View
230
Download
0
Category
Preview:
Citation preview
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 1/38
L12 – electromagneticwaves
Thursday, June 30th, 1230 to
1345Bradley J. Nartowt, Gordon N.
Tam
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 2/38
Logistics
•
Bunch of logstcs to tal! a"out #rst$• %ll go through &uc!ly. 'ust lecture
on all of cha(ter 22 today.
•
)(ologes for the "lsterng (ace, "ut twll allow some tme at the end.
• )m s to re*st old materal and sol*e
com(rehens*e (ro"lems• +nal eam wll "e cumulat*e,
consstng of -a (ro*ded (ool of
com(rehens*e (ro"lems.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 3/38
/am hstogram• ets loo! at statstcs of /am
1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
10
20
30
40
average: 10.5, stdev: 2.89, max: 15, min: 1
score (out of 15
num!er of students
• ed lne a*erage f e*eryone guessed 315
• 1415 students too shar(ly dstngushed from 1515students.
• deal Bell6cur*e wth a*erage of 7 -md(ont "etween maand guessng
• /am was (oss"ly too easy.
• /am a*ala"le n my o8ce f you want to loo! at t.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 4/38
9an #t scores to Gaussan, woutler
0 2 4 6 8 10 12 14 160
2
4
6
8
10
12
f(x) =
R² = 0
"it to #aussian distri!ution
score (out of 15
s$rt(%&n(norma&i'ed score
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 5/38
Solutions to problems fromstudy guide, and HW questions
• Than!s to e*eryone who as!ed for solutons. :oure ta!ng ths course serously.
• Buld u( re(ertore of sol*ed (ro"lems the
-*ery e(ens*e course tet"oo! "ecomes a*alua"le reference.
• ;ome of you as!ed for solutons to (ro"lemsfrom homewor!.
• :ou already had solutons to those.• 9ould you (lease chec! and see whch
solutons you already ha*e "efore as!ng mefor them<
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 6/38
Cange in gradingtresolds
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 7/38
!wo "onus Homewor#s• There wll "e 12 homewor! assgnments n ths
course.• 12 homewor!s wll "e a*eraged to 10, wth 5 (onts
on #nal grade as ma.
• Two "onus homewor!s B1 on chs. 1=,1> -(osted
and B2 -(ro"a"ly on 1?,17 -not yet (osted.
• Both due at 700 @', )ug 4th -nght "efore #nal
• 9om(ensates for techncal d8culty
•
%ll also hel( (re(are for #nal eam-com(rehens*e (ro"lems from all cha(ters.
• +nal eam to em(hasAe chs. 1=61? to com(ensatefor dro((ed /am 1.
•
'a!e u( eam &ueston (ools of all cha(ters.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 8/38
$rades on Canvas• /1 s /am 1 -whch s out of 14 and doesnt count
• /2 s /am 2 -whch s out of 15, and s 25C of your #nalgrade.
• The grades n 9an*as for the nd*dual com(onents, l!ehomewor!, &uAAes, and tests, are accurate.
• Grades are (osted to 9an*as Dust to show you what we
ha*e recorded for you, wth any adDustments -e.g.,adDustment of &uA grades to ensure all sectons ha*e thesame a*erage for a g*en &uA.
• Eowe*er, wll use these recorded grades to come u(wth manually a #nal (ercentage.
• ;o dont trust what 9an*as clams to "e your #nal score,only the nd*dual scores.
• %hen course s com(lete, wll try to &uc!ly calculate a#nal grade for you.
• %ll "e done well n ad*ance of grades "eng #nalAed.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 9/38
!e ma#e up e%am
• Thursday, July 2?th, 201=, at ?30 @'.
• ocaton TB), "ut wll "e n (hyscs"uldng.
• %ll "e cumulat*e, and draw from all&ueston (ools.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 10/38
&nits• get the m(resson that a lot of you are
o*erwhelmed "y the onslaught of unts.
• Try to call thngs "y ther "ase ; unts.
• /.g., nstead of Hwe"ersI, say Tesla6meters6
s&uared. Eel(s you memorAe BKB) -f youha*ent done so already.
• Lr, say H9oulom"s (er *oltI, nstead of +arad.
• Lr say HTesla6m2 (er am(ereI, nstead of
Eenry.
• Mont Dust say a num"er. ;ay the num"er (lusts unts -e.g., 0.4> Eenres, not 0.4>.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 11/38
'lectromagnetic waves• @ro(agatng wa*e
• 9ool anmaton
• htt(ocw.mt.educourses(hyscs?60226(hyscs66electrcty6and6magnetsm6fall62
004
• )m(ltude y de(ends on and t,0 0
2( , ) sin( ) sin 2 y y x t y k x t y x f t
π ω π
λ
= = × − × = × − × ÷
Dispersionc f λ =
ˆ ˆPhase velocity in direction E B= ×
(i i d i l
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 12/38
(ispersion and universalspeed
• Ms(erson relaton &ute m(ortant
• %a*elength and fre&uency f
• ;(eed of lght s a law of (hyscs, not a!nematc (henomenon
• aws of (hyscs same n all frames ofreference
• ts m(oss"le to desgn an e(erment tomeasure a"solute *elocty.
