Electromagnetic (EM) Waves PDF

ELECTROMAGNETIC EM WAVES theproblemwithAmp ere'slaw upuntilnowwe'veonlyusedAmpere'slawwhencurrentissteady1constant Ampere'slawfallsshortwhencurrentchanges overtime RCcircuit recallthatcurrentdecreases overtimein an Rccircuit weknowthata currentexistsoneithersideofthecapacitor'spla...

ELECTROMAGNETIC EM WAVES theproblemwithAmp ere'slaw upuntilnowwe'veonlyusedAmpere'slawwhencurrentissteady1constant Ampere'slawfallsshortwhencurrentchanges overtime RCcircuit recallthatcurrentdecreases overtimein an Rccircuit weknowthata currentexistsoneithersideofthecapacitor'splatesandthiscurrentisduetothemovementofcharges what'shappening inbetweentheplates it charges cannotcrossthe gap 1 t L itturnsoutmovingchargesaren'ttheonlythingthatcanproduce a Bfield achangingEfieldcanalsoproduced a Bfieldthisiscalled adisplacementcurrent Es dI Ba s Id at Eo Is A FAcoso where Ioe Eod It s I 1d d displacement current achangeinelectric ftEisuniform anditisflat fluxovertime ex acharging capacitor in an RCcircuit recallthatthecurrentgoingthruthewire4resistor is I ERe M nowwe'llfindthedisplacementcurrent betweenthecapacitor plates weknowthevoltagebetweentheplates yet El etire andweknowthe Efieldbetweenparallelplates e Vq soweget e Klatt Ed i e t m find Id Id e diff e a e adadEli e date D EofpegeHrc using c ETA the Id PEe sameascurrentthruresistor1wire murmur Maxwell'scans Qenclosed 1Gauss'slaw toE di Eo theelectricfluxthru anyclosedsurface isequaltotheelectricchargeQenaenclosedbythesurface describestherelation betweenanelectricchargeandtheelectricfielditproduces 2 Gauss'slawformagnetism toBodi O themagneticfluxthruanyclosedsurface iszero thismeans Bfieldlinesare continuous 3 Faraday law toE di diff End achanging Bfieldinduces an emfwhichproduces an Efieldthatformsaclosedloop 4 AmpereMaxwelllaw toBdi noIenanoId noIena Eon dI dt Bfieldsareproducedbymovingchargesorbychanging Efields propagation oflight light is a transverse electromagnetic wave in a vacuum the speedoflightis c 3 00 108mfs Co 8.85 10 I µ 4 x10 7 TI eoM µ Nm A notin a vacuum speed oflightis I met thesource ofany electromagnetic wave is an oscillating accelerating electron which produces oscillating electricand magnetic fields 2 a Eo direction.in rneeamehio tie.snavei Bo xL solutionstothewaveeqn Eix e Eocosckx wt j thiswaveispropagating traveling inthe x directionandtheEfieldis oscillating inthe ydirection costKx wt I Bix t Bo thiswaveispropagatinginthe directionandtheBfieldisoscillatingintheZ direction thesewon'talwaysbetheeqnsbutthedirectionofpropagation EandB should be perpendicular to eachother e Elze Eocoslketwt I Edirection f wavetraveling in E oscillating in itdirection Blz.tl Bo cos1kt wt g Boscillatingin Jdirection Eand Bfield strengths arerelated bytheir propagation speed in a vacuum E C Bo thespeed of light is relatedtoits wavelength X and frequency It for all EMwaves v Xf in a vacuum v c wavelength X distancebetween successive peaks orwhere it crosseszero m Is distance distance wavevector k thenumberofwavelengthsthatfitinto a distance of 21T K units frequency f cycles per second measured in Hertz Hz period T timeittakestocomplete onecycle measured in seconds s T ft n T T w 2ITf c L l l f I t s angularfrequency units raf a s  wavelength ofvisiblelight approx 400nmto700hm APPROX COLOR WAVELENGTH nm low frequency red 660 orange yellow 610 q low energy 580 green 550 highfrequency blue violet 470 410 y high energy power p time ener9Y_ units Watts W Is energy density U Eoe _foB units Y e Is Poyntingvector vectorthatdescribes theflowofEMenergythru a surface 5folExB units PIET Fz 5pointsinthedirection ofwavepropagation if we average 5overtime wetheintensity ofthelight I _Save ceo Eino Eoff units PoaY Fz 4 power intensity relation I IT radiationpressure forceperareaapplied anEMwaveon by a surface units thread m ifthe surface is a perfect absorber prawn timeaveragedprad P radiationpressured Inintensity if thesurfaceis aperfectreflector prad ZU timeaveragedprad p EI