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Electromagnetic Waves 1
Administrative
◦ Quiz Today
◦ Review Exam Grades
◦ Review Exam
Begin Chapter 23 – Electromagnetic Waves
No 10:30 Office Hours Today. (Sorry)
Next Week … More of the same.
Watch for still another MP Assignment
◦ Will they ever stop??? (No)
Electromagnetic Waves 2
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Electromagnetic Waves
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Electromagnetic Waves
Electromagnetic Waves 5
What do we learn from this?
6
Some of you studied.
Some of you didn’t.
If you didn’t, do.
Or take my Studio Class in the Spring!
Electromagnetic Waves
Electric Fields and Potential
Magnetic Fields
The interactions between E & M
E&M Oscillations (AC Circuits/Resonance)
James Clerk Maxwell related all of this
together is a form called Maxwell’s Equations.
Electromagnetic Waves 7
James Clerk Maxwell
1831 – 1879
Electricity and magnetism
were originally thought to
be unrelated
In 1865, James Clerk
Maxwell provided a
mathematical theory that
showed a close relationship
between all electric and
magnetic phenomena
Electromagnetic theory of
light
Electromagnetic Waves 8
Maxwell Equations
closed surface enclosed charge closed surface no mag. charge
closed loop linked flux closed loop linked current + flux
• Conservation of energy • Conservation of charge
Lorentz force law
Electromagnetic Waves 9
When an E or B field is changing in time, a
wave is created that travels away at a speed c
given by:
1
c 3 108 m / s
0 0
This is the experimental value for the speed
of light. This suggested that Light is an
Electromagnetic Disturbance,
In depth experimental substantiation
followed.
Electromagnetic Waves 10
Can travel through empty space or through
some solid materials.
The electric field and the magnetic field are
found to be orthogonal to each other and
both are orthogonal to the direction of travel
of the wave.
EM waves of this sort are sinusoidal in nature.
◦ Picture a sine wave traveling through space.
Electromagnetic Waves 11
Hertz’s Confirmation of
Maxwell’s Predictions
1857 – 1894
First to generate and
detect electromagnetic
waves in a laboratory
setting
Showed radio waves
could be reflected,
refracted and diffracted
(later)
The unit Hz is named for
him
Electromagnetic Waves 12
An induction coil is
connected to two large
spheres forming a
capacitor
Oscillations are initiated
by short voltage pulses
The oscillating current
(accelerating charges)
generates EM waves
Several meters away
from the transmitter is
the receiver
◦ This consisted of a single
loop of wire connected to
two spheres
When the oscillation frequency of the
transmitter and receiver matched, energy
transfer occurred between them
Hertz hypothesized the energy transfer was in
the form of waves
◦ These are now known to be electromagnetic waves
Hertz confirmed Maxwell’s theory by showing
the waves existed and had all the properties of
light waves (e.g., reflection, refraction,
diffraction)
◦ They had different frequencies and wavelengths which
obeyed the relationship v = f λ for waves
◦ v was very close to 3 x 108 m/s, the known speed of
light
Two rods are connected to an oscillating source, charges
oscillate between the rods (a)
As oscillations continue, the rods become less charged, the field
near the charges decreases and the field produced at t = 0
moves away from the rod (b)
The charges and field reverse (c) – the oscillations continue (d)
Because the oscillating charges in
the rod produce a current, there is
also a magnetic field generated
As the current changes, the
magnetic field spreads out from
the antenna
The magnetic field is
perpendicular to the electric field
A changing magnetic field produces an
electric field
A changing electric field produces a magnetic
field
These fields are in phase
At any point, both fields reach their maximum value
at the same time
Electromagnetic Waves 19
Electromagnetic Waves 20
Was It Magic?
Electromagnetic Waves 21
Electromagnetic Waves 22
• The waves are transverse:
electric to magnetic and both
to the direction of
propagation.
•The ratio of electric to
magnetic magnitude is E=cB.
•The wave(s) travel in vacuum
at c.
•Unlike other mechanical
waves, there is no need for a
medium to propagate.
The old RH-Rule
◦ turn E into B and
you get the
direction of
propagation c.
◦ Rotate c into E and
get B.
◦ Rotate B into c and
get E.
