RY + wif Plane Wove in Condusling Medium >) - ne E set | Rw, cin me ge > ; fe) \ Now, T= A. "ey Wy + (yuerestt | > change donsiby. T= A.M Ey = 2 _, a J: Z = me ytlE . ral Rm) =e ~ Condusivily ()m) nck change = 0 [ave/-ve coneds ous: } Lano.e-rosenpic property] bub shangis ore moving 40 9 THO “te. Awe de no edvurol sourte, OL the mediun te excibed by EM wones. > VE = 0 — [for isotropic} > wee © CE + jock €= & by ‘ \ J \ tundacchion digplacemeat errr a eurremt alia WH: joelty HYP a of ase Nae by ye /\ cena : | Loss Tangent A_| weece Ls Good Dieleebic | Bod. Conduator [iep. cervonk dowinabss) + Good Conduckse a (cond. runt Asminokes) Sr ea) | ; Va} &8(&- 2S) Som (YEE J \ = Lonple. Dideebie tansiaw By iahieg wil o& gxE & VHD . (ve. jw, fesjueye | (2. . : VE= jue i 725) |: a jwa(esjwe) vi: jolie + joe) 8 | vO" Fu oplanised, UPWS peli \ gy sowing 7 ~h jot e- it | L/ tee sce hk iY | ¢ TE?) y= FEL 2) E> Ee te + &e - 4 ae oT o=0, = je } k ‘ Ti, i was Ke ¢ Nex. Tk te obuoniys cert 3 th rao, a ajo Deg! de =| | (1- ue) jotpe frig,Now, y= at ]p = joe (1 1- Jt. iia « Wwdme fl- w of IP oS J a € [: 2) «78 = elk y jolpe € = ; . fm : a = WAE zh, CPropopohion env.) ara lZ : i i! ’ > a 2 eG j lok -w ez) “Che j (at- 2) +§ [Be 5g jfut-o4 [eB Efe e@ + Re Le \ + . . | | 5 ae _ le Z > f { Ps for 0 good, conadnclse T yy we 7 qz jorpal 5+ jue) a qe [jones { mf \"/ 4] i { Oo e fa) > sms Se a4\p > {wpe c = fot (ENG) . v= \4 (was p= [ee oy, ne> 4 job % t E mee = jwb jae +2. Cee=~ * UPW tn anbibrary direction & isocfeghancyy surface (fee) We kuow, Bet okNaxwells Eqs He homopenveeis & teobropi smedivewa] &. sourrte- free wegion \ P _ 4) Nur, ture is eonehoink ow K Ten-fiequney : ie a foud freq sec whats value f eg ga + v(vE)- Te = 0 juee UeVxe = jor: GR) Es wee > scenes quee © GP 7 Ev ae mete opet «| (ms pe) e=0 | a are | ay, | (IRE spe) #9 | wy | (REEMANou-trivinl so, > ©, W #0 (Rl aye =0 7 kt byte = wus 2 TK wipe kk OLR [free apa] _ ie Sean Kee+ foynting Vector Tw alendy stale, Power rm iv ah dissipalsa, art Te Li] R po Ty How is pone _trawsfouncd. 2 write power tus tins of E. p22 LK Veet A A 242 pe Ek x celta) = oy Yeh XK a alter Tota), power dissipated. gen wil volume ~ =>] oe Ge » (Re TE | Vv lorevk2 Foren = (Er) chore analy 8 Ty > oe ce ms volume = Pleu ) yy walk volume = Fev Toner sivewd| dissinolss, (pe ee Y = (ev le = per ee). B= ARE) mo yaya Mowe Fy. Rv ye tye dee = o£]New, ME: Val= Fae. 2€ at ~—t = “ Js Uxi-e. 3E ab Se ea B.(vH) ~ 6, 6.88 “Skew LEB ==8( Vx H- =Ael Ye 8’) 2 WT) ‘esr Hunky) New, ME ve > pt = > oh = 3k _ opt heb. fe eV (Eee) ene oe ae = ge tos, 8 BE) = LEP) = 2B S , SE) (Er) iE Poe Lb ep Eta aDefine Elaine Fidd Envgy Dewey [Ug > Lelep Magrohic Fad, Energy Density, Uy = sap = -2 v.