• Thus, s(eed of lght s constant n all frames
of reference.
the phase speed of "the speed
electromagnetic waves of light"
= =
8300 !0 m
c f s
λ = = ×0 0
!
ε µ =
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 13/38
)uic# fun aside onrelativity
•
s(eed of lght s constant n all frames ofreference.
• No mass*e o"Dect can tra*el O the s(eed of lght.Pn*erses s(eed lmt.
•
m(les une(ected and seemngly6outlandsh -"uta"solutely true structure of s(acetme -relat*ty.
• /*en f the s(eed of, say, mashed (otatoes wasun*erses s(eed lmt, relat*ty would stll "e
m(led -ht, @rof. Ma*d 'orn.• 9alculatons n relat*ty are E)M -for me, at
least.
• 9once(ts are fun to (hloso(hAe a"out, though.
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 14/38
*mplitudes 'm and "m
• /lectromagnetc wa*es eert no forceu(on mass*e mono(ole n referenceframe
• Eence, QvQKc, and,
• 9om"nng,
• 9onfesson No mass*e o"Dect can enter lghtsframe of reference. Mer*aton s u(on #cttous(hyscal system.
• Eowe*er, the result s correct. s mnemonc at worst.
0 ( ) E B F F F qE qv B q E v B= = + = + × = + ×∑ r r
ˆ ˆ ˆ ˆ ˆ ˆ m mv vx cx E E y E y B B z B z = = = = = =r
ˆ ˆ ˆ ˆˆ0 ( ) ( ( ))m m m m m m
q E y cB x z q E y cB y E cB= + × = + − ↔ =
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 15/38
s ng e re a on e ween amp u es'm and "m
• +roblem 22-2./0 The electric feld in
a microwave traveling through air hasamplitude 0.60mV/m and requency 30G!.
•
)uestion0 "ind the amplitude o themagnetic feld# in units o $0%$& Tesla.
( ) !# ( ) 20 ( ) 2# ( ) 30a b c d
$nd the answer is% !2( ) 20 !0b T −×
( ) ( )3m
!2m
8& 0'0 !0 m & 300 !0 m s 20 !0 B E c − −= = × × = ×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 16/38
&sing te dispersionrelation
• +roblem 22-/0 'our avorite radiostation# ())*# +roadcasts a signal, anelectromagnetic wave o requency
-0.- !.• )uestion0 alculate the wavelength
o this wave.( ) 33 m ( ) ** m ( ) ## m ( ) '' ma b c d
$nd the answer is% ( ) 33 ma
8
'
300 !0& 33
+0+ !0c f c
m sm
z f
H λ λ
×= ↔ = = =
×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 17/38
'lectromagneticspectrum
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 18/38
efraction
• ;(eed of lght n matter almostalways slower n matter *s. *acuum
• Mue to -#nte6tme (rocesses of -1ncdence, -2 a"sor(ton, -3emsson that doesnt ha((en n*acuum
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 19/38
Speed of Ligt in 3atter
• +roblem 22-14/0 iamond has aninde1 o reraction o &.2$6.
• )uestion0 alculate the speed olight in diamond.
8 8 8 8( ) !02 !0 ( ) 28* !0 ( ) !2* !0 ( ) 88* !0m m m m s s s s
a b c d × × × ×
( )
8 8& 300 !0 m s & 2*!'8 !2* !0 m scv n= = × = ×
$nd the answer is% 8( ) !2* !0 m sc ×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 20/38
Speed of Ligt in 3atter
• +roblem0 The multiple choiceanswers in the previous question areindicated ater the 4uestion.
• )uestion0 5hich o the ollowing is a physically impossi+le speed
8 8 8 8( ) !02 !0 ( ) 28* !0 ( ) !2* !0 ( ) 88* !0m m m m s s s s
a b c d × × × ×
$nd the answer is% 8( ) 88* !0 m s
d ×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 21/38
'lectromagnetic waves as a particle,and te energy of a 5piece6 of ligt
• ght s a wa*e.• ght s a (artcle.
• LR to thn! of as "othS.
• /nergy of a sngle (artcle of lght-(hoton
• !e cK3.00S10? ms, the h s also a constantof nature, and t s hK=.=2=S10634 JSs.
