See ar 22 N The Rebmed Potential the time. VaAsing Potato) mp) a une K Mmennetic VA- -Uy V8 >¥ (xe) exo) = 36 7 So new ey is E=-U0ViNn VXE = = UXCWV) § Sk VXE = Vx NRE eS “ & - OB = Uxn Ot 1B Vea - d(Rsa) = xy at - Vx []- Van Vv- Ba. JVASE =ag saan € V-e=Lv = € VC wen] - A ( 2 Vx(oxa) = 4 L0 eae] et Vee fe & Tv 1d (oa) at ° (9.9) A= UT ae 3 V- (oA) Fad neg Ee aa] Ea aco to -VAeus- HEI. - Hed bee Maxwell equation inteyml fom ' {Dds = [fav . $B: ds =O : E-dt =-(ep ds Fe-dl_= =f ip da Bedi <- t' [dO ds # ie ;Eu - Ea Dg = Par > 5 ?, Hu = Mer Towel mawell eatin o Vx = 31 ot eo Vee oe wd c alt oO VE ey fy to Q:8-0 8 moxwell equation IN Vaccume | @ VKH = es ‘> Db ~ © Fey relanige ee uin- magnetic — wave, sonale bor Elk elechu fied | 87181 and magneiic| Ka 121 +? 2, he . conn iH 2) field one ac No fave = Bay = Bo | \I 4F chamctenistic. 9 polanized I gh i) AIL EMW Atk -tranayerre in Natune 6-40" i) €/B/K ae mute encliculory (all otthem Ine 40” om a in) Al Emw travel wrth speed oF light re C= Bx10%m fs w) £ and Ban in phare 28 -W-22D ) were RIN vaccumel & S=o ii) VR =O Go So in) Yxe 7-88 Tye ee wv) Jxb = Ae & BE iv) Nixb = Lol Sa 20) at ot iii) Qxt_= TEP. at % Pp yg x(yxe) 77 VK 2B et g (WE) -VE = 2 (0x8) He - Ve > 2 [pt 2) : at ty dv >» Eee ete Colo te at - VE ~ Mo bo at E =O att9 UNrrokn fave Wave (VEER Ace The wave rave Ging nm the 2 diectin Md me no 4 aM dependency are calla plane wave wo O(KZ-we) = | Eh) = Be S| S mw ithe -b) & Baw = ber | > vue aomben fe 28 | | | + By putting E ancl B iA rade laws a> kK Uxét) w 2 eit oe 7 Power and Energy 0 Emus / Pointing therm vee ‘eae ye =e | VxE = 206 © | Ct 4 nbs Maj OD fala EMW tromfn energy /fowen Take dot product 09 @ with H \ shsndinalsialaalDg (exn)= -W Coxe) E (OXH) ———— PT (KE) = “AAgey{ © ae € = - aoe F Es(gxr)= ES + 6:22 a) eq (4) = evs) EL 0xH) -H- (xe) 2 E31 6824 V- 6 ot ot Dt a _| cre [PERLE Be ret => pore due te He ob - 2 |Hut| | Seve Bield 2 at Ok LZ wm y power clue & magnetic bield Se = V(Ext Tet var t tn] _ at ___— | -f alesse = [ese + fa (we t wom)du 7 v Vv exw dA «fore av au =O meet “aL EAH =) IASa us f ot ¥ =e scar oF EMW smifo —> € Dkr fo Se Mo 2 Ll = My Hoe = Hell holtz equation Ve fee eee i | > ke wl6 Glow 3 zw Feed €y Uy = 4 [Ks he Téa] 7 ue I abe = ln, chi dz _—4 ——4| Kin dielectric Man be Complex 4 5X = Ad (B Exe = Ex eNG eas = ie Sp 2 Ex, = Eox_@ e€ | Y Bag = Eon &%* Cos (wt= fe Reflection and transmition oF EMw | ep at normal Meident é x polanige in OE mediom Df — medvm @ | p7 incident Vi Er, Uy Voy Er Ve fave io Be Z asec eld Etiny = box € an 4 z E(Kizee vt) A 3 Bran) = Bxe yp ramomiss ion) men KO deflection ; j oe get) for tra SS) oT eye t-wt) 4 = } a -( (W2- wt) Et = bop @ D. f Be = -ton € A iar; : gmat) | vi 4 Br = Cor a | earn 4Ete = Ey Bu > ae dc A \ Eox 4 Gok = €or \ | Box = Re = Bot Ale A dh Eos — Eog = €or Vy dt WU) Var. Esx - Cog < View For ” B= wy, ; Var vey ~ Fox - fox = B bor 4 Eos + foe = Cor oO Q ber = (146) ber a mull ey @ with B | B bos + BER = Blot compare with © 4 Eon = ee © 3 Lib 4 B= Mv Vian br VE : —| ar a i Wes Ds 1B 7M ary |pt Bin ey ® and @ Re Eo Be. bor T = te cot 6-12-22 | Electromapeti wtve Keflction — and Ioaecndaea objective Sncident eee 2h pes a e Fu 3 8 opcident 5 for neident ; at fig Fete - = Nes ett | Baas xx) Ae 5 oe fe Sere snes | oN = fer peplection ee =e Z -E C (Kad wt) , ; az bop € of quency would be al 7 (% xk) Same gor all Ber Pp Beooe) = 1 Ke Xe / its only clepead on ess — sown not on mediem orn {ss} of é, Gor Lares : oO oh -20 1 (ryt) = boy € 7 « MePd 2 Az ¥ Brow) = L, Ut x Ey) want 4 ~ v ew dF 7 We wi we KVaw Waviz ais 2 favs e eM ME a= Ke x Mt “9 ok Me vs oat 220 (at bounds) a ttgsewa) [Key =e) ( \ rey ~ a é < ) ( ye + : ) oe (wt) is Sang | 2 spatod 0 Kr-6 = KR-S = KB ar at Beundlg 2 a(hade # Yltady = rc(iwret lhiadg = lac + Sry 4 of X=0 ] 4 Oss) = ylta)y = 45 Cin)y if . Ry je : wAKeyx =x (Hae = xCere Alea lile) et fee (ale = Cnelx = ny) _4 # Ast law ot reflect! KY Sin 01 = KR Sin O = Mr Sib 22nd lan oy Refledion — Ox = Og : — fe=. @ Boundary Condition tt Em E — Onr= On Bn = Boo Oe (Ea 4 foe le = & (Exe @ (Bos + foe a al Be © l(t: 1 Feta = ber) 6s 1 (fo + Boe) a4 = L (gor) @ ‘i rea ir Last _twe _ ayatons ond _@_ have peo farm in. form 0 analy «as * Suppose ware is polanize such tha Eis // te plane ot Sncident b Es afk thee ot hem tt EB are 40° from - each. eth ftom ew O E, (- €or Sin Ont bor Sin Og) = 2 (- Bor sin) —-@ Cor CosO1 + (RCosOR = Koi SO) > @ from ey © “1 Ufa= fe) = Lb 3 AVI Ur va Cop seat = TOU Cor Leevt ay B12-12-22. 4) Absorption and - Brpeiecbey oF Emy) vIn cancluctoy = VxB = Mb ck + Uk be — a et 4 V-B =o @ : . for AeN cencluctivits, medium | ae a ne O ij fing cont on @ and © _| Ve Selle Es + Uo Be __| ot _4 Whe Mee 4 Me Ob _ 4 au! at } ie C1 Hr = we) q Cony = boe ———| Se now KK > COMPIRK TORT wey | oo Pax= bo ¢ He? 15 ned for pl ae Sap Ke rth ditto — al Kovctaen © abot? =\E= i “ey °} Vs = J continu ae | Viee)= - Oh y ot olvt)s al ™ © (EL) -- oh € € ay pang O_O ef 2 - of at € ue = Sew et Tek e for penfeck. tonductr of = Ob ad at=0 Jp <9 So aftt all tis Yeco © Vero . ae — Ve = 2 OP ‘@) 4 at t | vxe = EGE 1 MoE 4) yl at := pi fterl Taga + aca 3 - | i [+ bet lr + CESS) ] +1 N —~y o fie [TE oe 3 2 tw —~ 7 3 e Sole by S 4 x — afer Selving this R= fae | fie. af 4 eee ee Solahion 03 E | = aya ¢(H2 wt) i ca Eo Ber eee,