l12 - electromagnetic waves

7/25/2019 L12 - Electromagnetic Waves

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L12 – electromagneticwaves

Thursday, June 30th, 1230 to

1345Bradley J. Nartowt, Gordon N.

Tam



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.



/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.



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



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<



Cange in gradingtresolds



!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.



$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.



!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.



&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>.



'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

http://ocw.mit.edu/courses/physics/8-022-physics-ii-electricity-and-magnetism-fall-2004/










(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 =



)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.



*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= + × = + − ↔ =



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 − −= = × × = ×



&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

×= ↔ = = =

×



'lectromagneticspectrum



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



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 ×



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 ×



'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



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 → = → =



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 = = =



'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 =



!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

−

−⟨ ⟩ ⟨ ⟩ ×

= = = =×



+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= = = = =

× × ×



-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




• 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 −= + = +




• %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=




• +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

×−

×

⟨ ⟩ = = ↔ = = = =×




• +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

− ×⟨ ⟩ = = ↔ = = = × =×



+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



+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



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



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 <



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




• +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 =

= ° ° = = ÷ ÷



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

+ −′ ′= > = <

− +

l12 - electromagnetic waves

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