Vvj

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. Electromagnetic Boundary Conditions
(i) Electric Boundary condition
(ii) Magnetic Boundary
condition

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. 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. 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. 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. 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. 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. 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. 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