Download What are electromagnetic waves?

Physics 201
Professor P. Q. Hung
311B, Physics Building
Physics 201 – p. 1/3
What are electromagnetic waves?
Electromagnetic waves consist of electric
fields and magnetic fields which are mutually
perpendicular and also perpendicular to the
direction of propagation ⇒ Electromagnetic
waves are transverse waves.
Physics 201 – p. 2/3
What are electromagnetic waves?
Electromagnetic waves consist of electric
fields and magnetic fields which are mutually
perpendicular and also perpendicular to the
direction of propagation ⇒ Electromagnetic
waves are transverse waves.
Electromagnetic waves can travel in vacuum
or in a material.
Physics 201 – p. 2/3
What are electromagnetic waves?
Electromagnetic waves consist of electric
fields and magnetic fields which are mutually
perpendicular and also perpendicular to the
direction of propagation ⇒ Electromagnetic
waves are transverse waves.
Electromagnetic waves can travel in vacuum
or in a material.
The speed of electromagnetic waves in
vacuum is the speed of light in vacuum:
c = 3.00 × 108 m/s.
Physics 201 – p. 2/3
What are electromagnetic waves?
Electromagnetic waves can be created by
oscillating charges ⇒ Frequency of
electromagnetic waves = frequency of charge
oscillation. For example, oscillating electrons
in an antenna. More on this below.
Physics 201 – p. 3/3
What are electromagnetic waves?
Physics 201 – p. 4/3
What are electromagnetic waves?
Physics 201 – p. 5/3
What are electromagnetic waves?
Physics 201 – p. 6/3
What are electromagnetic waves?
Physics 201 – p. 7/3
Maxwell’s contribution
Recall Faraday’s law of induction: changing
magnetic flux ⇒ electric field that changes
with time
Can a magnetic field be created by a
changing electric flux?
Physics 201 – p. 8/3
Maxwell’s contribution
Recall Faraday’s law of induction: changing
magnetic flux ⇒ electric field that changes
with time
Can a magnetic field be created by a
changing electric flux?
Maxwell: Ampere’s law is good only for a
continuous current. What happens between
the two plates of a capacitor? If one were to
measure the magnetic field around the gap,
one would find out that the magnetic field is
non-zero! But where is the current between
the gap?
Physics 201 – p. 8/3
Maxwell’s contribution
Gauss’ law: EA = q/0 ⇒ q = 0 AE ⇒
∆E
I = ∆q
=
A
0 ∆t
∆t
Physics 201 – p. 9/3
Maxwell’s contribution
Gauss’ law: EA = q/0 ⇒ q = 0 AE ⇒
∆E
I = ∆q
=
A
0 ∆t
∆t
There is a uniform electric field between the
plates and assume the surface area of each
plate is A. The electric flux through an area A
is ΦE = EA.
Physics 201 – p. 9/3
Maxwell’s contribution
Maxwell: Imagine a fictitious current which he
called a displacement current:
∆E
E
Id = 0 ∆Φ
=
A
0 ∆t = I.
∆t
Add that displacement current to the
right-hand-side of Ampere’s law ⇒ changing
electric field ⇒ magnetic field that changes
with time.
That’s Maxwell’s contribution ⇒ Maxwell’s
equations. Why is it so important?
Physics 201 – p. 10/3
Maxwell’s contribution
The solution to Maxwell’s equations ⇒
Electromagnetic waves
⇒ Speed of the waves in vacuum:
c = √10 µ0 = 3.00 × 108 m/s
Physics 201 – p. 11/3
Maxwell’s contribution
The solution to Maxwell’s equations ⇒
Electromagnetic waves
⇒ Speed of the waves in vacuum:
c = √10 µ0 = 3.00 × 108 m/s
Light is an electromagnetic wave!
Physics 201 – p. 11/3
What is the electromagnetic spectru
Accelerating charges ⇒ Radiation.
Physics 201 – p. 12/3
What is the electromagnetic spectru
Accelerating charges ⇒ Radiation.
Like any wave, there is a relationship between
the speed of the wave and the frequency and
wavelength. Here v = c in vacuum.
c = fλ
Physics 201 – p. 12/3
What is the electromagnetic spectru
Accelerating charges ⇒ Radiation.
Like any wave, there is a relationship between
the speed of the wave and the frequency and
wavelength. Here v = c in vacuum.
c = fλ
High frequency ⇒ Short wavelength and vice
versa.
Physics 201 – p. 12/3
Spectrum
Radio waves: λ ≈ 104 m − 0.1m. Generated
by electronic devices like an LC oscillator.
