Download Electromagnetic Waves

Electromagnetic Waves
Unit 9
Where we are…
• We will finish the 3rd quarter with a general study
of electromagnetic waves.
• When we return from break, we will begin our
study of optics.
• There will be a daily exercise quiz on Friday.
• There will be a unit quest next Friday.
• Your essay rough drafts are due next Friday.
Maxwell’s Equations
• When James Clerk Maxwell
began his work in the 1860’s,
there was some evidence of a
relationship between
electricity and magnetism.
• For example, it was known that
electric currents produce
magnetic fields.
• However, the two were
considered to be separate
subjects.
Maxwell’s Equations
• Maxwell showed that all the phenomena of
electricity and magnetism can be described
using only 4(!) equations.
• These equations are fundamental laws of
nature like Newton’s laws of motion.
• They are actually more fundamental since
they are also consistent with Relativity.
Maxwell’s Equations
1. Gauss’s Law: Electric field lines start on
positive charges and end on negative
charges. The strength of the field depends
on the amount of charge within a closed
region of space.
2. Gauss’s Law for Magnetism: Magnetic field
lines neither begin nor end. They form
closed loops.
Maxwell’s Equations
3. Faraday’s Law: A changing magnetic field
generates an electric field.
4. Ampere’s Law with Maxwell’s Correction:
Magnetic fields are generated by electric
currents or by a changing electric field.
• Equation 4 contains Maxwell’s great insight: a
changing electric field produces a magnetic
field.
Maxwell’s Equations
r
Ñ×E =
e0
Ñ×B = 0
¶B
Ñ´E =¶t
¶E
Ñ ´ B = m 0 I + m 0e 0
¶t
Electromagnetic Waves
• Let’s examine Maxwell’s insight more closely.
• According to Maxwell, a magnetic field will be
produced in empty space if there is a changing
electric field.
• But, the strength of the B field varies with the
E field. So, the B field is also changing.
Electromagnetic Waves
• But changing B fields generate E fields (Faraday’s
Law).
• So the B field produces its own E field, which is
also changing in time.
• As a result, the original changing E field produces
a wave of changing E and B fields that travel
through space.
• These are electromagnetic waves.
Electromagnetic Waves
• Consider the following system
for generating EM waves.
• Two pieces of metal are
connected to opposite ends of
a battery.
• The switch is initially open.
Electromagnetic Waves
• When the switch is closed, the
the battery creates a potential
difference.
• The top rod becomes positively
charged and the bottom rod
becomes negatively charged.
• While this rearrangement is
occurring, there is a current
flowing in the direction
indicated.
Electromagnetic Waves
• As a result of the current, a
magnetic field is generated
near the rods.
• These magnetic fields vanish
quickly near the source.
• However, they generate E
fields further away, which
generate more B fields.
Electromagnetic Waves
• The result is a wave pulse that
travels away from the source.
• There is also a static E field
due to the charge
arrangement.
• This is unrelated to the wave
propagation.
Electromagnetic Waves
• Now let’s consider what
happens if we connect the rods
to an AC source.
• In this case, the direction of the
current is continually changing
direction.
Electromagnetic Waves
• When the current is running up,
the E and B fields are a shown.
• When the current switches to
pointing down, opposite fields
are generated.
• However, the old fields do not
disappear.
Electromagnetic Waves
• Instead, the E field lines fold
back on themselves to form
closed loops.
• This region of E and B fields no
longer depends on the antenna
and continues to travel out into
space.
Electromagnetic Waves
• The E and B fields near the
antenna are referred to as the
near field.
• These fields are complicated
and we will not be concerned
with them.
• The fields far away from the
antenna are called the
radiation field.
Characteristics of EM Waves
• EM waves have several important
characteristics.
• EM waves are spherical. They propagate out
in all directions.
Characteristics of EM Waves
• As with all spherical waves, the field lines
become very flat far from the source.
• At this point, the wave is referred to as a plane
wave.
Characteristics of EM Waves
• Second, notice that at every point the electric
and magnetic fields are perpendicular to each
other and to the direction the wave is
traveling.
Characteristics of EM Waves
• Based on these facts, we can see that the fields
vary from a maximum in one direction, to zero, to
a maximum in the other direction.
• The E and B fields are also in phase. The reach
their maximums at the same time and are zero at
the same time.
Characteristics of EM Waves
• If the source voltage changes sinusoidally,
then so will the E and B fields.
• Animation!
Characteristics of EM Waves
• Based on this, it is easy to see that EM waves
are transverse waves.
• Note that they are oscillations in the E and B
fields, not matter.
Characteristics of EM Waves
• We have also seen that waves are created by
electric charges that are oscillating.
• In order to oscillate, these charges must be
accelerating.
Characteristics of EM Waves
• This leads us to an important conclusion:
Accelerating electric charges give
rise to electromagnetic waves.