S 'ore (recsely lght "eha*es as a wa*e when (ro(agatng, and a (artcle
f one attem(ts to measure the (artcle wth a localAed measurement6de*ce. The trc!y thng s that -*ery oddly the state the lght s n "efore
energy of a piece of light with&
fre-ency & E hf hv
f vλ
λ
= = = =
C i l t t
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 22/38
Cange in wavelengt atinterface
• /nergy s conser*ed when lght
enters nto nterface "etween n1 andn2.
• %a*elength shortens on enterng medum whgher nde of
refracton -lower s(eed more energy• To Hcom(ensateI for lower s(eed lost !netc energy
• But only mass*e (artcles ha*e !netc energy$<
• Mont ta!e too lterally trou"le can ha((en when you try tothn! of lght as strctly (artcle or wa*e. Eold on loosely$
! 2 ! 2 ! ! 2 2& & E E hf hf v vλ λ = → = → =
! 2! 2 ! ! 2 2& &c cn n
n nλ λ λ λ → = → =
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 23/38
Sift in wavelengt at n17n2 interface
under energy8conservation
• +roblem 22-29/0 The inde1 o reraction o la7ewater is $.33. 8ome light rom the 8un9 withwavelength :$: nm passes rom air into thesurace.
• )uestion0 alculate the in%water wavelength othe light# in nanometers ;nm<.
S %hte lght emanates from the ;un -and from any ncandescent or Uuorescent lght
"ul", whch s a su(er(oston of *rtually all *s"le wa*elengths -from red to *olet(lus some n*s"le wa*elengths -ultra*olet, nfrared, etc.. n ths (ro"lem, we
( ) 2#* ( ) 28+ ( ) 33# ( ) 38.a b c d
$nd the answer is% ( ) 38.d
vw & #!# nm &!33 38. nmnλ λ = = =
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 24/38
'nergy !ransport by '3Waves
• Now thn! of lght as wa*es.
• ;(ec#cally, l!e a s(hercal wa*e6front.
• @lanar wa*e6front seen n (ond.
• /nergy (er unt tme @ -(owerdel*ered to an area ) "y a
wa*e6front of ntensty .
• ntensty s to densty as mass sto (ower as area s to *olume
• VntenstyWK%m2.
P IA=
m V ρ =
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 25/38
!ime8averaged +oyntingvector
• +roblem 22-:1/0 The cylindrical +eam o a$0.0 m5 laser is 0.: cm in diameter.
• )uestion0 alculate the laser=s intensity.
2 2 2 2( ) .0 ( ) '0 ( ) !!0 ( ) !80W W W W
m m m ma b c d
$nd the answer is% 2( ) !80 W
md
32
2 2 2! !2 2
!00 !0 /!80 / m
( ) ( 08# !0 m)
P P I
A Dπ π
−
−⟨ ⟩ ⟨ ⟩ ×
= = = =×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 26/38
+oynting vector
• @oyntng *ector S de#ned as
• 'agntude of tme6a*eraged S s ntensty -%atts(er m2. ;how ths n net slde.
• +rst, chec! unts
• Mrecton of S s (arallel to wa*es (hase*elocty -drecton of (ro(agaton.
• Mrecton of(ro(agaton from rght
hand rule
0&S E B µ = ×
[ ] [ ][ ]
[ ] [ ]0
E B E BS µ
= =
r
[ ] B [ ] [ ][ ] [ ]
[ ]& E I
L L I =
2 2&
C N
sC N m W
m m s m s m s m= = = = =
× × ×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 27/38
-3-S- and averagevalues
• )uestion0 onsider an oscillatingelectric feld with requency 60.0 !and amplitude $.2$2& >/.
• +roblem0 5hat is the average valueo the electric feld# and what is the?..8. value o the electric feld# in
>/<( ) !00 ,0.0! ( ) 0 ,!00
( ) 0.0! ,!00 ( ) 0.0! ,0.0!
N N N N
C C C C
N N N N
C C C C
a b
c d
$nd the answer is% ( ) 0 ,!00 N N C C
b
ero "average" val-e of electric field is reason why 1 val-es -sed4
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 28/38
!ime8averaged +oyntingvector
• Tme6a*eraged @oyntng *ectorsmagntude s ntensty.
• 9alculate QSQ wth .'.;. #elds(lugged n,
• Tme6a*eraged energy densty,
0time5average
&!ms !ms I S E B µ = =r r r
2 2!! !
time 0 02 25ave
( ) E B !ms !ms" " " E Bε µ −= + = +r r
! ! !0 022 2
& &m m m m E B E B µ µ = =
( ) ( )2 ! 2 2 2 2! ! !0 0 0 0* * *
( )m m m m E B E c Bε ε µ ε −= + = +
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 29/38
!ime8averaged +oyntingvector
• %e therefore ha*e ntensty andenergy (er unt *olume,
• 9ould (ut "oth n terms of the electrcor magnetc #eld am(ltudes /mKcBm,
• 9an com"ne to relate and u
( )2 2 2! !0 02 *
& " "m m m m I E B " E c B µ ε = = +
2 2
0 02 2
m mcB E I c µ µ
= = ( )2 2
2 2 2 200 0
0
! !* 2 2 2
m
m m m mc B" E E E Bε ε ε
µ = + = = =
&" I c=
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 30/38
!ime8averaged +oyntingvector
• +roblem 22-:9b/0 @ntensity o the sunlightthat reaches AarthBs upper atmosphere is $2005/m&.
