Electromagnetic Waves Short notes | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

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Short Notes on Electromagnetic W a v es
1. In tro duction
• Electromagnetic (EM) w a v es are oscillating electric and magnetic fields that propagate through
space, carrying energy .
• Go v erned b y Maxw ell’s equations, they include radio w a v es, micro w a v es, infrared, visible ligh t,
UV, X-ra ys, and gamma ra ys.
• T ra v el at the sp eed of ligh t c =
1
v
µ0?0
˜ 3×10
8
m/s in v acuum.
2. Maxw ell’s Equations
• Gauss’s La w (Electric) : ?·E =
?
?0
.
• Gauss’s La w (Magnetic) : ?·B = 0 .
• F arada y’s La w : ?×E =-
?B
?t
.
• Amp ère’s La w (with Maxw ell’s correction) : ?×B = µ
0
J+µ
0
?
0
?E
?t
.
• In v acuum (? = 0 ,J = 0 ), these lead to the w a v e equation: ?
2
E = µ
0
?
0
?
2
E
?t
2
.
3. W a v e Characteristics
• T ransv erse W a v es : E andB are p erp endicular to eac h other and to the direction of propagation.
• Plane W a v e Solution : F or a w a v e propagating in z -direction:
E = E
0
cos(?t-kz)ˆ x, B = B
0
cos(?t-kz)ˆ y, E
0
= cB
0
where ? = 2pf is angular frequency , k =
2p
?
is w a v e n um b er.
• W a v elength and F requency : c = f? .
• P olarization : Direction ofE (e.g., linear, circular, elliptical).
4. W a v e Propagation
• Phase V elo cit y : v
p
=
?
k
= c in v acuum.
• Energy Densit y : u =
1
2
?
0
E
2
+
1
2µ0
B
2
.
• P o yn ting V ector : Energy flo w direction and in tensit y:
S =
1
µ
0
E×B
• In Media : Sp eed r educes to v =
c
v
µr?r
, where µ
r
, ?
r
are relativ e p ermeabilit y and p ermittivit y .
5. EM Sp ectrum
• Ranges from lo w-frequency radio w a v es (f < 10
6
Hz) to high-energy gamma ra ys (f > 10
19
Hz).
• Applications dep end on frequency: Radio for comm unication, micro w a v es for heating, visible ligh t
for imaging, X-ra ys for medical diagnostics.
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Page 2


Short Notes on Electromagnetic W a v es
1. In tro duction
• Electromagnetic (EM) w a v es are oscillating electric and magnetic fields that propagate through
space, carrying energy .
• Go v erned b y Maxw ell’s equations, they include radio w a v es, micro w a v es, infrared, visible ligh t,
UV, X-ra ys, and gamma ra ys.
• T ra v el at the sp eed of ligh t c =
1
v
µ0?0
˜ 3×10
8
m/s in v acuum.
2. Maxw ell’s Equations
• Gauss’s La w (Electric) : ?·E =
?
?0
.
• Gauss’s La w (Magnetic) : ?·B = 0 .
• F arada y’s La w : ?×E =-
?B
?t
.
• Amp ère’s La w (with Maxw ell’s correction) : ?×B = µ
0
J+µ
0
?
0
?E
?t
.
• In v acuum (? = 0 ,J = 0 ), these lead to the w a v e equation: ?
2
E = µ
0
?
0
?
2
E
?t
2
.
3. W a v e Characteristics
• T ransv erse W a v es : E andB are p erp endicular to eac h other and to the direction of propagation.
• Plane W a v e Solution : F or a w a v e propagating in z -direction:
E = E
0
cos(?t-kz)ˆ x, B = B
0
cos(?t-kz)ˆ y, E
0
= cB
0
where ? = 2pf is angular frequency , k =
2p
?
is w a v e n um b er.
• W a v elength and F requency : c = f? .
• P olarization : Direction ofE (e.g., linear, circular, elliptical).
4. W a v e Propagation
• Phase V elo cit y : v
p
=
?
k
= c in v acuum.
• Energy Densit y : u =
1
2
?
0
E
2
+
1
2µ0
B
2
.
• P o yn ting V ector : Energy flo w direction and in tensit y:
S =
1
µ
0
E×B
• In Media : Sp eed r educes to v =
c
v
µr?r
, where µ
r
, ?
r
are relativ e p ermeabilit y and p ermittivit y .
5. EM Sp ectrum
• Ranges from lo w-frequency radio w a v es (f < 10
6
Hz) to high-energy gamma ra ys (f > 10
19
Hz).
• Applications dep end on frequency: Radio for comm unication, micro w a v es for heating, visible ligh t
for imaging, X-ra ys for medical diagnostics.
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6. Applications
• Wireless comm unication (Wi-Fi, cellular, satellite).
• Radar and remote sensing.
• Optical systems (lasers, fib er optics).
• Medical imaging (MRI, X-ra y).
• Micro w a v e o v ens and industrial heating.
7. Practical Considerations
• A tten uation: EM w a v es lose energy in l ossy media (e.g., conductors, dielectrics).
• Reflection and Refraction : Occur at b oundaries, go v erned b y Snell’s la w and F resnel equations.
• Disp ersion : V elo cit y v aries with frequency in non-v acuum media, affecting signal in tegrit y .
• In terference and Diffraction : Impact w a v e b eha vior in c omplex en vironmen ts.
8. Conclusion
• EM w a v es are cen tral to mo dern tec hnology , describ ed b y Maxw ell’s equations and c haracterized
b y transv erse, propagating fields.
• Understanding their prop erties, propagation, and in teraction with media is crucial for applications
in comm unication, imaging, and b ey ond.
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