Department of Physics,
Chulalongkorn University
Electromagnetic
Waves
by
Assist. Prof. Dr. Somchai Kiatgamolchai
Dept. of Physics, Chulalongkorn University
34.2 Maxwell’s Equations and Hertz’s
Discoveries
Department of Physics,
Chulalongkorn University
1. Gauss’s law
2. Gauss’s law in magnetism
3. Faraday’s law (law of induction)
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
2
1
34.2 Maxwell’s Equations and Hertz’s
Discoveries
Department of Physics,
Chulalongkorn University
4. Ampere-Maxwell law
G G
dΦ
B
v∫ ⋅ d s = μ0 I + μ0ε 0 dt E
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
34.2 Maxwell’s Equations and Hertz’s
Discoveries
3
Department of Physics,
Chulalongkorn University
The observation showed that the
sparks at the transmitter and receiver
happen at the same time.
Hertz’s experiment confirmed that…
HEINRICH
RUDOLF HERTZ
(1857-1894)
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
4
2
34.3 Plane Electromagnetic Waves
Department of Physics,
Chulalongkorn University
Maxwell’s equations could be rearranged to these two differential WAVE equation
∂ 2E
∂2E
=
μ
ε
0 0
∂x 2
∂t 2
∂ 2B
∂ 2B
=
μ
ε
0 0
∂x 2
∂t 2
Substitute solutions into the differential equations, we obtain the followings:
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
5
34.3 Plane Electromagnetic Waves
Department of Physics,
Chulalongkorn University
It has been proved that “the electric field is perpendicular to the magnetic field
and both are perpendicular to the direction of wave propagation.”
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
6
3
34.3 Plane Electromagnetic Waves
Department of Physics,
Chulalongkorn University
The meaning of plane wave
spherical
wave front
At very far from the source, the wave
front is looked like a plane and every
point on this plane has the same
property – different plane, different
property.
E
c
E
E
B
E
c
E
B
E
c
B
c
B
c
B
E
B
E
B
15 January
2014
c
B
c
c
Assist.Prof.Dr.Somchai Kiatgamolchai
7
Example: EMW from a radio station.
Department of Physics,
Chulalongkorn University
antenna
JG
E
100-200 m
JG
B
Think about the direction of each field…
Radio
Station
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
Earth surface
8
4
Example: Dipole & Loop Antennas
Department of Physics,
Chulalongkorn University
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
34.4 Energy Carried by
Electromagnetic Waves
9
Department of Physics,
Chulalongkorn University
Poynting vector
Using
E
=c
B
15 January
2014
, we obtain…
Assist.Prof.Dr.Somchai Kiatgamolchai
10
5
34.4 Energy Carried by
Electromagnetic Waves
1
uE = ε 0 E 2
2
B2
Magnetic energy density u B =
2 μ0
(in the solenoid)
Electric energy density
(in the capacitor)
Department of Physics,
Chulalongkorn University
J/m3
J/m3
Total instantaneous energy density is
Average energy density is
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
11
example: radiation from a light bulb
Department of Physics,
Chulalongkorn University
I = S avg =
Em2
cB 2 E B
= m = m m
2μ0 c 2μ0
2 μ0
r=3m
100 W,
2.5%
becomes
light.
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
12
6
Example: Poynting vector of
conducting wire
Department of Physics,
Chulalongkorn University
I
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
34.5 Momentum and Radiation
Pressure
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
13
Department of Physics,
Chulalongkorn University
14
7
34.5 Momentum and Radiation
Pressure
Department of Physics,
Chulalongkorn University
(a) Complete absorption
(a)
energy
U
c
(b) Complete reflection
c
(b)
(c) Partly absorption
(c)
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
34.5 Momentum and Radiation
Pressure
F=
15 January
2014
15
Department of Physics,
Chulalongkorn University
dp (1 + f ) dU
=
dt
c
dt
Assist.Prof.Dr.Somchai Kiatgamolchai
16
8
Example: pressure from laser pointer
Department of Physics,
Chulalongkorn University
15 mW
laser pointer
λ = 632.8 nm
φ = 2 mm
The energy of 1-m laser beam is…
The momentum of 1-m laser beam is…
Pressure on 80%-absorption screen is…
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
34.6 Production of Electromagnetic
Waves by an Antenna
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
17
Department of Physics,
Chulalongkorn University
18
9
34.6 Production of Electromagnetic
Waves by an Antenna
Department of Physics,
Chulalongkorn University
+
-
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
19
34.6 Production of Electromagnetic
Waves by an Antenna
2
Department of Physics,
Chulalongkorn University
2
<S> = sin θ/r
r=1
330
r=2
1.0
0
30
0.8
300
0.6
60
0.4
<S>
0.2
Intensity ∝
0.0
sin θ
r2
2
270
90
0.2
0.4
0.6
Q: If you stay at the top of the
antenna, the signal would be…
240
120
0.8
1.0
210
150
180
Computer-generated intensity in polar coordinate.
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
20
10
34.7 The Spectrum
of Electromagnetic
Waves
15 January
2014
Assist.Prof.Dr.Somchai Kiatgamolchai
Department of Physics,
Chulalongkorn University
21
11