# Lecture 5. Chapter 3. Electromagnetic Theory, Photons, and Light

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1 Lecue 5 Chape 3 lecomagneic Theo, Phoons, and Ligh

2 Gauss s Gauss s Faada s Ampèe- Mawell s + Loen foce: S C ds ds S C F dl dl q Mawell equaions d d qv A q A J ds ds In mae fields ae defined hough ineacion wih chages

3 Mawell equaions: fee space, no chages Cuen J and chage ae eo Inegal fom of Mawell equaions in fee space: ds no magneic chages S no elecic chages ds changing magneic field ceaes changing elecic field changing elecic field ceaes changing magneic field S C C dl dl A d ds d ds A Thee is emaable smme beween elecic and magneic fields!

4 Mawell equaions: diffeenial fom (fee space) Noaion: j i ˆ ˆ ˆ Laplacian: ) ( div j i ˆ ˆ ˆ cul()

5 lecomagneic waves (fee space) Changing field ceaes field Changing field ceaes field Is i possible o ceae self-susaining M field? Can manipulae mahemaicall ino:

6 lecomagneic waves ˆ ˆ ˆ j i Resembles wave equaion: v ach componen of he M field obes he scala wave equaion, povided ha v

7 Ligh - elecomagneic wave? Mawell in ~865 found ha M wave mus move a speed v A ha ime pemiivi and pemeabili wee nown fom elecic/magneic foce measuemens and Mawell calculaed v 3,74 m/s Speed of ligh was also measued b Fieau in 849: 35,3 m/s Mawell woe: This veloci is so neal ha of ligh, ha i seems we have song eason o conclude ha ligh iself (including adian hea, and ohe adiaions if an) is an elecomagneic disubance in he fom of waves popagaed hough he elecomagneic field accoding o elecomagneic laws. cele (la. - fas) ac value of speed of ligh: c = m/s

8 lecomagneic wave Assume: efeence fame is chosen so ha =(,,) longiudinal wave, popagaes along does no va wih This canno be a wave! Conclusion: i mus be ansvese wave, i.e. =. Similal =. Since is pependicula o, we mus specif is diecion as a funcion of ime Diecion of veco in M wave is called polaiaion Simple case: polaiaion is fied, i.e. diecion of does no change

9 Polaied elecomagneic wave We ae fee o chose -ais so ha field popagaing along is polaied along : (,,). Also: = =cons (=) -field of wave has onl componen -field of wave has onl componen (fo polaied wave popagaing along ) In fee space, he plane M wave is ansvese

10 Hamonic polaied elecomagneic wave Hamonic funcions ae soluion fo wave equaion: cos c, / Find : polaied along ais c d popagaes along ais cos c, / c This is ue fo an wave: - ampliude aio is c - and ae in-phase

11 Hamonic polaied elecomagneic wave lecomagneic waves * diecion of popagaion is in he diecion of coss-poduc: * M field does no move in space, onl disubance does. Changing field ceaes changing field and vice vesa

12 neg of M wave I was shown (in Phs 7) ha field eneg densiies ae: u u Since =c and c=( ) -/ : u u - he eneg in M wave is shaed equall beween elecic and magneic fields Toal eneg: u u u (W/m )

13 The Poning veco M field conains eneg ha popagaes hough space a speed c neg anspoed hough aea A in ime : uac S uac A neg S anspoed b a wave hough uni aea in uni ime: uc c c c c John Hen Poning (85-94) The Poning veco: S powe flow pe uni aea fo a wave, diecion of popagaion is diecion of S. (unis: W/m )

14 The Poning veco: polaied hamonic wave S Polaied M wave: cos cos Poning veco: S cos This is insananeous value: S is oscillaing Ligh field oscillaes a ~ 5 H - mos deecos will see aveage value of S.

15 Iadiance (used o be called Inensi) Aveage value fo peiodic funcion: need o aveage one peiod onl. S cos I can be shown ha aveage of cos is: cos And aveage powe flow pe uni ime: I Iadiance: c S T Alenaive eq-ns: c I c T S T T T c Iadiance is popoional o he squae of he ampliude of he field Usuall mosl -field componen ineacs wih mae, and we will efe o as opical field and use eneg eq-ns wih Fo linea isoopic dielecic: I v Opical powe adian flu oal powe falling on some aea (Was) T

16 Spheical wave: invese squae law Spheical waves ae poduced b poin souces. As ou move awa fom he souce ligh inensi dops v cos, A Spheical wave eq-n: cos cos S cos c S I T Invese squae law: he iadiance fom a poin souce dops as /

17 Radiaion pessue Using classical M heo Mawell showed ha adiaion pessue equals he eneg densi of he M waves: P u S uc P S c This is he insananeous pessue ha would be eeed on a pefecl absobing suface b a nomall inciden beam Aveage pessue: S T I P (N/m ) T c c * fo eflecing suface pessue doubles

18 Radiaion pessue applicaion Sa was episode NASA o Launch Wold's Lages Sola Sail in Novembe 4: Sunjamme hp:// hp:// how-do-sola-sails-wo-.hml

19 ample poblem A lase poine emis ligh a 63 nm in plane a =45 o ais (coune cloc-wise). The ligh is polaied along ais, beam coss-secion is A= mm and is powe is P= mw.. Wie an equaion of and componens of his M wave fo he egion of he beam. cos Find : c iˆcos ˆj sin Find : Find : lecic field: Iadiance: P A I c P Ac P ˆ cos Ac P Ac iˆcos ˆsin j ˆ c

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