Electromagnetic waves
Physics 114
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Lecture X
1
Concepts
•
•
•
•
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EM waves – frequency and wave length
EM spectrum
Antennas
Radio
Amplitude and frequency modulations
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Lecture X
2
Maxwell’s equations in vacuum
• No charges, no currents
 
 EdA  0
closed surface
 
 BdA  0
closed surface
• Changing magnetic field
creates electric field
• Changing electric field
creates magnetic field
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 
d B
Edl  

dt
closed path
 
d E
B
d
l



0
0

dt
closed path
Lecture X
3
EM wave
 
EB
 
E v
 
Bv
v
E y  E0 sin( kx  t )
k

  2f

f   v
Bz  B0 sin( kx  t )
vx  v
E/Bv
1
 0 0
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
2
k
1
8.85 10 124 10 7
 3.0 108 m / s
The speed of light!!
Lecture X
4

EM spectrum
f
c  f
• c – speed of light (m/s)
• f – frequency (Hz=1/s)
  – wavelength (m)
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Lecture X
5
Waves
Matter
• Propagating oscillation =
wave.
• Waves transport energy
and information, but do
not transport matter.
• Examples:
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Wave
Lecture X
–
–
–
–
Ocean waves
Sound
Light
Radio waves
6
Waves
• Wavelength – 
• Period T
• Frequency f=1/T
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• Wave velocity:
v=/T=f
The only equation that you need
to remember about waves.
• Wave velocity is NOT the
same as particle velocity of
the medium
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7
Transverse and longitudinal waves
• In transverse wave the velocity of particles of the
medium is perpendicular to the velocity of wave.
• In EM wave electric field is perpendicular to the wave
velocity and so is the magnetic field. Thus EM wave is a
transverse wave.
Matter
Wave
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Lecture X
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Transverse and longitudinal waves
• In longitudinal wave the velocity of particles of
the medium is parallel (or anti-parallel) to the
wave velocity.
• Example of longitudinal wave is sound.
Wave
Matter
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Lecture X
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Description of waves

•
•
•
•
•
•
w2f – cyclic frequency, k=2/ –wave vector
D=D0sin(kx-wt+d), dphase at t=0, x=0
Riding the wave kx-wt+dconst
kx-wt=c
x=c/k+(w/k)t = x0+vt
Thus, wave velocity v=w/k=2f/ (2/)f  /T
D=D0sin(kx-wt) – wave is moving in +x direction
D=D0sin(kx+wt) – wave is moving in -x direction
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Lecture X
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Energy in EM wave
• EM waves transport energy
1
1 2
2
• Energy density:
u  0E 
B
1
1
2
2
 0 E0 
B0
2
20
20
2
B0  E0 / c
• Poynting vector (energy transported by EM wave per
unit time per unit area) 
1  
S
0
EB
• Average energy per unit time per unit area
S
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Lecture X
1
0
Erms  Brms
11
Average intensity
• Displacement D follows harmonic oscillation:
D  D0 sin( t )
• Intensity (brightness for light) I is proportional to
electric field squared
I  D 2  I  I 0 sin 2 (t )
• Average over time (one period of oscillation) I:
T
T
1
1
2
2
I  I 0  sin (t )dt  I 0
sin (t )dt 

T 0
T 0
1
 I0
2
2
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2
I0
1 1
2
0 sin xdx  I 0 2 2 0 (1  cos 2 x)dx  2
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Energy transported by waves
• Intensity of oscillation I
(energy per unit area/ per sec)
is proportional to amplitude
squared D2
• 3D wave (from energy
conservation):
D12 4r12= D22 4r22
D1/D2=r2/r1
• Amplitude of the wave is
inversely proportional to the
distance to the source:
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Lecture X
1
D
r
13
Radiation from an AC antenna
• Changing electric field
creates magnetic field
• Changing magnetic field
creates electric field
• Change propagates with
a finite velocity
• Electromagnetic wave –
proof of unification
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Lecture X
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Transmission and reception
• Antennas are used to transmit and to receive EM waves
• Rod antennas – transmit and receive E component
E || to rod
• Loop antennas – B component (use induction)
B  loop
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Lecture X
15
Modulations
• Amplitude modulation (AM)
• Frequency modulation (FM)
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Lecture X
16
Interference of waves
• When two or more waves pass through the same
region of space, we say that they interfere.
• Principle of superposition (fancy word for sum of
waves): the resultant displacement is the
algebraic sum of individual displacements created
by these waves.
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Lecture X
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Constructive and destructive
interference
in phase
Constructive
out of phase
Destructive
not in phase
Partially destructive
A
2A
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<A
0
Lecture X
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