Speed of EM Waves
• Maxwell was also able to calculate the speed
an electromagnetic wave travels at:
E
v=c=
B
Speed of EM Waves
• He was also able to show that the speed could
be calculated using physical constants.
c=
1
e0m0
Speed of EM Waves
• If we plug in for these values, we get the speed is
c = 299, 792, 458 » 3.00 ´10
m
s
• This turns out to be exactly equal to the
measured speed of light.
8 m
s
Questions
• If light travels at the same speed as EM waves,
what does that imply about the nature of
light?
• The speed of light does not specify what it is
measured relative to. Why is this
problematic?
Homework
• Read sections 22-1 and 22-2.
• Work on your paper.
Light and the
Electromagnetic Spectrum
The EM Spectrum
• Maxwell’s equations produced two startling
results:
– The existence of electromagnetic waves
– Electromagnetic waves travel at the speed of light
• Light had been known to have wave properties.
• However, it was not known what was oscillating
in a light wave.
• Maxwell argued that light must be an EM wave.
The EM Spectrum
• Since EM waves (including light) are wave
phenomena, they have both a frequency and
a wavelength.
• As with previous wave phenomena we have
studied, the frequency and wavelength are
related to the speed of the wave by
c=lf
Light
• The wavelengths of light were measured long
before light was thought to be an EM wave.
• The wavelengths range from 4.0 x 10-7 m and 7.5
x 10-7 m.
• Because these wavelengths are so small, they are
usually reported in nanometers (nm).
• Using these units, the wavelengths of light range
from 400 nm to 750 nm.
The EM Spectrum
• But light is only one kind of EM wave.
• There are many other possible frequencies.
• This range of waves is known as the
electromagnetic spectrum.
The EM Spectrum
• The first electromagnetic waves generated in the
lab had a frequency of roughly 109 Hz.
• Today, we refer to these as radio waves.
• Radio waves are the lowest frequency EM waves.
The EM Spectrum
• Microwaves are EM waves of higher frequency.
• Above microwaves are infrared (IR) light.
• IR waves from the sun is primarily responsible for
the sun’s warming effect.
The EM Spectrum
• Above the violet end of the visible spectrum is
the ultraviolet (UV) range.
• UV light from the sun can cause skin damage
with prolonged exposure.
The EM Spectrum
• Above the UV range are X-rays.
• X-rays are generally produced with electrons
strike a metal target and are rapidly decelerated.
• X-rays have a very high frequency and can be very
damaging to human tissue.
The EM Spectrum
• The highest frequency waves are known as
Gamma rays.
• Gamma rays are produced through natural
processes, or through the collision of fastmoving atoms in a particle accelerator.
Example: Wavelengths of EM Waves
Calculate the wavelength of
a) a 60 Hz EM wave.
b) a 91.5 Hz FM radio wave.
c) a beam of 4.74 x 1014 Hz red light from a
laser pointer.
d) a dental X-ray with a frequency of
5 x 1018 Hz.
Homework
• Read section 22-3.
• Do problems 5, 7, 9, and 10 on pages 629-630.
Measuring the Speed of Light
Galileo
• Galileo was the first to attempt a
measurement of c.
• He tried to measure the time it
took light to travel between two
hilltops.
• If he knew the spacing of the
hills and could measure the
time, he could figure out c.
Galileo
• In the experiment, Galileo stood
on the top of one hill with a
covered lamp.
• His assistant stood on the top of
the other hill with a lamp that
was also covered.
Galileo
• Galileo would open the cover on
his lamp, causing the light to travel
toward his assistant.
• Once the assistant saw the light
from Galileo’s lamp, he would
open the cover on his lamp.
• Galileo would then measure the
time between the moment he
opened the first lamp and the
instant he saw the light from his
assistant’s lamp.
Galileo
• Although Galileo’s method was
sound, light travels so fast that the
time Galileo measured was
extremely short.
• It was so short that it could not be
distinguished from human reaction
time.
• Galileo could only conclude that
the speed of light was very high.
Michelson
• One of the first scientists to successfully
measure c was Albert Michelson.
• From 1880 to the early 1920s, he conducted a
series of high-precision experiments to
measure the speed of light.
Michelson
• In the experiment, light from a source was
directed at an eight-sided rotating mirror.
• The mirror reflected the light to a stationary
mirror a large distance away.
Michelson
• The stationary mirror reflected the light back
to the rotating mirror.
• The light would then be reflected depending
on what point the mirror was at in its rotation.
Michelson
• If the mirror was rotating too slowly or too
quickly, the light would be deflected to the right
or the left of the observer.
• However, if the mirror is rotating at just the right
speed, the light will be reflected at the observer.
Michelson
• By knowing the distances of the setup and
measuring the speed of the rotating mirror,
Michelson was able to determine the speed of
light.
Practice
• Review sections 22-4 and 22-7.
• Do problems 12, 13, 16, 17, and 27 on page
630.