20140428170425 Ch 32 A
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Transcript of 20140428170425 Ch 32 A
2005 Pearson Education South Asia Pte Ltd
ELECTROMAGNETISM
FE1001 Physics I NTU - College of Engineering
31. Alternating Current
32. Electromagnetic Waves
37. Relativity
38. Photons, Electrons, and
Atoms
39. The Wave Nature of
Particles
2005 Pearson Education South Asia Pte Ltd
ELECTROMAGNETISM
FE1001 Physics I NTU - College of Engineering
40. Quantum Mechanics
41. Atomic Structure
42. Molecules and
Condensed Matter
43. Nuclear Physics
44. Particle Physics and
Cosmology
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Chapter Objectives
• Maxwell’s equations for understanding
electromagnetic waves
• Properties of sinusoidal electromagnetic waves
• Types of electromagnetic waves
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Chapter Outline
1. Maxwell’s Equations and Electromagnetic Waves
2. Plane Electromagnetic Waves and the Speed of
Light
3. Sinusoidal Electromagnetic Waves
4. Energy and Momentum in Electromagnetic
Waves
5. Standing Electromagnetic Waves
6. The Electromagnetic Spectrum
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.1 Maxwell’s Equations and Electromagnetic Waves
• An electromagnetic wave is an electromagnetic
disturbance, consisting of time-varying electric and
magnetic fields, that can propagate through space
from one region to another, even when there is no
matter in the intervening region.
• Such a disturbance will have the properties of a
wave.
• The basic principles of electromagnetism can be
expressed in terms of the four equations that we
now call Maxwell’s equations.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.1 Maxwell’s Equations and Electromagnetic Waves
• Because the electric and magnetic disturbances
spread or radiate away from the source, the name
electromagnetic radiation is used
interchangeably with the phrase “electromagnetic
waves”.
• Electromagnetic waves can be used for long-
distance communication via devices such as a
radio transmitter.
• Fig. 32.2 shows electric field lines of a point charge
oscillating in simple harmonic motion.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.1 Maxwell’s Equations and Electromagnetic Waves
Fig. 32.2
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
• A plane wave is a wave in which at any instant the
electric and magnetic fields are uniform over any
plane perpendicular to the direction of propagation.
• Fig. 32.3 shows an electromagnetic wave front.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
Fig. 32.3
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.1 Maxwell’s Equations and Electromagnetic Waves
• To satisfy Maxwell’s first and second equations, the
electric and magnetic fields must be perpendicular
to the direction of propagation; that is, the wave
must be transverse.
• Fig. 32.4 shows the Gaussian surface for a plane
electromagnetic wave.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
Fig. 32.4
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.1 Maxwell’s Equations and Electromagnetic Waves
• The wave must be consistent with Faraday’s law,
where the wave speed c and the magnitudes of the
perpendicular vectors and are related as in
Eq. (32.4):
• Fig. 32.5 shows the application of Faraday’s law to
a plane wave.
E B
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
Fig. 32.5
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
• The wave must also be consistent with Ampere’s law where B, c, and E are related as in Eq. (32.8):
• The basis of the plane wave obeying Maxwell’s equations is Eq. (32.9):
• Fig. 32.6 shows the application of Ampere’s law to a plane wave.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
Fig. 32.6
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
• Electromagnetic waves have the property of
polarization.
• A wave in which is always parallel to a certain
axis is said to be linearly polarized along that axis.
• An alternative derivation of Eq. (32.9) for the speed
of electromagnetic waves includes the derivation of
the wave equation.
• Fig. 32.7 shows how Faraday’s law is also applied
in this alternative method.
E
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
Fig. 32.7
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.2 Plane Electromagnetic Waves and the Speed of Light
• Fig. 32.8 shows how
Ampere’s law is also
applied in this
alternative method.
Fig. 32.8
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
• In a sinusoidal electromagnetic wave, and at
any point in space are sinusoidal functions of time,
and at any instant of time the spatial variation of the
fields is also sinusoidal.
• Waves passing through a small area at a
sufficiently great distance from a source can be
treated as plane waves (Fig. 32.9).
E B
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
Fig. 32.9
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
• Fig. 32.10 shows a linearly polarized sinusoidal
electromagnetic wave traveling in the +x-direction,
where the electric and magnetic fields oscillate in
phase.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
Fig. 32.10
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
• We can describe electromagnetic waves by means
of wave functions.
• Eq. (32.17) shows in vector form the wave function
for a sinusoidal electromagnetic wave propagating
in +x-direction:
• Together with Eq. (32.4), we now get
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
• Fig. 32.11 shows the electric and magnetic fields of
a wave traveling in the negative x-direction.
• Note that as with the wave traveling in the +x-
direction, at any point the sinusoidal oscillations of
the and fields are in phase. E B
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
Fig. 32.11
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 Fields of a laser beam
A carbon dioxide laser emits a sinusoidal
electromagnetic wave that travels in vacuum in the
negative x-direction. The wavelength is 10.6 m and
the field is parallel to the z-axis, with maximum
magnitude of 1.5 MV/m. Write vector equations for
and as functions of time and position.
