Topic 9 Electromagnetic Waves
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7/25/2019 Topic 9 Electromagnetic Waves
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http://goforward/http://find/http://goback/
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7/25/2019 Topic 9 Electromagnetic Waves
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http://find/http://goback/
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7/25/2019 Topic 9 Electromagnetic Waves
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= , = =
t ,
=
t,
u
t
=
u
t =
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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(x,y,z, t) = (x,y,z)ejt
= f, = =j , = f+j ,
=
+ , =
=
e , =m
= =
=
( +e) =
( +m)
http://find/http://goback/
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7/25/2019 Topic 9 Electromagnetic Waves
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+k
=
=
V
ejkR
R dv
u= /
V+k V=/
V( ,t) =
V
ejkR
R dv
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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= ,
= =j , =j ,
+k =
+k =
, ,
= = / =/
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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x +
y +
z +k
z
z +k
=
= Ex(z) x Exz
+k
Ex=
Ex(z) = E+
ejkz+E
ejkz
E
=
E+
Ex(z, t) =E+ ejkzejt= E+ (tkz)
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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Ex(z, t) =E+
ejkz
ejt
= E+
(tkz)
k
k
=
(z, t) = yE+
(tk
z)
=
=
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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(x,y,z) =
ejkxxjkyyjkzz
kx+k
y+k
z= k
=
= kx x+ky y+kz z= k n
= x x+ y y+ z z
(
) =
ej
n
=
OP
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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(x,y,z) =
ejkxxjkyyjkzz
=
=
n
=j , =j
=j
=
n =
n ej
=
ej
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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(z) = (E
x+E y)ejkz
E
E
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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(z) = (E
x+E
y)ejkz
|E
|= |E
|
(z) = E
( xj y)ejkz
(z) = E ( x+j y)ejkz
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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=
=j + =j+ j
c= +
j
=
j
=
j
= , =
= =
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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+kc =
kc= c
= +j=jkc=jc
(z) =
ez=
ezejz,
= c
http://goforward/http://find/http://goback/
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7/25/2019 Topic 9 Electromagnetic Waves
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= +j=jc=j
j
= +j=j j
+
=
, =
+
c=
c=
j
/
=
+j
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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= +j=jc=j
j
= +j
=j= ( +j)f= =
f
c=
c
=
j
/ =
j
= ( +j)f
c= ( +j)
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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=
f
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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=t
,
= + t
,
( ) = ( ) ( )
( ) =t
t
( ) = t
E +
H
S(
) d
=
t
V
E +
Hdv
V
dv
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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S(
) d
=
t
V
E +
H
dv
V
dv
PPP= ( , t) ( ,t)
SPPPd =
t
V(we+wm)dv
Vpdv
we=
E
=
=
wm =
H =
=
p= E
=J
= =
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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PPP= ( , t) ( , t) PPPav=
{ ( , t) ( , t)}
we=
E =
we,av=
|E| =
wm =
H =
wm,av=
|H| =
p= E =
J
= p=
|E| =|J|
=
http://find/
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7/25/2019 Topic 9 Electromagnetic Waves
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=j , = +j ,
( ) = ( ) ( )
( ) =j +j
(
) =j |
E
|
|H
|
|E
|
S( ) d =j
V(we,avwm,av)dv
Vpdv
http://find/
