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Chapter 34
Electromagnetic Waves
Electromagnetic Waves
•Mechanical waves require the presence of a medium.
•Electromagnetic waves can propagate through empty space.
•Maxwell’s equations form the theoretical basis of all
electromagnetic waves that propagate through space at the
speed of light.
•Hertz confirmed Maxwell’s prediction when he generated
and detected electromagnetic waves in 1887.
•Electromagnetic waves are generated by oscillating electric
charges.
– The waves radiated from the oscillating charges can be
detected at great distances.
•Electromagnetic waves carry energy and momentum.
•Electromagnetic waves cover many frequencies.
James Clerk Maxwell
•1831 – 1879
•Scottish theoretical physicist
•Developed the electromagnetic
theory of light
•His successful interpretation of the
electromagnetic field resulted in
the field equations that bear his
name.
•Also developed and explained
– Kinetic theory of gases
– Nature of Saturn’s rings
– Color vision
Maxwell’s Equations
Correcting Ampere’s Law
Two surfaces S1 and S2 near the
plate of a capacitor are bounded by
the same path P. Ampere’s Law
states that
But it is zero on S2 since there is no
conduction current through it. This
is a contradiction. Maxwell fixed it
by introducing the displacement
current:
Fig. 34-1, p. 984
Maxwell hypothesized that a changing electric field
creates an induced magnetic field.
Displacement Current
d  E d( EA) d(q / ε0 ) 1 dq



dt
dt
dt
ε0 dt
dq
dE
 ε0
dt
dt
The displacement current is equal to the conduction current!!!
 B  ds  μ
o
I  μoεoId
Maxwell’s Equations
In his unified theory of electromagnetism,
Maxwell showed that electromagnetic waves
are a natural consequence of the fundamental
laws expressed in these four equations:
q
 E  dA  εo
d B
 E  ds   dt
 B  dA  0
d E
 B  ds  μo I  μoεo dt
Maxwell’s Equations in Vector Form
Maxwell’s Equations in Free
Space
No charges or conduction currents:
 E  dA  0
 B  dA  0
dB
 E  ds   dt
dE
 B  ds  μoεo dt
E  0
B
E  
t
Divergence:
Curl:
E
B

x
t
B  0
E
  B  μ0ε0
t
dB
 E  ds   dt
dE
 B  ds  μoεo dt
Fig. 34-6, p. 989
A sinusoidal electromagnetic wave
moves in the positive x direction with
a speed c.
Fig. 34-8, p. 990
EM Wave Equations
From Maxwell’s equations applied to empty
space, the following partial derivatives can be
found: 2
E
 2E
 2B
 2B
 μoεo 2 and
 μoεo 2
2
2
x
t
x
t
These are wave equations with
v c 
Substituting the values for μo and εo gives
c = 2.99792 x 108 m/s
1
μoεo
E & B Waves
•The simplest solution to the partial
differential equations is a sinusoidal wave:
E = Emax cos (kx – ωt)
B = Bmax cos (kx – ωt)
•The angular wave number is k = 2π/λ
– λ is the wavelength
•The angular frequency is ω = 2πƒ
– ƒ is the wave frequency
ω 2π ƒ

 λƒ  c
k 2π λ
E & B Waves
E(x,t) = Emax cos (kx – ωt)
B(x,t) = Bmax cos (kx – ωt)
Emax
ω
c 
Bmax
k
Properties of Electromagnetic
Waves
The energy flow of an electromagnetic wave is described
by the Poynting vector defined as
The magnitude of the Poynting vector is
The intensity of an electromagnetic wave whose electric
field amplitude is E0 is
Intensity
I  Savg
2
2
E max Bmax E max
c Bmax



