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Lectures 20,21 (Ch. 32) Electromagnetic waves

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Lectures 20,21 (Ch. 32) Electromagnetic waves Maxwell s equations Wave equation General properties of the waves Sinusoidal waves Travelling and standing waves – PowerPoint PPT presentation

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Title: Lectures 20,21 (Ch. 32) Electromagnetic waves


1
Lectures 20,21 (Ch. 32) Electromagnetic waves
  1. Maxwells equations
  2. Wave equation
  3. General properties of the waves
  4. Sinusoidal waves
  5. Travelling and standing waves
  6. Energy characteristics the Pointing vector,
    intensity, power, energy
  7. Generation, transmission and receiving of
    electromagnetic waves

2
Maxwells equations
Two Gausss laws Faradays law Ampers law
James Clerk Maxwell (1831 1879)
Maxwell introduced displacement current, wrote
these four equations together, predicted the
electromagnetic waves propagating in vacuum with
velocity of light and shown that light itself is
e.m. wave. 1865 Maxwells theory of
electro-magnetism 1887 Hertzs experiment 1890
Marconi radio (wireless communication)
3
Mechanical waves
Transverse waves oscillation is in the
direction perpendicular to the propagation
direction (waves on the rope, on the surface of
water) Longitudinal waves oscillation in the
direction of the propagation (sound, spring) E.M.
waves are transverse waves In mechanical waves
there is collective oscillations of particles. E
and B oscillate in e.m. waves. Matter is not
required. E.M waves may propagate in vacuum.
4
Wave equation and major characteristics of the
wave
5
Maxwells equations in the absence of charges and
currents take particular symmetric form
Look for solution in the form
To satisfy Gausss laws it is necessary to have
If there is a component of E or B parallel to v
Gausss laws are not satisfied . It may be
verified choosing the front of the Gaussian
surface ahead of the wave front.
6
Faradays law
Ampers law
7
Derivation of the wave equation Look for plane
waves Ey(x,t) and Bz(x,t)
Faradays law
Ampers law
8
E and B in e.m. wave
This is y-polarized wave. The direction of E
oscillations determines polarization of the
wave. Do not confuse polarization of the wave
with polarization of dielectric (i.e.separation
of charges in E).
9
The frequency range (spectrum) of e/m. waves
Radio waves, microwaves, IR radiation, light, UV
radiation, x-rays and gamma-rays are e/m waves of
different frequencies. All of them propagate in
vacuum with vc3x108m/s
Frequency of e.m.wave does not depend on the
medium where it propagates. It is determined by
the frequency of charge oscillations. Both the
speed of propagation and the wavelength do depend
on the medium vc/n,
10
  • Example. A carbon-dioxide laser emits a
    sinusoidal e.m. wave that travels in vacuum in
    the negative x direction. The wavelength is
    10.6µm and the wave is z-polarized. Maximum
    magnitude of E is 1.5MW/m. Write vector equations
    for E and B as functions of time and position.
    Plot the wave in a figure.

NB1 Since BE/c?B (in T) ltltE (in V/m)
NB2 in general, arbitrary initial phase may be
added
To find initial phase one needs to know either
initial conditions E(x,t0) or boundary condition
E(t,x0).
11
  • Example. NdYAG laser emits IR radiation in
    vacuum at the wavelength 1.062µm.
  • The pulse duration is 30ps(picos). How many
    oscillations of E does the pulse contain?

The shortest pulses (100 as (attos),1as10-18s)
obtained today consist of less then 1 period of E
oscillations.They allow to visualize the motion
of e in atoms and molecules.
12
Ends of string are fixed?nodes on the ends
Max possible wavelength is determined by the
length of string
13
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14
Reflection from a perfect conductor. Standing
waves
Total E is the superposition of the incoming and
reflected waves. On the surface of the conductor
E total parallel to the surface should be zero.
Perfect conductor is a perfect reflector with E
in ref. wave oscillating in opposite phase.
E(x)0 at arbitrary moment of time in the
positions where sinkx0, that is kxpn,
n0,1,2,3,..
15
If two conductors are placed parallel to each
other the nodes of E should be on the ends just
as on the string with fixed ends
Example.In a microwave oven a wavelength 12.2cm
(strongly absorbed by a water) is used. What is
the minimum size of the oven? What are the other
options? Why in the other options rotation is
required?
16
The Energy Characteristics of e.m. waves
The energy density
The Poynting vector is the energy transferred
per unite time per unite cross-section, i.e.
power per unite areathe energy flow rate in the
direction of propagation
Intensity is the power per unite area averaged
over the period of oscillations For travelling
waves
17
Standing waves do not transfer the energy
Example. The distance from the sun to the earth
is 1.5x1011m.1) What is the power of radiation of
the sun if its intensity measured by the earth
orbiting satellite is 1.4 kW/m. 2) If the area of
the panels of the satellite is 4m and is
perpendicular to the radiation of the sun, what
is the power received by satellite?
NB the life on the earth is due to this power of
radiation received from the sun!
18
Example
  • A radio station on the surface of the
    earth radiates a sinusoidal wave with an average
    total power 50kW. Assuming that transmitter
    radiates equally in all directions, find the
    amplitudes of E and B detected by a satellite at
    a distance 100km.

19
E.m. waves are produced by oscillating charge or
current
20
v
Richard Feynman ( 1918  1988)
21
Optimal position of antenna (maximizing the
induced current in antenna) corresponds to the
wire parallel to E
Optimal size of antenna?/2
Optimal position of antenna (maximizing the
induced current in antenna) corresponds to the
loop perpendicular to B.
22
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25
Radiation Pressure
EMW carry both energy and momentum
Absorbing plane
Example. Find the force due to a radiation
pressure on the solar panels. I1.4kW/m2,A1m2.
Reflecting plane
However over long time it influences the
satellite orbit! Comet tails, some stars formation
26
r
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28
Laser cooling Nobel Prize,1997
Steven Chu,Claude Cohen Tannoudji,Bill Phillips
atom
Photon
atom
Photon
atom
Photon
atom
Photon
Photons
29
Polarization
Dichroism (dependence of absorption on
polarization) is used for construction of the
polarization filters for em waves A grid of wires
is a polarization flter for radio waves
When E in a radio wave is parallel to the
wires the currents are induced in the wires and
wave is absorbed. Long molecules play a role of
wires for light and used for building of
polarization filters (polaroids)
Linear polarized, namely, y-plz e.m.wave
Axis of the filter. If em wave is polarized along
this axis it goes through without asborption.
Linear plz em wave with orthoginal to this axis
in not transmitted (fully absorbed by the filter).
30
Maluss law (1809)
In general case when linear plz wave goes through
the filter only its projection on the axis of the
filter goes through.
Eout
Ein
Unpolarized em wave (random polarization)
NB After the filter em wave is always linear
polarized along the axis of the filter.
Sun, lamp and other thermal sources produce
unpolarized light
31
How to check polaroid glasses?
Crossed polaroids do not transmit light
32
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33
Circular polarization
y
Ey
Ez
Ey
x
z
Ez
Left circular polarization If elliptic
polarization
34
Birefrigent materials refractive index depends
on polarization
x
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