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Excpes Eyz,t=looCas(laSt -Dsz 136) Vm
a s a phasoe
j(1o-o]
t3)
Exponential hotatioin Éylz,t) = Re[1a o e
Jot7
ReExe
e
phcso1 91m
es e
Ayslz) l00 JOSZtL30
ve ha Compax _ampltude etue Rlechc eld
ea unu plane ve D
E lo00+_ L30 ay
phoso
Y/m- Constaud the
Ond Ral stantaneas ads
nouon-
eond Zdirecfon- poPak
in eaOpace
Uttu
oloOHZ
E toc oLas ay
Jkoz
Exs Ex e Phaso1
Eslz)
_2ix lo
Ko O-2 Tad/m
Beal_islantaneou
Jkozjiat
ElzE) =Relaoe e
=Raooe
e - 2 z ot
e
J30
e
0212 JRUREE
-Rel1oDe
J(2 t -
o-2t
+
0 .J(27 xi't-
o.21z136) a
ECt) loo Cos(27 xiot -o21z) Ax f
ad
20 Cos( o1 xjat -
o.2/Z t 30) 9
The The moximum amplitudla e te Rlache ield a
propkaatinq
negatiue Uz. dlsuttou
The elohc eld spolasiged
SO HZ urlor
eo
plaina ove
pacaU along he
o.S V/m
- oLueefot and ts manu m Yalue w
hsexved at to and Z=-12cm Obtam
eKpLUmiona Lstonlaneous
R moqnetie kieldls Ako uY
Magnetic
pleere
the e id
he Soienlatiou
eetos.
he Alochiceld
Y-dusctou, popgatrn alorg
Jstenlanetu oim
pola e
-z diste elo
ECt) - a E4Cos(uot+Koz+ o)
L 24=
2nx 2Sox L
slo8 aLosad/<
L S H o 8 x o 7
wavenumber Ko
Ko 5.236 Tad ls
MaxRleehiceldio v.as D-5V/, u
ohSerued-at t+o, and Z 2cm
wtK Xo+
Sinte tha max. amplituoo otu reld auld
be oblained CAnen oReume 0flosine
PnChou becoms Onu ustu nol,2 -
O-(536)x12 p
S236 x 12x1 tcoao
0-6.283
.E(zE) a0s Cas(c1o8xiott
536Z t) Vm
Sin lu Rleche
eld polazed aleng
-ucttou uottu
tnhe
UWave
propmqa ting
- dn thou
0vientd
magetie ield
dlo ng the KdLLtioU
e
Bhold be
X X
THx
the) 4Eyo/314
344to5D5/374
Hzaof 826 m
magnUc
exprexs/oM ot tha
Lnstantantous
eeld
=a1326 (os S1ogxiot+324
mA
exetsiou s a magrutiu
travetlng u
im-domqin
e ea wuprm plane wgve
#(z.t)a ay s Cos1251Xot-z)
Am
nd a)HduLehton e Oave PoPagato
opoualigyn
phase conslanT
d_dime-domai RxpA0AoM Rleclstueield
toaiingo Manuwels
6
e polizaton Rlaclne Rield 19eetol
thephoo of RleciML magnubie eld
a Hyo_Casluet-koZ+4
au Cas( 12-4xudt -ko)
-25 7 xmo
@long Hhe +z
a)t wae
duetiou
prD2 ahnq
25 xo 200 MHz
Ko 2 xo
Ko A19 9Lado
d)
Ot
az
dt
H Hy H
Magnetic kreld es ony Conipornt
elds-alms
No Spatial
duéhou
hyD
D O dt
DH J
S_ca(L24xet -KezD
d2
Sin
Sin 1-2sxt -Koz AD
koz
E Sn12S7xe t
Ko-ctt
xid Ko-
EO Cac1.25 x-koz
C
Ko= 4.9 sadIm lo
sXIDx D O lo44
O 0l1l21
0H12
E 0-912 Cas28rA Atot - koz
the
e) Elechie eld polo zed alonq fhe
+ deton
Eleehceld,
J21xio't-4.19
LE) = Re-942e V
U 2 5 7 / t JA-19z
Re o.1412 e
UH-19Z
VI
Estz)
J 4 - 1 9
mAlm
Hst a s

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Problems in electromagnetic fields

