Upload
marfizal
View
217
Download
0
Embed Size (px)
Citation preview
8/18/2019 Persamaan MAxwell Okf
1/43
FISIKA DASAR 2
PERSAMAAN MAXWELL
8/18/2019 Persamaan MAxwell Okf
2/43
Energi dan Momentum gelombang elektromagnetik dibawaoleh medan listrik E dan medan magnet B yang menjalarmelalui vakum.
Sumber gelombangnya berupa muatan-muatan listrik yangberosilasi dalam atom, molekul, atau mungkin juga dalamsuatu antene pemancar radio.
Untuk medan listrik E dan medan magnet B yang berubahdengan waktu, keberadaan E selalu disertai B, dansebaliknya. eterkaitan antara E dan B dituangkan dalampersamaan Ma!well yang mendasari teori medan magnetik.
PENDAHULUAN
8/18/2019 Persamaan MAxwell Okf
3/43
GELOMBANG ELEKTROMAGNETIK
PERSAMAAN MAXWELL PERSAMAAN HELMHOLTZ
PEMANTULAN DAN TRANSMISI
TRANSMISI MELALUI TIGA MEDIUM
PENYESUAIAN IMPEDANSI
8/18/2019 Persamaan MAxwell Okf
4/43
PERSAMAAN MAXWELL
"ersamaan Ma!well dirumuskan dalam besaran medan
listrik E dan medan magnet B. Seluruh persamaan Ma!well
terdiri dari # persamaan medan, yang masing-masing dapatdipandang sebagai hubungan antara medan dan distribusisumber, baik sumber muatan ataupun sumber arus.
8/18/2019 Persamaan MAxwell Okf
5/43
0H0HB
0E0E0D
H jtH
tBE
E jt
E
t
DH
=•∇→=µ•∇=•∇
=•∇→=ε•∇→=•∇
ωµ−=∂∂µ−=
∂∂−=×∇
ωε=∂∂
ε=∂∂
=×∇
ω
µ
ε
jt
H B
E D
=∂∂=
=
0B
0D
t
BE
t
DH
=•∇=•∇
∂∂
−=×∇∂
∂=×∇
PERSAMAAN MAXWELL
8/18/2019 Persamaan MAxwell Okf
6/43
0B
D
t
BE
t
DJH
v
=•∇
ρ=•∇∂∂−=×∇
∂∂
+=×∇
0B
0D0
t
BE
t
DH0EJ0
v
=•∇
=•∇→=ρ∂∂−=×∇
∂∂
=×∇→=σ=→=σ
RUANG HAMPA
8/18/2019 Persamaan MAxwell Okf
7/43
EE) j( j
)H( j
)H j()E(
2
εµω=ωεωµ−=
×∇ωµ−=ωµ−×∇=×∇×∇
0H
0E
H jE
E jH
=•∇=•∇
ωµ−=×∇
ωε=×∇
E0
EE)E(2
2
∇−=∇−•∇=×∇×∇
0EE 22 =εµω+∇
PERSAMAAN HELMHOLTZ
8/18/2019 Persamaan MAxwell Okf
8/43
!
"
#
)!t( j
## $EE β−ω=
)!t( j
"" $HH
β−ω
=##%EE =
""%HH =
8/18/2019 Persamaan MAxwell Okf
9/43
22
)!t( j
#
2)!t( j
#
0
0$E$E) j)( j(
εµω=β→=εµω+β−
=εµω+β−β− β−ωβ−ω
vv
f ω π
λ
π
β === 22
)!t( j### $E)!&t(EE β−ω==
2
2
2
2
2
22
!
A
"
A
#
AA
∂∂
+∂∂
+∂∂
=∇
'v εµ=
0EE #2
#
2 =εµω+∇
0E!
E#22
#
2
=εµω+∂∂
B%*+%* +$,-%*+
K$.$/%t%* +$,-%*+ 1#'0 ,34,3H'0#5
,3F'0#657
8
'2
−
−
π=µ
=ε
8/18/2019 Persamaan MAxwell Okf
10/43
)!t( j
#
"$E j
!
