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eb679e305964ae1624534fc21bcd37c7 (1).docx

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eb679e305964ae1624534fc21bcd37c7 (1).docx

  1. 1. Cr RAMERR.COLLEGEOFENGCNEENGNDTECHNOLOGY M RSM Nagar. Poudyal - 601 206 DEPARTMENT OF ECE EC 8451 ELECTRO MAGNETIC FIELDS UNIT IV TIME VARYING FIELDS AND MAXWELL'S EQUATIONS Dr. KANNAN K AP/ECE
  2. 2. Electromagnetic Boundary Conditions (i) Electric Boundary condition (ii) Magnetic Boundary condition
  3. 3. BOUNDARY CONDITIONS FOR ELECTROMAGNETIC FIELDS in horrogenwus media, electromagnetic quantities vary smoothly and Continuously.. At a biundary betwen dissimilar media. however, i 1 is possible for elceirornagnetic quantities to be discontinuous. Continuitie,s and discontinuities in fields can be described mathematically by boundary conditions andused to constrain solutionsforfieldsawayfromtheseboundaries.. Boundary conditiorN are derived by applying the integral form of Maxwell's uquatiorts to a small region at an knell- ace (limo media BO liDARY CONDITIONS FOR ELECTRIC FIELDS Consider dte E fluid existing in u region that consists of two dilrerent dieFeetries characterized by e e, The fields El and Ez in media I. and media 2 can be decomposed as Ei Eqi Ellp = COTISidi:r Ilk dosed path abcda shown in the below figure . By conservative property • dL = 0
  4. 4. According lo Amperes. Law, When magnetic field enter from une medium to moth:et. modiunt. t1- Lira may ha discontinuity in the magnetic field, which earl be explained by magnetic boundary condnion To study ihe condilions.olEi and E at [111.2 butIlltillry, both 1-1u1i.1.174areVI2SOIN.Ttlitltsi IWo.2411111%.1.111211K (i)Taugentiat to the boundary Par-oll.el ii:Pbele niiii ry ( 1 1 1 1N O r n i d i buundary (Pcrpcndieular10 'boundary) Those 11 0e0 Ceimponents are re teed or derived uMnir. Ampere's law kind Gauss's law ComiidertwoEmytropic lionwiteousi linear irialaiJils at the boundary wish perranbilitius ond147 Consider a rectangular path and gaus.si an 5L111:FICC to klek-rmine the boundary conditions
  5. 5. 6.14' T=LEI 5.411.jr : fe d 5 . . 1 1 - 0 - fd a =o ]Ike rectangular path height L- .8it and W filth = Aar E„„il 41x -F - 1.:,;(V)- Em3(dliv- F.,24 U At die boundary = 0 (1412- 1::„„i0Ow) -E„„.2(Ilew)= Etiru(1 w1 = E.:411 w) Tani = Eisol the umgentinr componcru Vrcetrie field inwitsity arv. Continuous across the houndary In vce[or tbrm, (Timm - 1 . . t ) 1 2 = Since I> = E E 1 h ohcro: ciuiil i curl writtcn as. _ m e _ m u ir (2 3
  6. 6. Cons idor a cylindrical Gaussian &ileac, : (Pill box) shown in the Figure with hciglit Ali and with top and bottom surface arms as As En! a 4— 19 " —Jib C EI2 Boundary Conditions for Nflrui al ("Dm porn e nit CiCiSthi CiaildMian surrace in the formoicircal OT cylinder is comider lo find the normal .component of. According to riakiss's law s n_ .17=Q
  7. 7. Top Bottom Laieral Atthebounclar!..., = 0,So Gni top anti bottom 6urfno. coniributu in the surface liaq..tra - DC rniVni LULL cif Hormal onnirKpriem u I IT) ii D. and 101,1. top surinc: Alio} ds °No" =D1 OroPds Dm As For houom surface Comm 5..'15 kirtiCirri D N:11118 =DN2 firorromds = Ds (—as) For Lalerd1 SIbleO.C.0 tateratD. ~s Sr i = r;" _ t=a Dto — DNI As = p,As
  8. 8. ELN —D = = pi r ttlvectorform.. For perfect dielectric, = 0 - =o b p i = N i z The normal -components of she electric flux density are continuous across the boundary if there is no free surface charge densiiy. Si nice D = E £1Ens En2
  9. 9. ih MediumI 0 Mcdiurn2 01 2 BOUNDARY CONDITIONS FOR MAGNETIC FIELDS Consider a magnetic boundary formed by Iwo isotropic homugcnous linear materials with permeability m I and ,u 2 erpmc.1 i corn 1 i A.1:12 euJil l - )1 rrY c R u i n 2
  10. 10. Boundary conditions For - fa ngentioi Component AccordingtoArroperesCircuitallaw = Jr: H. di, = f H,+ fb c H. car f:________+ Jr:H.a=1=1„,0 w J 1‹-SurfacecurrentdensitynormaltothePail~05.0 Hererectangularpath11(11,rlit=ItiandWidth Liw .81h .8h = Hi.i(aw) HNI(Ate 7)4 1-IN,( fir')li iana(AW ) —I NAT)—I I NA) Atthe boundary+ =13 .012- AF021 = 1.1„„,,(Aw)- IC,,,„,w) 3 = Hlikni— Hran2 In vector form, - tang I X 5 Ni2

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