Formula sheet: Electromagnetic Waves | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

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Electromagnetic W a v es F orm ula Sheet for GA TE
(Electromagnetics)
Maxw ell’s Equations (Differen tial F orm in F ree Space)
• Gauss’s La w for Electric Field :
?·E = 0
• Gauss’s La w for Magnetic Field :
?·B = 0
• F arada y’s La w :
?×E =-
?B
?t
• Amp ere’s La w with Maxw ell’s Correction :
?×B = µ
0
?
0
?E
?t
where E is electric field ( Vm
-1
), B is magnetic field ( T ), µ
0
is p ermeabilit y of free
space (4pe-7H/m ), ?
0
is p ermittivit y of free space (8854e-12F/m ).
W a v e Equation
• W a v e Equation for Electric and Magnetic Fields :
?
2
E = µ
0
?
0
?
2
E
?t
2
, ?
2
B = µ
0
?
0
?
2
B
?t
2
• Sp eed of Electromagnetic W a v es in F ree Space :
c =
1
v
µ
0
?
0
˜ 3×10
8
ms
-1
Plane W a v e Propagation
• General F orm of Plane W a v e (in z -direction):
E =E
0
e
j(?t-kz)
, B =B
0
e
j(?t-kz)
where ? is angular frequency (rads
-1
), k is w a v e n um b er (m
-1
).
• W a v e Num b er:
k =
?
c
=
2p
?
where ? is w a v elength (m ).
• Relation Bet w een E and B :
|B| =
|E|
c
, B =
1
c
(
ˆ
k×E)
where
ˆ
k is the unit v ector in the direction of propagation.
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