H β−ωωε=
∂
∂−
)!t( j
""" $H)!&t(HH β−ω==
!#"
"!#
#
"! %
"
A
#
A%
#
A
!
A%
!
A
"
AA
∂
∂−
∂
∂+
∂
∂−
∂
∂+
∂
∂−
∂
∂=×∇
E jH ωε=×∇
!#"
"!#
#
"! %"
H
#
H%#
H
!
H%!
H
"
HH
∂∂−
∂∂+
∂∂−
∂∂+
∂∂−
∂∂=×∇
## %E jH ωε=×∇
8/18/2019 Persamaan MAxwell Okf
11/43
Ω=π=
ε
µ=η 188'20
)!t( j
#
"$E j
!
H β−ωωε=∂∂
−
η="
#
H
E
#
#
#
" EEEH µ
ε
=εµω
ωε
=β
ωε
=
ε
µ=
"
#
H
EI,/$9%*4 *4t:*4; <
)!t( j
"" $HH β−ω=
)!t( j#
)!t( j" $E j$H) j( β−ωβ−ω ωε=β−−
8/18/2019 Persamaan MAxwell Okf
12/43
PEMANTULAN DAN TRANSMISI
E & H
E: & H:
Et & Ht
! 0
η' η2
)!t( j
'
'
)!t( j
'
'
'
$A
H
$AE
β−ω
β−ω
η=
=
)!t( j
2
2t
)!t( j2t
2
2
$A
H
$AE
β−ω
β−ω
η=
=
)!t( j
'
':
)!t( j
':
'
'
$B
H
$BE
β+ω
β+ω
η−=
=
S"%:%t=4"%:%t -%t%4 /%9% ! 0 <
t:
t:
HHH
EEE
=+
=+
8/18/2019 Persamaan MAxwell Okf
13/43
E & H
E: & H:
Et & Ht
! 0
η' η2 S"%:%t=4"%:%t -%t%4 /%9% ! 0 <
t:
t:
HHH
EEE
=+=+
2
2
'
'
'
'
2''
ABA
ABA
η=
η−
η
=+
'2
'2
'
'
A
B
η+η
η−η
=Γ =
'2
2
'
2 2T
A
A
η+η
η==
F%;t: R$>$;4
F%;t: T:%*4,4
8/18/2019 Persamaan MAxwell Okf
14/43
( )
0B
0D
H jtBE
E jE jEt
DJH
=•∇
=•∇
ωµ−=∂∂−=×∇
ωε+σ=ωε+σ=∂∂
+=×∇
MEDIUM DIELEKTRIK 0
EJ σ=
8/18/2019 Persamaan MAxwell Okf
15/43
0E) j( jE
E) j( jE0EE
E) j( j
)H( j
)H j()E(
2
22
=ωε+σωµ−∇ωε+σωµ−=∇−=∇−•∇
ωε+σωµ−=×∇ωµ−= ωµ−×∇=×∇×∇
( )
0E
H jE
E jH
=•∇ ωµ−=×∇
ωε+σ=×∇
8/18/2019 Persamaan MAxwell Okf
16/43
) j( j
) j( j
0$E) j( j$E
0E) j( j
!
E
$EE
2
!
!
2
2
2
!
ωε+σωµ±=γ
ωε+σωµ=γ
=ωε+σωµ−γ
=ωε+σωµ−
∂
∂=
γ γ
γ
0E) j( jE2 =ωε+σωµ−∇
K*4t%*t% /$*j%%:%* ( propagation constant )
8/18/2019 Persamaan MAxwell Okf
17/43
) j(
j
) j(
) j( j
) j(H
E
$E) j($H
$E) j(!
H
"
#
!
#
!
"
!