(BxA) = Sy (Yet Uy) ~ Py th us detine Ps Ex RD as Toynting Veohae Pz Suet) - Py. pe Ve a et Uy) = Py ; yo / << Ly suite closed value inbcgra ae Cote maw = B[eu) ar (eletav wt wt. Tiuerem - . a lee =2 [ (uceua)ay = (Cte) Ryeting's : ab. vel. Theorem vol th Je shady pole cose, Ug k Uy dowt shang, with Hime b (EW) de = 7{olel dv : “vot v AY indizales over a closed surface, Tole[ je) poe * the total, power Bdroin aaa aad + Ts is a infouk ig the um(ve) | S a a . [ OFT ouside gral, cae ; of nate of change of v! a weed not be dieiptel energy. dina a woNe “nergy a et+ Back fo how power is bouswitted : . Ly TI — > wite has no E Le ro > 1 i > is) —>3 nie J ta r wire Ys e > an Fei veelor of Thie-Kounanis Fide \ n/abs (neh. Avg. iP v.) = jut E= E, (uy,2) e : : it jut. iF : : B= &uy.2).e@ ce @ © = wnt veckos ie, jo the din of € “pide |, lube), ' E-Re @ — jot +d,) 4 . t. Xt veel in f H= We Pde = wait veeko tn vt ‘ " the din, of # Now, rab-vobud EF : E, = Ftos(uk oh) e veol-vobucd MF ; Un ee hate Fayting Neckar, Fa = Fe Me |1 Bey = St msltab eed) + olew)] (Be roseillabing with vite the frequney nam feet + fa SUT 1am (amt 14,» 4) | (exh) \ <5 tin vobue =D wh b- 4, = >My 3 Ra = ot 08 (aut + + or) ee i) oT ' : 5 the wiigg fy =| Ralthdt = a ws(teqy (exh) co T a = 4] arelErt) * Q.RelExH | \ re(exn) = La (ert) 4 a a | | : i Paw - Te-vorry ng q = gajet ad is zeae beef Bxt*]| = SB e6(h-#) Ged) L + Cwoler Poynting Vector — (Tivee Averaged.) we By LA 7 Whur 2 -b=0 ~ perdy veo Fh y , = Whew fa %, = 40 lake imaginary fe Pp a se va ee es la to \ Lf -e.(wet) + Bt (ve) a J 7 ou Nour, xE = ~JapH 5 oe ck atte GET [wee Vek = gE + jwek VxH / J ——- ane . lar oo > el pla. Now, Ue & ele| y ong. enn domnily of eam bine Yoni eleobne fi, ong. enevey demsib, comple, i io ae tls fds.. Uy Lyfe -) r > pe : Ve tolE ee aye (ne) > Poms aes oF c eu a Compre yi Porwring THEOREM ‘ energy esti Wabin yt crn ure Toke He volume iwbeqral, [eR \ tr = foyefan - Lm { qunl'-eley) a J vat. . vol _ ae ane : oan hd > z [ olelor - dof quimr-elet*) du) oS vot. Sy Integear ] Form ~ > Acbial Power Dedinered, —— Corea), pot) *) who dius Hee conlin, pont inbeabs % 3 - a a sinfoce V,I ove Phrosors Ceoneptere| V { a Nour, We cam shavarkeytise the aL a J _ dovice!Iod, iuside the surface ow. by suing te beminall, vere" vhadour : =1Z co ' Ly twpcdome (a cinwuil “Sevel absbraehion) { E = t vr’) (og. pt) — :, Complex Twpedanee k Complore Poynting. Veokor 7 (Hime eweraged) \¥ 4 , Z: cowie impedance ~~ o} 2 = Raj X 1 i ™ i] / Now, 2 is vhonrarkenised, by hk tovminal behaviowr . \ Ve2T, ’ > bourne vd val L Tower ddiveued, to toad, houninal vi ae won Rye tur fi -$ Reda = -[iv.e dv vol denotes thal powers is Housing dn. fine ta [olel dy + Lj [ Gulnl: ele) av val. vol. el, pont = Ong. Power, Nor eR, Wet \ae =)e ee ery 2 \q? 2 L vot vol asi! etelar 4s jw cai a7) 4] Real Img. ee a | [PRt Now, = weal Up = 4 ddine i dw vol. We f te dar vot Now, Z=R+]X => = 1 —)* ) = ot, [olél dy Sis a ca When Wy>We + X >0 Whon Wy < We Whon wWysWe + * =O * Zz mou also founinals ore chosew Exbu wire Jength may add, ponaaibie capacitance | stan defer resONaNCL, Jae of = induhive Load, yed = capacitive Dood. rane ape 4 dupond. ow where - We)a Bounpary ConDITIONS (Mopute - 3) ers NDITIONS 20) 3) ‘ Gidertrie - Bidkeobie Tubotface SD de > Jone Now, er Gifr . $ Bde . aL GM) bed 2 “BU Bde By. = fo Fda + 2 [Bude % We use Maaedls Eqps te Vudbegrod. oe os diseovdinuily arises ok inburfaces q d Sowiee- Ku Regia % oy Avante, = d= %do Now, y-2 plane is eL ‘ hy ay Aha, iubnfore Boundony vondiis & stil dw uit 0 | Nownal, Cowporenl [ia Bde, + PBA) do A A [a.di + [Bax = Ay byIn te 4,70 Jimit h>0 : A90, -D,A + DA =0 © Dy Pan How, % is he moral, daw (i) *Dy . (a. >) i). 