  • 1. Excpes Eyz,t=looCas(laSt -Dsz 136) Vm a s a phasoe j(1o-o] t3) Exponential hotatioin Éylz,t) = Re[1a o e Jot7 ReExe e phcso1 91m es e Ayslz) l00 JOSZtL30 ve ha Compax _ampltude etue Rlechc eld ea unu plane ve D E lo00+_ L30 ay phoso Y/m- Constaud the Ond Ral stantaneas ads nouon- eond Zdirecfon- poPak in eaOpace Uttu oloOHZ
  • 2. E toc oLas ay Jkoz Exs Ex e Phaso1 Eslz) _2ix lo Ko O-2 Tad/m Beal_islantaneou Jkozjiat ElzE) =Relaoe e =Raooe e - 2 z ot e J30 e 0212 JRUREE
  • 3. -Rel1oDe J(2 t - o-2t + 0 .J(27 xi't- o.21z136) a ECt) loo Cos(27 xiot -o21z) Ax f ad 20 Cos( o1 xjat - o.2/Z t 30) 9 The The moximum amplitudla e te Rlache ield a propkaatinq negatiue Uz. dlsuttou The elohc eld spolasiged SO HZ urlor eo plaina ove pacaU along he o.S V/m - oLueefot and ts manu m Yalue w hsexved at to and Z=-12cm Obtam eKpLUmiona Lstonlaneous R moqnetie kieldls Ako uY Magnetic pleere the e id he Soienlatiou eetos. he Alochiceld Y-dusctou, popgatrn alorg Jstenlanetu oim pola e -z diste elo ECt) - a E4Cos(uot+Koz+ o)
  • 4. L 24= 2nx 2Sox L slo8 aLosad/< L S H o 8 x o 7 wavenumber Ko Ko 5.236 Tad ls MaxRleehiceldio v.as D-5V/, u ohSerued-at t+o, and Z 2cm wtK Xo+ Sinte tha max. amplituoo otu reld auld be oblained CAnen oReume 0flosine PnChou becoms Onu ustu nol,2 - O-(536)x12 p S236 x 12x1 tcoao
  • 5. 0-6.283 .E(zE) a0s Cas(c1o8xiott 536Z t) Vm Sin lu Rleche eld polazed aleng -ucttou uottu tnhe UWave propmqa ting - dn thou 0vientd magetie ield dlo ng the KdLLtioU e Bhold be X X THx the) 4Eyo/314 344to5D5/374 Hzaof 826 m
  • 6. magnUc exprexs/oM ot tha Lnstantantous eeld =a1326 (os S1ogxiot+324 mA exetsiou s a magrutiu travetlng u im-domqin e ea wuprm plane wgve #(z.t)a ay s Cos1251Xot-z) Am nd a)HduLehton e Oave PoPagato opoualigyn phase conslanT d_dime-domai RxpA0AoM Rleclstueield toaiingo Manuwels 6 e polizaton Rlaclne Rield 19eetol thephoo of RleciML magnubie eld
  • 7. a Hyo_Casluet-koZ+4 au Cas( 12-4xudt -ko) -25 7 xmo @long Hhe +z a)t wae duetiou prD2 ahnq 25 xo 200 MHz Ko 2 xo Ko A19 9Lado d) Ot az dt H Hy H
  • 8. Magnetic kreld es ony Conipornt elds-alms No Spatial duéhou hyD D O dt DH J S_ca(L24xet -KezD d2 Sin Sin 1-2sxt -Koz AD koz
  • 9. E Sn12S7xe t Ko-ctt xid Ko- EO Cac1.25 x-koz C Ko= 4.9 sadIm lo sXIDx D O lo44 O 0l1l21 0H12 E 0-912 Cas28rA Atot - koz the e) Elechie eld polo zed alonq fhe + deton
  • 10. Eleehceld, J21xio't-4.19 LE) = Re-942e V U 2 5 7 / t JA-19z Re o.1412 e UH-19Z VI Estz) J 4 - 1 9 mAlm Hst a s