#
"
ωε+σωµ
=ωε+σ
ωε+σωµ=
ωε+σγ
==η
ωε+σ=γ
ωε+σ=∂
∂−
γ −γ −
γ −
"
!
"
!
#
!
#
!
%$H$HH
%$E$EE
γ −γ −
γ −γ −
==
==
!#"
"!#
#
"! %"
H
#
H%
#
H
!
H%
!
H
"
HH
E) j(H
∂∂
−∂∂
+
∂∂
−∂
∂+
∂∂
−∂∂
=×∇
ωε+σ=×∇
8/18/2019 Persamaan MAxwell Okf
18/43
?*t@ S% 17'
S%t +$,-%*+ $$;t:,%+*$t; ,$*j%%: 9 9%%, 4%t
,$9,7 K*4t%*t% /$*j%%:%* 9%* ,/$9%*4 *t:*4;*"%
,%4*+=,%4*+ γ (0&26 j 2) ,='
9%* η (C00 j 86) Ω7Ht*+ µR & ε
R 9%* σ 9%: ,$9, t$:4$-t7
J%%- <
08&1
'0#5
'0#8&1,3H'0#8&1
)'0#60(2
86&'2'
86&'2'86&'2' j)86 jC00)(2 j26&0( j
86 jC00 j
j2 j26&0) j( j
8
C
R
C
C =
π
=
µ
µ=µ→=
π
=µ
=ωµ→=++=ωµ=γη
+=ωε+σ ωµ=η+=ωε+σωµ=γ
−
−−
'C2&''0#65&'0#26&'0'0#26&'0
)'0#60(2'0#21'&1
'0#21'&1,3,S2'&0
'0#)21'&1 j2'&0(86 jC00
2 j26&0 j
'2
'2
R '2
C
1
1
1
==εε=ε→=π=ε
=ωε=σ
+=++
=ωε+σ=ηγ
−
−
−
−
−
−
8/18/2019 Persamaan MAxwell Okf
19/43
S$-%@ /$4%%t t$:-%*+ ,$*++*%;%* %t,$t$: :%9%: *t;,$*$*t;%**"% ;$t*++%**"% "%t 9$*+%* ,$,%*.%:;%*
+$,-%*+ $$;t:,%+*$t; -$:>:$;$*4 8 GH! ;$ -%%@ 9%*,$*$:,% +$,-%*+ "%*+ 9/%*t;%* $@ /$:,;%%* 9
-%%@*"%7 B% /$4%%t t$:-%*+ t$:4$-t -$:%9% 9 %t%4 /$:,;%%* %t 9$*+%* /$:,tvt%4 :$%t/ ε
R '&
/$:,$%-t%4 :$%t/ µR ' 9%* ;*9;tvt%4 4t:; σ 5S3,& @t*+ /$:4$*t%4$ -$:;:%*+*"% 9%"% %;-%t /$,%*t%*
/$:,;%%* %t7
?*t@ S% 172 <
ωε+σ
ωµ=η
j
j
P$t*j; < I,/$9%*4 4%t ,$9, t$:@%9%/
+$,-%*+ $$;t:,%+*$t; %9%%@ <
8/18/2019 Persamaan MAxwell Okf
20/43
η
ηL
I
L
2
I
2
η=
η+η==
2
G
L
L
G
F
2
F
2
F
2
'
)IFR$(2
')
GFFR$(
2
')IIR$(
2
'P
η=η=
=η
=η=
LT' η=η→=α
T
P
P=α
Jawab : (Analogi Rangkaian Lis!ik"
8
8/18/2019 Persamaan MAxwell Okf
21/43
2
1
2
2
F'0#'6C&11188
2
F
2
'2
F
2
'P −=
=η
=
1
F'0#)8&6 j5&(F)C2&2 jC'0&5'(188
)C2&2 jC'0&5'(FF −+=++ +=η+η η=
1
'0#)0'6&0 j5&2()C2&2 jC'0&5'(188
I −−=
++=
η+η=
2
1
11
F'0#82&''
F'0#)0'6&0 j5&2('0#F)8&6 j5&(2
'R$)F#I