4 = 9] —{) a Ind, Bed J _o «ow dee 24/3/95) Fr tine hh _ - fitin (84/3 [ae bea’: -jw [Bde $H.al = jo [3 ‘ Ben eveesed. yelp nN a diab bag ins. 0 MTS: obtained: in the tinnil Za A> 2, A-O : jw BeBe _ RESO =o + Eek » -E LL iz ae -uns= Ey! - be : , az Ean (along & z aswdl) [(W-W)xin=0] J Fee Ex a=] My. aeUniform, Banc Wave of Media Irbenfaces XA A = : ke, ky, k a /% a #2 > one popagatisn. wand Earned Sivts of inwidanh, ; ie, ~ floss. heoysrilted, wove \ here, propagobion % \y in x-2 plane mw hl y-dir | 7 ) Tots tw te plane | Tromsverse Elesiric (TE) is iw %-2 plone Hig in yedir® } Tinnstonse Mognekie (T™) nee hoi ae = kif Y era | ne -Oeky #4 an fT / 2 HQ 4] rk { sy {ih ~ . aN { \ }k, k _ | 7 \ \3 AF Joh row PLE jlwe “KE rn 4 . B= 2 € a y ky = kyowsb & + ky stu; 2 = H(t -ky.*) 4 4 7 oo E> fe! y j 5 Ke, = oy est, yah 2 = jek), — » uf. B & = he J Ky = Kot ® +h ante © Relation Gelli [ / of TE 1 By Trammizsion — Orellin [_ & | OAL heivieut 7, 24 w jlot ~ k\sinb 2 jest - ksi) 2 E, Ry , + he = oy : -k2 ako, 2 wk B.e + Be - hye when, oe , sib ke, > ksh, ks, = k, sh: Fepaclion & Total Internal, Kelection, ae 7 (te f \ Peon toy a gues “4 OO& ae oe Vromsniest on ‘21% , li z Se hee y coeff of Tm! YY Teo- Fequeney sunfoees ‘ “at beh 7 as a [_ ( pr \ \\ bh ne i (26/2 /as](2/25 ] tal = = perfec debric conductor (Pee) Le T > » Didlesbrie- Metal Tolufare At 2 =) Ad Win B.D Balt =0 WiLL Nowmal. din” (Mn) ig assuunand. 0 Te be cay me he melo te $o.an - | dv Tn didedbric-diekedne t , 2 Bub Jue, aurface oh igh be 7 present aan ie ra ie Th didi > dhonge qradually gl sled, of aunface Th mobo sere & dansity. v \\ _/ GBS) gan Renee ans viume dange adage [aA aa » |B aed 1 & My, |B -n=0 7 My v a #4, magrobie fil a must be, tangentiod,’ a bea, ( / Now: E=0 7 poe > Ber Bio oF BP o > Bxne0 moa, GRaDs (eEAR JoeB Ny kine gh : Serra 7 (r- So Se0)) Ys dui Js ; Wea lan ei lo (chil foe) Ein / : — : a Rbbshion ton Malnl (PEC) as + TE is a. polurisabion eS J (kx + kz) Ge fe — r _ e e+ . one e J = k,c6s6; : Aa het gk1 => eee eee pe Gea es We =) xe) -2 Db jon PS! p> ak 220, Beet po. Begley Nove cee 670 : By +B =O (gr &)e 20 Reryso + ye-&, [Rit 74] : ge oo Phare hal] = & felt ce ih po ahs t. Hnltge) th? gy i |~ : f seme Wve] fn x a} tied, ob trberfnce : . . i fh ty wove Ww X x )_, Be propagating iv a-dir® if k,#0 dubie fy Ni) fits@ { ae a c a i" jhgsilhi ke ky ee ey ee eee vee Te Stl” Po) *(e5] po 5 = =| => +A7B. [_ a a we ahoes SY %) (ye 42053) JY jo 02 | orf j kg? kz al = as ~sinr(ky x) jhJo" 38 k, cllagt) | (ei) Boundary Cowtitions NW He x20: Hy=0 v Oo My, = paramo. {oudinode) () “ei 2- LER) se = £8 IME [ physiol) a + byl) 3] Ext e Y ® |. (Es | 3 (-Eyhy)