Used in radio and television communication
systems. AM radio waves have λ ≈ 104 m
while FM radio waves have λ ≈ f ew m.
Easier to diffract long wave lengths than short
ones ⇒ AM waves can bend around buildings
much more easily than FM waves.
Physics 201 – p. 13/3
Spectrum
Radio waves: λ ≈ 104 m − 0.1m. Generated
by electronic devices like an LC oscillator.
Used in radio and television communication
systems. AM radio waves have λ ≈ 104 m
while FM radio waves have λ ≈ f ew m.
Easier to diffract long wave lengths than short
ones ⇒ AM waves can bend around buildings
much more easily than FM waves.
Microwaves: λ ≈ 0.5m − 10−4 m. Generated
by electronic devices. Short wavelenghts.
Suited for radars, atomic and molecular
studies, etc... Microwave oven: λ = 0.122m.
Physics 201 – p. 13/3
Spectrum
Infrared waves: λ ≈ 10−3 m − 7 × 10−7 m.
Generated by molecules and
room-temperature objects. Readily absorbed
by many materials. Applications: physical
therapy, vibrational spectroscopy, etc.
Physics 201 – p. 14/3
Spectrum
Infrared waves: λ ≈ 10−3 m − 7 × 10−7 m.
Generated by molecules and
room-temperature objects. Readily absorbed
by many materials. Applications: physical
therapy, vibrational spectroscopy, etc.
Visible light: λ = 7 × 10−7 m (red) to
λ ≈ 4 × 10−7 m (violet). Maximum sensitivity of
human eye at λ = 5.5 × 10−7 m (yellow-green)
⇒ Color of tennis balls.
Physics 201 – p. 14/3
Spectrum
Ultraviolet waves:
λ ≈ 4 × 10−7 m − 6 × 10−10 m. Sun: big source
of UV light ⇒ sunburn. Sun screen: the
higher the number the better the blocking of
UV light becomes. Danger of cheap sun
glasses: They do not block UV light and since
the pupils are dilated there is more of UV light
striking the lenses ⇒ potential damage.
Better not having those sun glasses because
at bright sun light, the pupils are contracted
⇒ less UV light striking the lenses.
Most of UV light from the sun is absorbed by
the ozone (O3 ) layer. Very important layer in
Physics 201 – p. 15/3
Spectrum
X-rays: λ ≈ 10−8 m − 10−12 m. Generated by
high-energy electrons bombarding metal
targets. Used in medicine, and studies of
crystal structure.
Physics 201 – p. 16/3
Spectrum
X-rays: λ ≈ 10−8 m − 10−12 m. Generated by
high-energy electrons bombarding metal
targets. Used in medicine, and studies of
crystal structure.
Gamma rays: λ ≈ 10−10 m − 10−14 m. Emitted
by radioactive nuclei such as 60 Co and 137 Cs.
Also by high-energy cosmic rays entering the
Earth’s atmosphere.
Physics 201 – p. 16/3
Spectrum
Physics 201 – p. 17/3
Energy in electromagnetic waves
Energy density carried by the electric field:
uE = 12 0 E 2 .
Physics 201 – p. 18/3
Energy in electromagnetic waves
Energy density carried by the electric field:
uE = 12 0 E 2 .
Energy density carried by the magnetic field:
uB = 2µ1 0 B 2 .
Physics 201 – p. 18/3
Energy in electromagnetic waves
Energy density carried by the electric field:
uE = 12 0 E 2 .
Energy density carried by the magnetic field:
uB = 2µ1 0 B 2 .
In an electromagnetic wave in vacuum or air:
uE = u B .
⇒ Total energy density:
u = uE + uB = 0 E 2 = µ10 B 2
Physics 201 – p. 18/3
Energy in electromagnetic waves
Since c =
E = cB
√1 ,
0 µ0
uE = uB gives
Physics 201 – p. 19/3
Energy in electromagnetic waves
Since c =
E = cB
Also:
Erms =
Brms =
√1 ,
0 µ0
uE = uB gives
E√
max
2
B√
max
2
Physics 201 – p. 19/3
Energy in electromagnetic waves
Physics 201 – p. 20/3
Energy in electromagnetic waves: Ex
Sunlight enters the top of the Earth’s atmosphere
with an electric field whose rms value is 720 N/C.
Find (a) the average total energy density of this
electromagnetic wave and (b) the rms value of
the sunlight’s magnetic field.
Solution:
2
ū = 0 Erms
= (8.85 ×
10−12 C 2 /(N.m2 ))(720 N/C)2 = 4.6 × 10−6 J/m3 .