2
'R$(P
−
−−
=
++==
08&16'00F'0#'6C&11
F'0#82&''
P
P
1
1
T ===α −
−
C2&2 jC'0&5'
)'0#65&)(')('0#8)(2( j5
)'0#5)(')('0#8)(2( j'2
8
+=
π+ππ
=η −−
η
ηL
I
? t @ S 1 1
8/18/2019 Persamaan MAxwell Okf
22/43
?*t@ S% 171 <
S%t +$,-%*+ $$;t:,%+*$t; -$:>:$;$*4 '0 MH!&
,$*j%%: 9%%, %:%@ a! 9 9%%, ,$9, 9$*+%*
;*9;tvt%4 4t:; σ C& # '0=5 ,@3,& /$:,tvt%4 :$%t/ε
R 8&'1 9%* /$:,$%-t%4 :$%t/ µ
R 5&667 T$*t;%*
-$4%:*"% ,$9%* ,%+*$t; /%9% ! 60 ., 9%* t 6 *4 -%
9;$t%@ %,/t9% 9%: ,$9%* 4t:; "%*+ ,$*j%%: 9%%,%:%@ a# %9%%@ 4$-$4%: '00 3,7
P$t*j; < K*4t%*t% /$*j%%:%* +$,-%*+
$$;t:,%+*$t; 9 9%%, 4%t ,$9, %9%%@ <
ωµωε+σ=β+α=γ j) j( j
J -
8/18/2019 Persamaan MAxwell Okf
23/43
J%%- <
06&0
'2C
8C
80&2115&268&28)'065&)('1&8)('0'0)(2(5
)'05)(66&5)('0'0)(2(
je j x x j
x x j
=+=+
= −−
π
π π η
'&''02&0
)'05)(66&5)(2()'065&)('1&8)('0'0(2'0&CK( 8'2C5
j
x j x x j x
+=
+= −−− π π π γ
m A
x xe
z t e E H
z
xo y
328&0
80&2
J06&0)6&0('&')'06)('0'0(2.4K'00
).4(
C)6&0)('02&0(
=
−−=
−=
−−
−
π η
β ω α
? @ S 1 5
8/18/2019 Persamaan MAxwell Okf
24/43
?*t@ S% 175 <
T*j;;%* -%@% 9%: ;*4t%*t% /$*j%%:%* <
''2
2
−
ωεσ
+µε
ω=α
''2
2
+
ωεσ
+µε
ω=β
) j( j j ωε+σωµ=β+α=γ ;*4t%*t% %t$*%4 9%* ;*4t%*t% >%4% ,%4*+=,%4*+
9%/%t 9@t*+ 9%: /$:4%,%%*=/$:4%,%%* <
J -
8/18/2019 Persamaan MAxwell Okf
25/43
J%%- <
05
02
22
j j2
) j)( j( j
222
225
2
2
2
222
=σµω−µεαω+α
=µεω+
αωµσ−α
αωµσ
=β→ωµσ=αβωµσ+µεω−=αβ+β−α
ωε+σωµ=β+α
2
22222522 σµω+εµω±µεω−
=α
22222522
8/18/2019 Persamaan MAxwell Okf
26/43
222225222 σµω+εµω±µεω−=α
''
2
2''
2'
'2
'
2
'
''2
'2
2
2
2
22
2
2
22222
2
2
222
+
ωε
σ+
µεω=β
µεω+ ωεσ+µεω=β
µεω+
ωεσ
+µεω−±µεω−=µεω+α=β
−
ωεσ
+µε
ω=α
ωε
σ+µεω−±µεω−=α
? t @ S 1 6
8/18/2019 Persamaan MAxwell Okf
27/43
?*t@ S% 176
S%t +$,-%*+ $$;t:,%+*$t; -$:>:$;$*4 200 MH!
