Transcript PPT - LSU Physics & Astronomy

Physics 2113
Jonathan Dowling
Heinrich Hertz
(1857–1894)
Lecture 38: FRI 24 APR
Ch.33 Electromagnetic Waves
Maxwell Equations in Empty
Space:
E
·
dA
=
0
ò
Fields without
sources?
S
B
·
dA
=
0
ò
S
d
B
·
ds
=
m
e
E
·
dA
0
0
òC
ò
dt S
d
E
·
ds
=
B
·
dA
Changing E gives B.
òC
ò
dt S
Changing B gives E.
Maxwell, Waves, and Light
A solution to the Maxwell equations in empty space is
a “traveling wave”…
d
òC B · ds =m0e 0 dt òS E · dA
d
òC E · ds = - dt òS B · dA
electric and magnetic fields can travel in EMPTY SPACE!
d2E
d2E
= - m0e 0 2 Þ E = E0 sin k(x - ct)
2
dx
dt
c=
1
m0 e 0
= 3 ´ 10 8 m/s
The electric-magnetic waves
travel at the speed of light?
Light itself is a wave of
electricity and magnetism!
Electromagnetic waves
First person to prove that electromagnetic waves existed:
Heinrich Hertz (1875-1894)
First person to use electromagnetic waves for communications:
Guglielmo Marconi (1874-1937), 1909 Nobel Prize
(first transatlantic
commercial wireless
service, Nova Scotia,
1909)
Electromagnetic Waves
A solution to Maxwell’s equations in free space:
E = Em sin(k x - w t )
w
B = Bm sin(k x - w t )
k
= c, speed of propagation.
Em
c=
=
Bm
1
m0 e 0
m
=299,462,954 = 187,163 miles/sec
s
Visible light, infrared, ultraviolet,
radio waves, X rays, Gamma
rays are all electromagnetic waves.
E = Em sin(kx - w t)
B = Bm sin(kx - w t)
33.3: The Traveling Wave, Qualitatively:
Figure 33-4 shows how the electric field and the magnetic field
change with time as one wavelength of the wave sweeps past the
distant point P in the last figure; in each part of Fig. 33-4, the
wave is traveling directly out of the page.
At a distant point, such as P, the curvature of the waves is small
enough to neglect it. At such points, the wave is said to be a
plane wave.
Here are some key features regardless of how the waves are
generated:
1. The electric and magnetic fields and are always
perpendicular to the direction in which the wave is traveling.
The wave is a transverse wave.
2. The electric field is always perpendicular to the magnetic
field.
3. The cross product always gives the direction in which the
wave travels.
4. The fields always vary sinusoidally. The fields vary with the
same frequency and are in phase with each other.
Radio waves are reflected by the layer of the Earth’s
atmosphere called the ionosphere.
This allows for transmission between two points which are
far from each other on the globe, despite the curvature of the
earth.
Marconi’s experiment discovered the ionosphere! Experts
thought he was crazy and this would never work.
Electromagnetic Waves:
One Velocity, Many Wavelengths!
with frequencies measured in “Hertz” (cycles per second)
and wavelength in meters.
http://imagers.gsfc.nasa.gov/ems/
http://www.astro.uiuc.edu/~kaler/sow/spectra.html
33.2: Maxwell’s Rainbow: Visible Spectrum:
Maxwell’s Rainbow
The wavelength/frequency range in which electromagnetic (EM) waves (light)
are visible is only a tiny fraction of the entire electromagnetic spectrum.
Fig. 33-2
Fig. 33-1
(33-2)
The Traveling Electromagnetic (EM) Wave, Qualitatively
An LC oscillator causes currents to flow sinusoidally, which in turn produces
oscillating electric and magnetic fields, which then propagate through space as
EM waves.
Next slide
Fig. 33-3
Oscillation Frequency:
w=
1
LC
Em
c=
=
Bm
1
m0 e 0
(33-3)
33.3: The Traveling Wave, Quantitatively:
The dashed rectangle of dimensions dx and
h in Fig. 33-6 is fixed at point P on the x axis
and in the xy plane.
As the electromagnetic wave moves
rightward past the rectangle, the magnetic
flux B through the rectangle changes and—
according to Faraday’s law of induction—
induced electric fields appear throughout
the region of the rectangle. We take E and E
+ dE to be the induced fields along the two
long sides of the rectangle. These induced
electric fields are, in fact, the electrical
component of the electromagnetic wave.
33.4: The Traveling Wave, Quantitatively:
Fig. 33-7 The sinusoidal variation of the
electric field through this rectangle,
located (but not shown) at point P in Fig.
33-5b, E induces magnetic fields along
the rectangle.The instant shown is that
of Fig. 33-6: is decreasing in magnitude,
and the magnitude of the induced
magnetic field is greater on the right
side of the rectangle than on the left.
33.4: The Traveling Wave, Quantitatively:
d 2E
d æ dB ö
d æ dB ö
dæ
dE ö
d2E
= - ç ÷ = - ç ÷ = - ç - m0e 0
÷ = + m0e 0 2
dx 2
dx è dt ø
dt è dx ø
dt è
dt ø
dt
d 2E 1 d 2E
=
wave eq. with velocity c=1 m0e 0
dx 2 c 2 dt 2
Solution:
E = Emax sin(kx - w t)
B = Bmax sin(kx - w t)
c=
w
k
1
m0 e 0
= 3 ´ 10 8 m/s
= c, speed of propagation.
33.3: The Traveling Wave, Qualitatively:
We can write the electric and magnetic fields as sinusoidal functions of position x
(along the path of the wave) and time t :
Here Em and Bm are the amplitudes of the fields and, w and k are the angular
frequency and angular wave number of the wave, respectively.
The speed of the wave (in vacuum) is given by c.
Its value is about 3.0 x108 m/s.
Mathematical Description of Traveling EM Waves
Electric Field:
Magnetic Field:
E = Em sin (kx - w t )
B = Bm sin (kx - w t )
Wave Speed:
c=
m0e 0
All EM waves travel a c in vacuum
Wavenumber: k =
EM Wave Simulation
1
w
=
c
2p
l
2p
Angular frequency: w =
T
Vacuum Permittivity: e 0
Vacuum Permeability:
Fig. 33-5
Amplitude Ratio:
Em
=c
Bm
Magnitude Ratio:
E (t )
=c
B (t )
m0
(33-5)
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