Electromagnetic Waves 26
l
Electromagnetic Waves 27
Electromagnetic Waves 28
Electromagnetic Waves 29
Seeing in the UV, for example, steers insects to
pollen that humans could not see.
Electromagnetic Waves 30
Electromagnetic Waves 31
Electromagnetic Waves 32
Two types of waves
Electromagnetic Waves 33
LikeSound Waves,the equation
for a moving EM wave is :
t x
E E m axSin(2 ) Em axSin(t kx)
T l
t x
B Bm axSin(2 ) Bm axSin(t kx)
T l
2
k
l
Em ax cBm ax
c
l
f
Suggestion – Look again at the
chapter on sound to solidify
this stuff.
Electromagnetic Waves 34
V c t
How much Energy
is in this volume?
Electromagnetic Waves 35
Light carries
Energy
and
Momentum
Electromagnetic Waves 36
&
Electromagnetic Waves 37
Energy 1 1
u 0E
2
B 2
Volume 2 20
From before
E cB
E E
B E 0 0
c 1
0 0
B 2 0 0 E 2
Electromagnetic Waves 38
So.
B 2 0 0 E 2
ng
Substituti into the previous,
1 1
u 0E 2
0 0 E 2
2 20
or
1 1
u 0E 0E2 0E2
2
2 2
Energy stored in the B and B fields are the same!
Electromagnetic Waves 39
• Electric and magnetic fields contain energy,
potential energy stored in the field: uE and uB
uE: ½ 0 E2 electric field energy density
uB: (1/0) B2 magnetic field energy density
•The energy is put into the oscillating fields by
the sources that generate them.
•This energy can then propagate to locations
far away, at the velocity of light.
Energy per unit volume is B
dx
u = uE + uB 1 ( 0 E 2 1 B2 )
2 0 area
E
A
Thus the energy, dU, in a box of
area A and length dx is
1
dU ( 0 E 2 1 B2 ) Adx c propagation
2 0 direction
Let the length dx equal cdt. Then all of this energy leav
the box in time dt. Thus energy flows at the rate
dU 1 1 2
( 0 E
2
B ) Ac
dt 2 0
B
Rate of energy flow:
dx
dU c 1 2
( 0 E
2
B )A
dt 2 0 area
A
E
We define the intensity S, as the
rate of energy flow per unit area:
S c ( E 2 1 B2 ) c propagation
2 0
0 direction
Rearranging by substituting E=cB and B=E/c,
we get,
S c ( cEB 1 EB ) 1 ( c 2 1 )EB EB
2 0 0c 20 0 0 0
B
In general, we find:
dx
S = (1/0) EB area
E
A
S is a vector that points in the
direction of propagation of the
wave and represents the rate of
S
propagation
energy flow per unit area. direction
We call this the “Poynting vector”.
Units of S are Jm-2 s-1, or
Watts/m2.
The Inverse-Square Dependence of S
A point source of light, or any radiation, spreads
out in all directions: Power, P, flowing
through sphere
Source is same for any
radius.
P
S
4r 2
Source
r
Area r 2
1
S 2
r
Intensity of light at a distance r is S= P / 4r2
P 1 2
I Erms
4r 2 0 c
P0 c ( 250W )( 4 107 H / m )( 3108 m / s )
.
Erms
4r 2 4 ( 18m )2
.
Erms 48V / m
Erms 48V / m
B 8m / s
0.16 T
c .
310
• When present in
large flux, photons
can exert
measurable force on
objects.
• Massive photon
flux from excimer
lasers can slow
molecules to a
complete stop in a
phenomenon called
“laser cooling”.
Momentum and energy of a wave
are related by, p = U / c.
Now, Force = d p /dt = (dU/dt)/c
pressure (radiation) = Force / unit area
P = (dU/dt) / (A c) = S / c
Radiation Pressure Prad S
c
Polarization
The direction of polarization of a wave is
the direction of the electric field. Most light
is randomly polarized, which means it
contains a mixture of waves of different
polarizations.
Ey
B Polarization
z direction
x
Polarization
A polarizer lets through light of only
one polarization:
E0 E Transmitted light
q has its E in the
direction of the
polarizer’s
transmission axis.
E = E0 cosq
hence, S = S0 cos2q
- Malus’s Law
At least of this
chapter.
Electromagnetic Waves 50
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