9$*+%* %,/t9% ,$9%* 4t:; 4$-$4%: E '00 3, "%*+
4$9%*+ ,$*j%%: ,$*+$*% %/4%* /$:%; t/4 (εR '& µR '& C'&8 MS3,) 4$t$-% 9 6 ,7 Ht*+ %,/t9% ,$9%*
4t:; E1 4$t$%@ ,$*$,-4 %/4%* t/4 t$:4$-t7
J%%- <
E E' E2 E1
9
J -
8/18/2019 Persamaan MAxwell Okf
28/43
J%%- <
µσπ≈
+ ωεσ+µεω=β
µσπ=µσπ
=ωεσµε
ω≈
−
ωεσ
+µε
ω=α
>>==ωεσ
−
> ''2
> 2
> 2
2''
2
''0#16)'0#65&)('0#200(
'0#8&C'
2
2
'2C
C
2
2
) j'(2
2
')564* j56(.4> 2
56$$'
j j
j
j
j
j
56 j0 j
+σωµ=+σωµ=ηµσπ=β=α
∠σωµ
=σωµ
=σωµ
=
σ
ωµ=
σ
ωε
ε
µ≈
+ωεσ
εµ
=
ωε+σ
ωµ=η
C8 )'08C')('05)('02(> ππσµπα −
8/18/2019 Persamaan MAxwell Okf
29/43
Ω+=+=η
∠=
∠ππ
=∠σωµ
=η
−−
−
−
11
2
1
C
8
2
'0#)688&1 j688&1() j')(808&0('0#06&6
56'0#06&6
56'0#8&C'
)'0#5)('0#2(256
,3F'0#8&'
'0#)688&1 j688&1(188
)188(2'0#0&0
2EE 1
1
1
2'
'21
−−
− =
++
=
η+η
η=
6
C8
222
'0#208&2
)'0#8&C')('0#5)('0#2(>
=
ππ=σµπ=α
,3'0#C5&2E'0#)&' j&'(
'0#)688&1 j688&1(188
'0#)688&1 j688&1(2)'00(
2EE
1
'
1
1
1
2'
2'
−−
−
−
=→+=
+++
=η+η
η=
,3F'0#0&0$'0#C5&2$EE 1)'0#6)('0#208&2(1!
'2
C62 −−−α− ===
−
E E' E2 E1
9
8/18/2019 Persamaan MAxwell Okf
30/43
P%9% ,$9, ' <
E ,%;4,, t$:j%9 -% E 9%* E: 4$>%4% <
J$$KEEEE
$$EE$EE
)!t( j)!t( j
:
j)!t( j
:
)!t( j
''
''
φ+β+ωβ−ω
φβ+ωβ−ω
Γ+=+=
Γ=ΓΓ==
π+φ
=β− *2
!,%;4E
'*2!! '' π+φ+β=β−
)!t( j
,%;4'$)'(EE β−ωΓ +=
#EL$M%AN# %ERDIRI
8/18/2019 Persamaan MAxwell Okf
31/43
Γ−Γ+
=='
'
E
E4
,*
,%;4
E ,*,, t$:j%9 -% E 9%* E: -$:%%*%* >%4% <
*2!! '' π+π+φ+β=β− π+π
+φ
=β− *22
!,*
E'
)!t( j
,*'$)'(EE
β−ωΓ −=
St%*9*+ W%v$ R%t (SWR) <
8/18/2019 Persamaan MAxwell Okf
32/43
Sal&!an T!ans'isi
η ηL
! =9 ! 0
η'
η*
βη+η βη+ηη=η 9t+ j9t+ j
L
L*
ZLZv
Z'
>
9Z'
*/t,/$9%*49! =η −=
#EL$M%AN# MELALUI TI#A MEDIUM
8/18/2019 Persamaan MAxwell Okf
33/43
0&0 ,
ε' 20 /F3,µ' 2 µH3,
ε2 60 /F3,
µ2 2&6 µH3,ε1 ε' µ1 µ'
D 9%$:%@ ' (! 0) t$:9%/%t ,$9, 9$*+%* ε' 20 /F3, 9%* µ
' 2 µH3,7 D
9%$:%@ 2 (0 ! .,) t$:9%/%t ,$9, 9$*+%* ε' 60 /F3, 9%* µ
' 2&6 µH3,7
M$9, /%9% 9%$:%@ 1 (! .,) 4%,% 9$*+%* ,$9, /%9% 9%$:%@ '7B% ,$9%* 4t:; "%*+ 9%t%*+ 9%: ,$9, ' %9%%@ E '000 .4 (5#'0 π t = β
' !)
