
A. Factorof256B. Factorof16C. Factorof4D. Factorof2E. Factorof1
I = Sav =EmaxBmax
µ0
=E2
max
2µ0c=12ε0cE
2max
Imaginethatwhenyouswitchonyourlamp,youincreasetheintensityoflightshiningonyourtextbookbyafactorof16.Bywhatfactordoestheaverageelectricfieldstrengthinthislightincrease?
Iclickeranswer
16
A. Factorof256B. Factorof16C. Factorof4D. Factorof2E. Factorof1
I = Sav =EmaxBmax
µ0
=E2
max
2µ0c=12ε0cE
2max
Imaginethatwhenyouswitchonyourlamp,youincreasetheintensityoflightshiningonyourtextbookbyafactorof16.Ifyourbookisr=1mfromyourlamp,howintenseisthelightsource?(i.e.,whatisthetotalenergyflow/unittimeoutofthelamp?)
Powerofthesource
17
I = Sav =E2
max
2µ0c
P =!Sav •d
!A"∫ = I(4πr2 )
I =P
4πr2
Electromagneticwavescarrymomentum• EMradiationismadeupof“particles”=photonsthatcarryenergyandmomentum• Momentumdensity:
• Averagerateofmomentumtransfer/area:wheredV=Acdt
Momentumflow&pressureinEMwave
19
p =energy
c
dpdt
1A=Savc=Ic
dpdV
=1cd(energy)
dV=ε0E
2
c=ε0EcB
c= ε0EB
µ0
µ0
=Sc2
dpdV
=Sc2
c = 1ε0µ0
!S =
1µ0
!E ×!B
E = cB
Electromagneticwavescarrymomentum• Averagerateofmomentumtransfer/area:
Pressure=force/unitarea=(dp/dt)/unitarea• AmountofpressuredependsuponwhetherEMwaveis
• Totallyabsorbed
• Totallyreflected(changeinmomentumdoubled)
Momentumflow&pressureinEMwave
20
dpdt
1A=Savc=Ic
prad =Savc=Ic
prad =2Savc
=2Ic
StandingEMwavesConsiderlinearlypolarizedEMwavetravelingin-xdirectiononaperfectconductor• Emustbezeroeverywhereonthey-z
conductingplane• ButincidentE≠0iny-zplane• NetEfield=0=incident+reflected
oscillatingE-field
21
Ey(x,t)�= Emax cos(kx +ωt)− cos(kx −ωt)[ ]
Bz(x,t)�= Bmax −cos(kx +ωt)− cos(kx −ωt)[ ]
cos(A±B)= cosAcosB ∓ sinAsinB
Ey(x,t)�= −2Emax sin kx sinωt
Bz(x,t)�= −2Bmax coskx cosωt
StandingEMwavesinacavity• Standingwaves
• Ehastobezeroatx=0andx=L• Definesnormalmodes
22
Ey(x,t)�= −2Emax sin kx sinωt
Bz(x,t)�= −2Bmax coskx cosωt
L
https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters_2017_Jan_1/quantum_theory_origins/index.html
λn =2Ln
n = 1,2,3...
fn =cλn
= nc2L
StandingEMwaves• Standingwaves
• Atx=0,Ealwayszero• E=0wheresinkx=0Ø NodalplanesofE
• AntinodalplanesofE(whenE=max)= NodalplanesofBwhencoskx=0• NoteE(t)issinωtandB(t)iscosωt
Ø EandBfieldsareoutofphasewheninastandingwave23
Ey(x,t)�= −2Emax sin kx sinωt
Bz(x,t)�= −2Bmax coskx cosωt
x = 0,λ2, λ,
3λ2
...
kx = 0, π , 2π ...
x =λ4,3λ4,5λ4
...
kx =π2,3π2,5π2...
StandingEMwaves• Standingwaves
• Atx=0,Ealwayszero• E=0wheresinkx=0• NodalplanesofE
• AntinodalplanesofE(whenE=max)= NodalplanesofBwhencoskx=0• NoteE(t)issinωtandB(t)iscosωt
Ø EandBfieldsareoutofphasewheninastandingwave24
Ey(x,t)�= −2Emax sin kx sinωt
Bz(x,t)�= −2Bmax coskx cosωt
x = 0,λ2, λ,
3λ2
...
kx = 0, π , 2π ...
x =λ4,3λ4,5λ4
...
kx =π2,3π2,5π2...