2 μo
2 μo c
2 μo
•The wave intensity, I, is the time average of S
(the Poynting vector) over one or more cycles.
– This defines intensity in the same way as
earlier.
– The optics industry calls power per unit area the
irradiance.
• Radiant intensity is defined as the power in watts
per solid angle.
•When the average is taken, the time average
of cos2(kx - ωt) = ½ is involved.
Section 34.4
Energy Density
•The energy density, u, is the energy per unit
c  1 μoεo
volume.
•For the electric field, uE= ½ εoE2
•For the magnetic field, uB = ½ μoB2
•Since B = E/c and
1
B2
uB  uE 
2
εo E 2 
2μo
The instantaneous energy density associated with the
magnetic field of an em wave equals the
instantaneous energy density associated with the
electric field. In a given volume, the energy is shared
equally by the two fields.
Energy Density
•The total instantaneous energy density is
the sum of the energy densities associated
with each field.
u =uE + uB = εoE2 = B2 / μo
•When this is averaged over one or more
cycles, the total average becomes
– uavg = εo(E2)avg = ½ εoE2max = B2max / 2μo
•In terms of I, I = Savg = cuavg
– The intensity of an em wave equals the average
energy density multiplied by the speed of light.
Radiation Pressure
It’s interesting to consider the force of an electromagnetic
wave exerted on an object per unit area, which is called the
radiation pressure prad. The radiation pressure on an object
that absorbs all the light is
I  Savg
where I is the intensity of the light wave.
For a perfectly reflecting surface, p = 2I/c=2S/c
Accelerating Charges
All forms of the various types of
radiation are produced by the same
phenomenon – accelerating
charges.
The EM Spectrum
•Note the overlap
between types of
waves
•Visible light is a small
portion of the
spectrum.
•Types are
distinguished by
frequency or
wavelength
Section 34.7
Oscillating Charges
Radio & Microwave
Frequency of EM wave is the same as the frequency of oscillation.
Heinrich Rudolf Hertz
•1857 – 1894
•German physicist
•First to generate and
detect electromagnetic
waves in a laboratory
setting
•The most important
discoveries were in
1887.
•He also showed other
wave aspects of light.
Section 34.2
Hertz’s Experiment
•From a circuit viewpoint, this is
equivalent to an LC circuit.
•Sparks were induced across the gap
of the receiving electrodes when the
frequency of the receiver was
adjusted to match that of the
transmitter.
•In a series of other experiments,
Hertz also showed that the radiation
generated by this equipment
exhibited wave properties.
– Interference, diffraction,
reflection, refraction and
polarization
•He also measured the speed of the
radiation.
– It was close to the known
value of the speed of light.
Production of EM Waves by an
Antenna
•This is a half-wave
antenna.
•Two conducting rods are
connected to a source of
alternating voltage.
•The length of each rod is
one-quarter of the
wavelength of the
radiation to be emitted.
Far Fields: Radiation Fields
Fields detach from the dipole and propagate freely.
EM Spectrum
cf
Increasing Energy
IR, Visible and UV Light is emitted
when an electron in an atom jumps
between energy levels either by
excitation or collisions.
Light Emission
Atomic Emission of Light
Each chemical element produces its own
unique set of spectral lines when it burns
Hydrogen Spectra
Visible Light
•Different wavelengths
correspond to different
colors.
•The range is from red
(λ ~ 7 x 10-7 m) to
violet (λ ~4 x 10-7 m).
Section 34.7
Thermal Excitation:
Incandescence
f ~T
Color shifts to shorter wavelengths (higher
frequency) as an object is heated.
increasing temperature
Limits of Thermal Excitation
Material breaks down before Xrays are
produced.
increasing temperature
X-Ray Production
By High Voltage Discharge
Accelerating Charges
Synchrotron Radiation
X-Ray and Radio
How can we SEE Black Holes?
We see the X Rays produced by matter falling into them.
X Ray Imaging
when X-ray light shines on us, it goes through our skin, but allows shadows of our bones to be projected onto and captured
by film.
When X-ray light shines on us, it goes through our skin, but allows
shadows of our bones to be projected onto and captured by film.
Gamma Ray Production
by Nuclear Decay
when X-ray light shines on us, it goes through our skin, but allows shadows of our bones to be projected onto and captured
by film.
239
P
U  He  
235
46
Gamma Ray Production
Matter-antimatter annihilation
Gamma Ray Burst
Ionizing Radiation:
UV, Xray & Gamma
Energy to ionize atom or molecule: 10-1000eV
Ionizing Radiation:
UV, Xray & Gamma
Light can Kill
Biological Effects of Gamma
Radiation
Atomic Thermal Blast
IR, VISIBLE, UV
Cosmic EM Radiation
The Atmosphere
Visible Sun: The Photosphere
Atomic Excitations: 400-700 nm at a few thousand Kelvin.
Radio Image of the Sun
Synchrotron Radiation: 10.7 cm – 2800MHz
Infrared Sun
More than half the Sun’s power is radiated in IR.
UV Sun
X-Ray Sun
Bremsstrahlung Radiation (braking, in German)
Gamma Ray Sun
Bremsstrahlung Radiation (braking, in German)