3,& t$*t;%* ,$9%* ,%+*$t; H "%*+ 9t$:4;%* ;$ ,$9, 17
Ω=== 2&1'C'
'1'
ε
µ η η
Ω== C&2212
22
ε µ η
sm xv 3'05&0'
22
2 ==ε µ
sm xvv 3'06'&''
''
1' ===
ε µ
Jawab :
ono) Soal *+, :
8/18/2019 Persamaan MAxwell Okf
34/43
66&68 j01&'1)C16&'(2&1'C jC7221
)C16&'(C&221 j2&1'CC&221* −=
++
=η
C16&'9t+022&')0&0('0#5&0
'0#22
9
MH!200> 9v
> 29
v9
22
22
2
2
2
2
22
=β→=π
=β
=π
=ω
=β
βη+ηβη+η
η=η2212
22212*
9t+ j
9t+ j
η' η*
E Ht
8/18/2019 Persamaan MAxwell Okf
35/43
η' η*
E Ht
6&C j
*
tt $&156C&0 j61&1
66&68 j01&'1
2'8&'55 j0&85EH =+=
−−
=η
=
2'8&'55 j0&85)'000(66&68 j01&'12&1'C
)66&68 j01&'1(2
E2
E *'
*t
−=−+
−=
η+ηη=
)!5&8t'0#5.4('000)!t.4(EE ' −π=β−ω=
,3:%95&8'0#6'&'
)'0#200(2
v
C
'
1'
=π=
ω=β=β
)6&C!5&8t'0#5.4(&1)!t.4(HH
1tt +−π=β−ω=
8/18/2019 Persamaan MAxwell Okf
36/43
S$-%@ $*4% ;%.%,%t% -$:*9$;4 -%4 '&C2 9%/4 $@ %/4%* %*t :$>$;47L%/4%* /$*"$4% ,/$9%*4 * -%4%*"% 9:%*.%*+ *t; ,$*$:4;%* .%@%"%
9$*+%* /%*j%*+ +$,-%*+ 660 *, (;**+) "%*+ 9%t%*+ 9%: 9%:% ;%:$*% ,%t%,$,/*"% 4$*4tvt%4 ,%;4,, /%9% %:*% ;**+7 S$/$:t ;t% ;$t%@.%@%"% t%,/%; ,$,/*"% 9%$:%@ /%*j%*+ +$,-%*+ 500 *, 439 800 *,7Ht*+ /$:4$*t%4 -$:;:%*+*"% *t$*4t%4 .%@%"% "%*+ 9t$:4;%* /%9% %:*%*+ (500 *,) 9%* ,$:%@ (800 *,)7 A/% ;,$*t%: 4%9%:%
*' '&C2 *2*1 '
5
kuning λ
ono) Soal *+- :
Jawab :
'
8/18/2019 Persamaan MAxwell Okf
37/43
oo
oo
v
cn
ε µ
µε
µε
ε µ ===
'
'
nnnn
o
o
o
o
o 188'2
===== η
ε
µ
ε
µ
ε
µ η
B%@%* **=,%+*$t; o µ µ =
o
nε
ε =
on ε ε 2=
Ω==Ω==Ω= 2&2C8&212
C2&'
188188 1'2'1 η η η η η
8/18/2019 Persamaan MAxwell Okf
38/43
η1
η*
I
*' '&C2 *2*1 '
5
kuning λ
η1 η*
8/18/2019 Persamaan MAxwell Okf
39/43
2
12
1
2
1
G
;**+ F'0#CC1&0)188(5
F
5
F
2
F
2
F)IFR$(P −==