Anti-node
Node
L =3λ2
• WhatisdistancebetweennodalplanesofE-field?
• NodalplanesofEfieldwhen
• Distancebetweennodalplanes=λ/2 = 5 m4=2.5 m
StandingwavenodalplanesforEandBfields
x = 0,λ2, λ,
3λ2
...
GivenstandingEMwavewithfrequencyf=30MHzWavelength λ = v
f=3×108 m/s30×106 /s
= 10 m
• NodalplanesofEfieldwhen
• Distancebetweennodalplanes=λ/2 = 5 m
• WhatisdistancebetweennodalplaneofE-fieldandnodalplaneofB-field?• NodalplanesofBfieldwhen(alsoanti-nodalplanesofEfield)
• DistancebetweennodalplanesofEandBfields=λ/4=2.5 m
StandingwavenodalplanesforEandBfields
x = 0,λ2, λ,
3λ2
...
GivenstandingEMwavewithfrequencyf=30MHzWavelength λ = v
f=3×108 m/s30×106 /s
= 10m
x =λ4,3λ4,5λ4...
IclickerquestionThedrawingshowsasinusoidalelectromagneticstandingwave.Whichofthefollowingstatementsabouttheaverage(averagedovereitherxort)PoyntingvectorinthiswaveisCORRECT?
27
A. TheaveragePoyntingvectorinthiswavepointsalongthex-axis.B. TheaveragePoyntingvectorinthiswavepointsalongthey-axis.C. TheaveragePoyntingvectorinthiswavepointsalongthez-axis.D. TheaveragePoyntingvectorinthiswaveiszero.
E. NoneoftheabovestatementsabouttheaveragePoyntingvectorinthiswaveiscorrect.
Sav =<1µ0
!E ×!B >sinacosa =
12sin2a
IclickeranswerThedrawingshowsasinusoidalelectromagneticstandingwave.Whichofthefollowingstatementsabouttheaverage(averagedovereitherxort)PoyntingvectorinthiswaveisCORRECT?
28
A. TheaveragePoyntingvectorinthiswavepointsalongthex-axis.B. TheaveragePoyntingvectorinthiswavepointsalongthey-axis.C. TheaveragePoyntingvectorinthiswavepointsalongthez-axis.D. TheaveragePoyntingvectorinthiswaveiszero.
E. NoneoftheabovestatementsabouttheaveragePoyntingvectorinthiswaveiscorrect.
Sav =<1µ0
!E ×!B >sinacosa =
12sin2a
IclickersolutionThedrawingshowsasinusoidalelectromagneticstandingwave.Whichofthefollowingstatementsabouttheaverage(averagedovereitherxort)PoyntingvectorinthiswaveisCORRECT?
29
Sav =<1µ0
!E ×!B >
Sav =<1µ0
!E ×!B >=<
1µ0
Emax sin kx sinωtBmax coskx cosωt >
=<1µ0
EmaxBmax sin kx coskx sinωt cosωt >
=<1µ0
EmaxBmax{12sin2kx
12sin2ωt}>= 0
sinacosa =12sin2a
SummaryChapter32• Maxwell’sequationsinvacuum,freespaceØ EMwaves
• Directionofpropagation
• Sinusoidal
• Power/unitarea=Poyntingvector
Ø IntensityofEMwave
• RadiationpressureofEMwave
• StandingEMwaves30
E = cB c = 1ε0µ0
= 3×108 m/s
!S =
1µ0
!E ×!B
!E ×!B
!E(x,t) �= y
∧
Emax cos(kx −ωt)!B(x,t) �= z
∧
Bmax cos(kx −ωt)
I = Sav =EmaxBmax
µ0
=12ε0cE
2max
prad (absorbed) =Savc=Ic
prad (reflected) =2Savc
=2Ic
SummaryChapter32(cont)StandingE-Mwaves• EandB90°outofphase
• NodeswhereE=0;antinodesB=max:
• AntinodeswhereE=max;nodesB=0:
• Standingwavesinacavity
31
Ey(x,t)�= −2Emax sin kx sinωt
Bz(x,t)�= −2Bmax coskx cosωt
kx =π2,3π2,5π2...
kx = 0, π , 2π ...
https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters_2017_Jan_1/quantum_theory_origins/index.html