Question

3. Derive homogenous wave equation for Hcomponent of an EM wave in a lossless, linear and isotropic medium.

Electromagnetic

Answer 1

ĒXĦ => P S xH given the propagation of p] & 1 => 1 A 2 - Gre Inadoni "El Teruntunited wamo LOCIVO - RET medium 1 12 Thoden ichi ( Diclocsic T >> Tsonsmited Wave нту Z. Reflection de 10 misicuch LOCIVO ERX medium 2 i Diclocinic) 0 HR-Y R- ² 220 E =n=1 -(-V0) 2 dito. H no = -> doima l # The normal field don't considos. 2. Ý → langential Omy congidor. targantial axis. [ Etie Et2 , Hiti =Ht2) novar Triciclontuovo albay (tve) 2-diac Ver Reflected wave HO "Eo Eti Et 2 sou nodium Corsido if samadium fonponytal ouunto Ei & Er in x direction with Same direction so add born. [medium having Incident uavo & Teflection Eichst Ei +ER = ET- When J. onits-o) como moto) Gazda ore Wave

] ET When HEL = HE 2. ] modior modium 2 1 (HR, Hp Opposito dire divociion Sobradi boin) Hi - He 2 HT [E/H = 2 H = Ein Change' Intoime of Electric field - Ei to FR = HT ni R2 Ei -ER = RIET 12 EQU ©+ @ 212 Ei nitha 1o.qe to ER OSub in @ = Te = 12-11 ER ET E n2+ (refraction Co-o Hilom) - Baso on two Transnission Co-ohuonet TE It ETE HR THE HO HT = CH = 2n1 nitha Triunsmission coHcion with H' Vonification - Casei 12>ni HR = "H= 21-22 nh2 hos Deflochon Co-omicio 07:10 H. ER = SE => ER = TEE Еe 22-11 Ei na ni

TOP SONUN It Ei = Er wo get some direction then it satisfied XEiL 22.>Ni Er=ſeet POSTive IZ go Hij HR = TH Hi HR = TE Hi ERX R-2 HR- 42? case 2: 2</ Eroflochod=R2-N27 Ejncident nathi Hiyo H reflected TE Hincident Hey ragnato frold -2R is added ER-

a at EM, WavÓ In non conducting med en Dod=ev V.B=0 Dxe -2B VxH = 5+2D at electric *Assuming fields que in free spaco C=o), assuming freld & Malgp along x direction & magnetic field along 4-direction only DID=Pv If we r'n - VXE =-A VAH J+2) in any at O=0, J-p=0 =) source free region. D.B=0 + it ben lie EMO. EXI HY DXE -OB WxH =25 at Hoo Conido On) Cu --- DX =- Maty VXĦ= E DE at chave -EJE, ay Ону ax ay az? - 424 az 2 at DEX = -Ha Hy - O ax ay dz at EX he APEX -- Malaty o 0 * Os doex alat DPEX = -lät rated from @ AA Va22 APEX Ello EU Mo Eo 22er { v= a tot 222 at soturco free rog 104 wo consider

ӘНу . 22 Hy DPEx = I D2E> d22 V2 at 2+2 222 L EM wave put EX2 50 t), HY (Z3Lt) It wo best any time varying field inpes any region wave SEM wave ) . that babaros Viles Unifom plane crave 2 a = jw 22 Ex az2 102 Ex at2 ot 2 2 = -2 D?EX = -() EX at2 B=W10 + D2E B 2 Ex zo 022 [ Dher simplification zo] JB2 +JB2 E(Z) = Exte + Ex é We represent in real term E(21 t = Eat cos (WEB2) +Ex cos(wt 1 B2) El 2) = Exto JB2 + Ex e +B2 Forward Reflected Cave (-2) disegi Along (+2) divacy leave From oquo a Ez = -ll Hy =-jwill Hy at Hy JWH az Jun 23 Dz[Exty 1824 E7 e 182].

ӘНу . 22 Hy DPEx = I D2E> d22 V2 at 2+2 222 L EM wave put EX2 50 t), HY (Z3Lt) It wo best any time varying field inpes any region wave SEM wave ) . that babaros Viles Unifom plane crave 2 a = jw 22 Ex az2 102 Ex at2 ot 2 2 = -2 D?EX = -() EX at2 B=W10 + D2E B 2 Ex zo 022 [ Dher simplification zo] JB2 +JB2 E(Z) = Exte + Ex é We represent in real term E(21 t = Eat cos (WEB2) +Ex cos(wt 1 B2) El 2) = Exto JB2 + Ex e +B2 Forward Reflected Cave (-2) disegi Along (+2) divacy leave From oquo a Ez = -ll Hy =-jwill Hy at Hy JWH az Jun 23 Dz[Exty 1824 E7 e 182].

. Hy = P_ Ext6-182 - B EX CBZ Hy = -1 Joy 1-jp Ext eiBz +jB E01B2] WH WH Hyt ну Hy = Hy tow]? + Hyºe JB2 Where Hy + = B. Ext ну =-B EX LOH он HO = HO VEO = WM -ov = B VHOED Cymie Ext - to Hyt = 12011 = No Coo) M. 377. fice space plinic imped ante LOCNVO impodonie Ezt Ex = :-WH = - no B. ly > DVD = wie =10 Hyt B D) wave along + direction of propagation (-3) HY = B/wr bat e 2 JBZ Du turi 3-ar Othogonal to cach oth Hy = x xř z go focale carl] y-dhony -direction Electric field in a direction DOT zap. XE, 2 120Ah ou HT E = nH direction » H x approaczaion vector WOVO J HOF

J Ex(2) =n Exto JB2 - Ext 6-1BZ Ну (z) #4821 n - En pa an with complex representation wows/m2 Pavo = = Re EXH* Exfasz x Ext: n 1 p 1/2 Re Ex *o 18B2 +2 Poyning Pż - EX - VOCTO 2n E(21t) --> BOPHUS function of sport . and time

. Hy = P_ Ext6-182 - B EX CBZ Hy = -1 Joy 1-jp Ext eiBz +jB E01B2] WH WH Hyt ну Hy = Hy tow]? + Hyºe JB2 Where Hy + = B. Ext ну =-B EX LOH он HO = HO VEO = WM -ov = B VHOED Cymie Ext - to Hyt = 12011 = No Coo) M. 377. fice space plinic imped ante LOCNVO impodonie Ezt Ex = :-WH = - no B. ly > DVD = wie =10 Hyt B D) wave along + direction of propagation (-3) HY = B/wr bat e 2 JBZ Du turi 3-ar Othogonal to cach oth Hy = x xř z go focale carl] y-dhony -direction Electric field in a direction DOT zap. XE, 2 120Ah ou HT E = nH direction » H x approaczaion vector WOVO J HOF

J Ex(2) =n Exto JB2 - Ext 6-1BZ Ну (z) #4821 n - En pa an with complex representation wows/m2 Pavo = = Re EXH* Exfasz x Ext: n 1 p 1/2 Re Ex *o 18B2 +2 Poyning Pż - EX - VOCTO 2n E(21t) --> BOPHUS function of sport . and time