η=
η==
η1
η*
I
'9t+
25
29
*,660
t22
2
2
22
1
=α→∞=β
π=λλ
π=β
=λ
1
1*
1*
2
I
2
η=
η+η==→η=η
a)a.a k&ning :
8/18/2019 Persamaan MAxwell Okf
40/43
( )
88&''00#'0#085&'
'0#066&''0#085&'P
'0#066&''0#)218&0 j'6&0()066&0 j61&0(IR$P
'0#)218&0 j'6&0(8&2125&6 j&2C1
I
)066&0 j61&0(8&2125&6 j&2C1
5&6 j&2C1
5&6 j&2C1)58&'(188 j2&2C
)58&'(2&2C j1882&2C
9; t+ j
9; t+ j
58&'9t+)186&'(
25
660
500
29*,500
2
0
1
2
0
12
0
1
2
0
1
0
1
0
*+
0
10
'*
0
00
'*
*
2212
22212*
22221
=−
=∆
=−+==
+=++
=η+η
=
+=++ +=η+η η=
+=
−+−+
=
η+ηη+η
η=η
−=β→π
=π
=β→=λ
−
−−
−
a)a.a &ng& :
8/18/2019 Persamaan MAxwell Okf
41/43
( )
8&0'00#'0#085&'
'0#0C8&''0#'085&0P
'0#0C8&''0#)'C2&0 j20&0()0188&0 j6'5&0(IR$P
'0#)'C2&0 j20&0(8&212&1C j&252
I
)0188&0 j6'5&0(8&212&1C j&252
&1C j&252
&1C j&252)6&2(188 j2&2C
)6&2(2&2C j1882&2C
6&29t+)8C&0(25
660
800
29*,800
2
0
1
2
0
12
0
1
2
0
1
0
1
0
,$:%@
0
10
'*
0
00'*
*
*
22221
=−
=∆
=++==
−=+−
=η+η
=
−=+−−
=η+ηη
=
−=
+
+=η
=β→π
=π
=β→=λ
−
−−
−
a)a.a '/!a) :
8/18/2019 Persamaan MAxwell Okf
42/43
S$-%@ 4,-$: t$+%*+%* 4$-$4%: 0 9$*+%* >:$;$*4 500 ;H!,$,/*"% ,/$9%*4 t/t 4$-$4%: '0 @,7 S,-$: t$+%*+%*
* %;%* ,$*t:%*4,4;%* 9%"% ;$ 4$-%@ -$-%* 4$-$4%: C0 @,,$% 4%:%* t:%*4,4 -$:/% ;%-$ ;%;4% 4$/%*j%*+ 86 ,9$*+%* Z
50 @, 9%* v 2&6#'0 ,347 Ht*+ 9%"% "%*+
9t:%*4,4;%* $@ 4,-$: t$+%*+%* t$:4$-t7
'0 Ω
C0 Ω
Z 50 Ω v 2&6#'0 ,34
0 > 500 KH!
ono) Soal *+ :
8/18/2019 Persamaan MAxwell Okf
43/43
[ ] W5C6&6)5C&0 j60&')(C2&5 j'6&C5(R$P
5C&0 j60&'
850&'6 j65&18
0I
C2&5 j'6&C5)0('0850&'6 j65&18
850&'6 j65&18
850&'6 j65&18)1&0(C0 j50
)1&0(50 jC050Z
1&0;9t+:%9865&0)86('0#6&2
'0#52
9v9
*
6
=−−=
+=
−
=
−=+−
−=
−=
++
=
=→=π
=ω
=β
Jawab :