Download Chapter 34 ... Definitions

Chapter 34
Electromagnetic Waves
Definitions
In a region of space in which there is a changing electric field, there
is a displacement current defined as
dFE
dt
where P0 is the permittivity of free space (see Section 23.3) and
S
S
FE 5 e E ? d A is the electric flux.
Id ; P0
The rate at which energy passes
through a unit area by electromagnetic radiation is described by the
S
Poynting vector S , where
(34.1)
S
S ;
S
1 S
E 3 B
m0
(34.22)
Concepts and Principles
S
S
S
When used with the Lorentz force law, F 5 q E 1 q S
v 3 B, Maxwell’s equations describe all electromagnetic
phenomena:
q
S
S
C E ?d A 5 P
0
(34.4)
dFB
S
S
C E ? d s 5 2 dt
(34.6)
C B ?d A 5 0
(34.5)
dFE
S
S
C B ? d s 5 m0I 1 P0m0 dt
(34.7)
S
S
Electromagnetic waves, which are predicted by Maxwell’s equations, have the following properties and are
described by the following mathematical representations
of the traveling wave model for electromagnetic waves.
r 5IFFMFDUSJDGJFMEBOEUIFNBHOFUJDGJFMEFBDITBUJTGZ
a wave equation. These two wave equations, which
can be obtained from Maxwell’s third and fourth
equations, are
'2E
'2E
5 m0P0 2
2
'x
't
(34.15)
'2B
'2B
5 m0P0 2
2
'x
't
(34.16)
r 5IFXBWFTUSBWFMUISPVHIBWBDVVNXJUIUIFTQFFEPG
light c, where
1048
1
c5
(34.17)
Chapter 34 "m
Electromagnetic
Waves
P
r /VNFSJDBMMZUIFTQFFEPGFMFDUSPNBHOFUJDXBWFTJO
a vacuum is 3.00 3 108 m/s.
r 5IFXBWFMFOHUIBOEGSFRVFODZPGFMFDUSPNBHOFUJD
waves are related by
l5
3.00 3 108 m/s
c
5
f
f
(34.20)
r 5IFFMFDUSJDBOENBHOFUJDGJFMETBSFQFSQFOEJDVMBS
to each other and perpendicular to the direction of
wave propagation.
S
S
r 5IFJOTUBOUBOFPVTNBHOJUVEFTPGE and B in an
electromagnetic wave are related by the expression
E
5c
B
(34.21)
r &MFDUSPNBHOFUJDXBWFTDBSSZFOFSHZ
r &MFDUSPNBHOFUJDXBWFTDBSSZNPNFOUVN
continued
0 0
Because electromagnetic waves carry momentum, they
exert pressure on surfaces. If an electromagnetic wave
S
whose Poynting vector is S is completely absorbed by a
surface upon which it is normally incident, the radiation
pressure on that surface is
P5
S
c
1 complete absorption 2
(34.28)
If the surface totally reflects a normally incident wave, the
pressure is doubled.
The electric and magnetic fields of a sinusoidal
plane electromagnetic wave propagating in the positive x direction can be written as
2
2
E max B max
E max
cB max
5
5
2m0
2m0c
2m0
(34.18)
B 5 B max cos (kx 2 vt)
(34.19)
where k is the angular wave number and v is the angular frequency of the wave. These equations represent
special solutions to the wave equations for E and B.
The average value of the Poynting vector for a plane electromagnetic
wave has a magnitude
S avg 5
E 5 E max cos (kx 2 vt)
(34.24)
The intensity of a sinusoidal plane electromagnetic wave equals the average value of the Poynting vector taken over one or more cycles.
The electromagnetic spectrum
includes waves covering a broad range
of wavelengths, from long radio waves
at more than 104 m to gamma rays at
less than 10214 m.