E
E
B
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
Identify and Set Up
Eqs. (32.19) describe a wave traveling in the negative
x-direction with along the y-axis – that is, a wave
that is linearly polarized along the y-axis. By contrast,
the wave in this example is linearly polarized along
the z-axis. At points where is in the positive z-
direction, must be in the positive y-direction for the
vector product to be in the negative x-direction
(the direction of propagation). Fig. 32.12 shows a
wave that satisfies these requirements.
E
E
B
E B
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
Fig. 32.12
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
Execute
A possible pair of wave functions that describe the
wave shown in Fig. 32.12 are
The plus sign in the arguments of the cosine
functions indicates that the wave is propagating in the
negative x-direction, as it should. Faraday’s law
requires that Emax = cBmax [Eq. (32.18)], so
To check unit consistency, note that 1 V = 1 Wb/s and
1 Wb/m2 = 1 T.
max maxˆ ˆ( , ) cos( ) ( , ) cos( )E x t kE kx t B x t jB kx t
63max
max 8
1.5 10 /5.0 10
3.0 10 /
E V mB T
c m s
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
We have = 10.6 x 10-6 m, so the wave number and
angular frequency are
Substituting these values into the above wave
functions, we get
6 5
8 5
14
2 / (2 ) /(10.6 10 ) 5.93 10 /
(3.00 10 / )(5.93 10 / )
1.78 10 /
k rad m rad m
ck m s rad m
rad s
6 14
5
3 14
5
ˆ( , ) (1.5 10 / )cos[(1.78 10 / )
(5.93 10 / ) ]
ˆ( , ) (5.0 10 )cos[(1.78 10 / )
(5.93 10 / ) ]
E x t k V m rad s t
rad m x
B x t j T rad s t
rad m x
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
With these equations we can find the fields in the
laser beam at any particular position and time by
substituting specific values of x and t.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
Evaluate
As we expect, the magnitude Bmax in teslas is much
smaller than the magnitude Emax in volts per meter.
To check the directions of and , note that
is in the direction of . This is as it should be for
a wave that propagates in the negative x-direction.
E B E Bˆ ˆ ˆk j i
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.1 (SOLN)
Evaluate
Our expressions for and are not the
only possible solutions. We could always add a phase
to the arguments of the cosine function, so that kx +
t would become kx + t + . To determine the value
of we would need to know and either as
functions of x at a given time t or as functions of t at a
given coordinate x. However, the statement of the
problem doesn’t include this information.
( , )E x t ( , )B x t
E B
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
32.3 Sinusoidal Electromagnetic Waves
• Other than traveling in a vacuum, electromagnetic
waves can also travel in matter, including
nonconducting materials such as dielectrics.
• The wave speed in a dielectric is given by:
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.2 Electromagnetic waves in different materials
a) While visiting a jewelry store one evening, you hold
a diamond up to the light of a street lamp. The heated
sodium vapor in the street lamp emits yellow light with
a frequency of 5.09 x 1014 Hz. Find the wavelength in
vacuum, the speed of wave propagation in diamond,
and the wavelength in diamond. At this frequency,
diamond has properties K = 5.84 and Km = 1.00.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.2 Electromagnetic waves in different materials
b) A radio wave with a frequency of 90.0 MHz (in the
FM radio broadcast band) passes from vacuum into
an insulating ferrite (a ferromagnetic material used in
computer cables to suppress radio interference). Find
the wavelength in vacuum, the speed of wave
propagation in the ferrite, and the wavelength in the
ferrite. At this frequency, the ferrite has properties K =
10.0 and Km = 1000.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.2 (SOLN)
Identify and Set Up
In each case we find the wavelength in vacuum using
c = f. The wave speed v is given in terms of c, the
dielectric constant K, and the relative permeability Km
by Eq. (32.21). Once we know the value of v, we use
v = f to find the wavelength in the material in the
question.
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.2 (SOLN)
Execute
a) The wavelength in vacuum of the sodium light is
The wave speed in diamond is
This is about two-fifths of the speed in vacuum. The
wavelength is proportional to the wave speed and so
is reduced by the same factor:
87
14
3.00 10 /5.89 10 589
5.09 10vacuum
c m sm nm
f Hz
883.00 10 /
1.24 10 /(5.84)(1.00)
diamondm
c m sv m s
KK
8
14
7
1.24 10 /
5.09 10
2.44 10 244
diamonddiamond
v m s
f Hz
m nm
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.2 (SOLN)
Execute
b) Following the same steps as in part (a), we find
that the wavelength in vacuum of the radio wave is
The wave speed in the ferrite is
This is only 1% of the speed of light in a vacuum, so
the wavelength is likewise 1% as large as the
wavelength in vacuum:
8
6
3.00 10 /3.33
90.0 10vacuum
c m sm
f Hz
863.00 10 /
3.00 10 /(10.0)(1000)
ferritem
c m sv m s
KK
92
6
3.00 10 /3.33 10 3.33
90.0 10
ferriteferrite
v m sm cm
f Hz
32. Electromagnetic Waves
2005 Pearson Education South Asia Pte Ltd
Example 32.2 (SOLN)
Evaluate
The speed of light in transparent materials like
diamond is typically between c and several percent of
c. As our results in part (b) show, the speed of
electromagnetic waves in dense materials like ferrite
can be far slower than in vacuum.