Physics 201 – p. 21/3
Energy in electromagnetic waves: Ex
Sunlight enters the top of the Earth’s atmosphere
with an electric field whose rms value is 720 N/C.
Find (a) the average total energy density of this
electromagnetic wave and (b) the rms value of
the sunlight’s magnetic field.
Solution:
2
ū = 0 Erms
= (8.85 ×
10−12 C 2 /(N.m2 ))(720 N/C)2 = 4.6 × 10−6 J/m3 .
Brms =
Erms
c
= 2.4 × 10−6 T .
Physics 201 – p. 21/3
Intensity of electromagnetic waves
Intensity = Power/Area.
After a time t, the waves travel a distance ct,
passing through a surface of area A.
Total energy = (Total energy density) x
(Volume) = u(ctA).
Physics 201 – p. 22/3
Intensity of electromagnetic waves
Intensity = Power/Area.
After a time t, the waves travel a distance ct,
passing through a surface of area A.
Total energy = (Total energy density) x
(Volume) = u(ctA).
Intensity: S =
S = uc = c0 E
u(ctA)
U
= tA = tA
= µc0 B 2
P
A
2
= uc.
Physics 201 – p. 22/3
Intensity of electromagnetic waves
A nyodenium-glass laser emits short pulses of
high-intensity electromagnetic waves. The
electric field has an rms value of 2.0 × 109 N/C.
Find the average power of each pulse that
passes through a 1.6 × 10−5 − m2 surface that is
perpendicular to the laser beam.
Solution:
P̄ = AS̄
Physics 201 – p. 23/3
Intensity of electromagnetic waves
A nyodenium-glass laser emits short pulses of
high-intensity electromagnetic waves. The
electric field has an rms value of 2.0 × 109 N/C.
Find the average power of each pulse that
passes through a 1.6 × 10−5 − m2 surface that is
perpendicular to the laser beam.
Solution:
P̄ = AS̄
2
2
S̄ = c0 Erms
⇒ P̄ = Ac0 Erms
= 1.7 × 1011 W .
Physics 201 – p. 23/3
Doppler effects
For a source moving with a speed very much
smaller than the speed of light, the shift in
frequency between source and observer is given
by:
fO = fS (1 ± vrel
c )
fO : frequency observed by the observer.
fS : frequency emitted by the source.
vrel : speed of the source and observer relative to
one another.
+: source approaching the observer
−: source receding from the observer
Applications: radar guns for example.
Important application in astronomy: redshift
Physics 201 – p. 24/3
Polarization
Electromagnetic wave: Transverse wave ⇒
oscillation of a field (e.g. the electric field)
occurs along one direction ⇒ linear
polarization (taken by convention to be the
direction of the electric field).
Physics 201 – p. 25/3
Polarization
Electromagnetic wave: Transverse wave ⇒
oscillation of a field (e.g. the electric field)
occurs along one direction ⇒ linear
polarization (taken by convention to be the
direction of the electric field).
Visible light: The electric field oscillates in a
random direction ⇒ light is unpolarized.
Physics 201 – p. 25/3
Polarization
Electromagnetic wave: Transverse wave ⇒
oscillation of a field (e.g. the electric field)
occurs along one direction ⇒ linear
polarization (taken by convention to be the
direction of the electric field).
Visible light: The electric field oscillates in a
random direction ⇒ light is unpolarized.
How do we get polarized light from an
unpolarized light?
Physics 201 – p. 25/3
Polarization
Polarizer: material such as a Polaroid that
has a transmission axis ⇒ Only the electric
field which is parallel to that axis can pass
through ⇒ polarization.
Physics 201 – p. 26/3
Polarization
Polarizer: material such as a Polaroid that
has a transmission axis ⇒ Only the electric
field which is parallel to that axis can pass
through ⇒ polarization.
Analyzer: the second polarizer with an axis
rotated by θ with respect to the first axis ⇒
reduction in intensity.
Physics 201 – p. 26/3
Polarization
Polarizer: material such as a Polaroid that
has a transmission axis ⇒ Only the electric
field which is parallel to that axis can pass
through ⇒ polarization.
Analyzer: the second polarizer with an axis
rotated by θ with respect to the first axis ⇒
reduction in intensity.
Malus’ law:
S̄ = S̄0 cos2 θ
When θ = 900 , no light passes through.
Explain the IMAX 3D.
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Polarization
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Polarization
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Polarization
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Polarization
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Polarization
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Polarization
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Polarization
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Polarization
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