• )uestion0 alculate ?..8. value o the A%feld.
( ) .30 ( ) #20 ( ) *+0 ( ) *'0 N N N N C C C C
a b c d
$nd the answer is% ( ) .30 N C
a
2
8
2
2
!*00
0
/ m2
300 !0 m s2 rms0 rms !2
0 0
&.30
88#* !0 C
N
!ms
m
I " E
c" E
B N
C ε
ε ε µ
×−
×
⟨ ⟩ = = ↔ = = = =×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 31/38
!ime8averaged +oyntingvector
• +roblem 22-:9b/0 @ntensity o the sunlightthat reaches AarthBs upper atmosphere is $2005/m&.
• )uestion0 alculate ?..8. value o the )%feld.
( ) *# ( ) 32 ( ) 2* ( ) !8a T b T c T d T µ µ µ µ
$nd the answer is% ( ) 2*c T µ
2 22 .rms
0 rms 0 80
0 !*00 / m(* !0 ) 2*
300 !0 m s!ms
T m A
" I
c B
B" E T ε π
µ µ µ
µ
− ×⟨ ⟩ = = ↔ = = = × =×
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 32/38
+olari;ation•
Lne (hoton s a H(eceI ofelectromagnetc oscllaton -sorryXwa*e(artcle dualty.
• Ths one (hoton may ha*e an electrc
#eld / (ontng n a certan drecton.• @hotons (olarAaton
• ) great num"er of (hotons may ha*e a
great *arety of (olarAatons-un(olarAed, or random (olarAaton
• L all may ha*e same (olarAaton-(olarAed
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 33/38
+olari;ation – a mecanicalanalogy
• )lthough (hotons are (eces, we need tooYer a mechancal analogy.
• @retend that lght s (urely a wa*e -for now.
• /lectrc #eld
determnes(olarAaton
• 9on*enton
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 34/38
3a#ing a +olari;er• Zery sm(le to ma!e.
• ecall that 'K9 n any conductor -metal.
• Just ma!e metal slots. / #eld that doesntlne u( wth slots s etngushed.
• / #eld that doesnt lne u( wth slots setngushed.
•
/tngush /
etngush B, "ecause /
Law of 3alus for
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 35/38
Law of 3alus forpolari;ers
• aw of 'alus go*erns transmtted ntensty
•
9onsder (n! arrows to "e (olarAaton -electrc #eld
•
@olarAers can "e (laced n seres
6-st the component remaining -n5e7ting-ished
0
0& cos &!ms !ms E E I I θ = == 4 44 > 4 4 4?
2
0& cos I I θ → =
W i t # bl <
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 36/38
Wy is te s#y blue<• 'etal etngushes a (olarAaton.
•
'echancal analogue (utty str!es amass*e o"Dect -(urely nelastc collson
• )r -our atmos(here scatters(olarAaton -(artally nelastc, elastc.
• No ar -*acuum, no scatterng, no "lues!y -l!e on the moon of earth.
*s
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 37/38
!ime8averaged +oyntingvector
• +roblem 22-.1/0 Cnpolari!ed light passes throughtwo polari!ers in turn with polari!ation a1es at 2:D toeach other.
• )uestion0 5hat is the raction o the incident light
intensity that is transmitted3! ! !
2 * 22( ) ( ) ( ) ( )a b c d
$nd the answer is% !*
( )b
202 ! !
0 0
cos I I I
I I
θ = =
2 2
0 !
0
cos cos
I
θ θ 2 2
0 !
2 2
2 2
cos cos
! ! !cos *# cos *#
*2 2
θ θ =
= ° ° = = ÷ ÷
7/25/2019 L12 - Electromagnetic Waves
http://slidepdf.com/reader/full/l12-electromagnetic-waves 38/38
elativistic (oppler sift•
9onsder an o"Dect emttngfre&uency f (hotons wth com(onentof *elocty * lyng along the
ds(lacement "etween an o"ser*er• +re&uency f emtted actually
o"ser*ed as f
•
f emtter s a((roachng o"ser*er, f O f • f emtter s recedng from o"ser*er, f [ f
!!
! !
vc
vc
f f f β
β
++′ = =− −
approaching receding
approaching receding
! !" "
! ! f f f f f f
β β
β β
+ −′ ′= > = <
− +
Recommended