Download From last time… Today: Electromagnetic waves, electricity and

Today: Electromagnetic waves,
electricity and magnetism
From last time…
• Interference of waves
– Constructive interference
– Destructive interference
•
•
•
•
• Doppler effect
– Change in apparent frequency due to motion
of source or observer
– Lorenz force on moving charged particle
– Faraday induction of currents by changing
magnetic field.
• Resonance
– Natural frequency of oscillation
– Object will tend to oscillate at that frequency
– Other frequencies (wavelengths) cancelled by
destructive interference reflections
Fri. Feb 17, 2006
Phy107 Lecture 13
Electromagnetic waves
Electric charge and electric forces
Magnetic forces
Unification of electric and magnetic forces
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Properties of EM Waves
Electromagnetic (EM) waves
• Has all properties of a wave: wavelength, frequency, speed
• At a fixed location,
electric and magnetic fields oscillate in time.
• Electric and magnetic fields in the wave
propagate in empty space at the wave speed.
1865: James Clerk Maxwell
published mathematical theory
relating electricity and magnetism
Predicted electromagnetic waves
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1887: Heinrich Hertz
produced and measured
electromagnetic waves in the
laboratory.
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• Electric and magnetic fields are perpendicular to
propagation direction: a transverse wave.
• Propagation speed c = 3 x 108 m/s (186,000 miles/second!)
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Sizes of EM waves
• Visible light has a typical wavelength of
500 nm = 500 x 10-9 m = 0.5 x 10-6 m
= 0.5 microns (µm)
Types of EM
waves
• A human hair is roughly 50 µm diameter
We are
familiar
with many
different
wavelengths
of EM waves
– 100 wavelengths of visible light fit in human hair
• A typical AM radio wave has a wavelength
of 300 meters!
• It’s vibration frequency is f = c / λ
= 3x108 m/s / 300 m = 1,000,000 cycles/s = 1 MHz
All are the
same
phenomena
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• AM 1310, your badger radio network,
has a vibration frequency of 1310 KHz = 1.31 MHz
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1
Question
Electric and magnetic fields
AM 1310, your badger radio network, has a vibration
frequency of 1310 KHz = 1310 x 103 Hz = 1.31 x 106 Hz
It travels at 3 x 108 m / s.
What is it’s wavelength?
• To understand electric and magnetic fields,
need to take a few steps back.
• Probably familiar with electrostatic shocks
A. 230 meters
B. 2.3 meters
C. 0.0043 meters
D. 4.3 meters
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• But what are electric, magnetic fields?
• This comes from electric charge
• We now know that there are two varieties of
electric charge, positive and negative.
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Pos and neg charges can be
separated
Electrical Charge
• Triboelectric
• Only the negative charge moves around.
These are the electrons.
– Charge is transferred as a result of mechanical
(frictional) action
• The positive charges are protons.
Protons and electrons form a ‘planetary’ atom.
• Conduction –
• Electrons orbit around a nucleus containing the protons.
Compare planets orbiting around a sun.
– charge transfer by contact (spark)
• Atoms are bound together, forming solid materials.
Electrons can be torn from atoms,
transferred to other materials.
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Separating charge
Electrical charge
Rod becomes
positively charged
after rubbing with fur.
• Electrons carry electrical charge, and can be
moved from one material to another.
• The electrons have a negative charge.
• The unit of electric charge is the Coulomb
• One electron carries only a tiny amount of charge
Electrons (negative
charges) have been
transferred from rod
to fur.
Charge on 1 electron = 1.6 x 10-19 Coulomb
• Positively charged rod can then be used to
transfer electrons from other objects.
Transferring 1 Coulomb of charge means that
6,250,000,000,000,000,000 electrons have moved!
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2
Charge by conduction (touching)
+- +
- -+ + - +
+ + + + + + + + + + ++
Positively charged rod
(too few electrons)
+ + + + + + + + + + ++
electron flow
+
+
+ +
Less positively charged rod
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Why did the electrons flow?
Neutral
metal
Phy107 Lecture 13
attractive force between positive and
negative charges.
repulsive force between two positive
or two negative charge
+-+
- -+ + - +
The positively charged rod attracts negative
charges to the top of the electroscope.
This leaves positive charges on the leaves.
+ +
+
+
+
+ + +
Interactions between charges
Positively
charged
metal
Pith ball 13
demo
The like-charges on the leaves repel each
other.
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Phy107 Lecture 13
Force between charges
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Question
+
Opposite charges attract
Force on positive particle
due to negative particle
Like charges repel.
• Other than the polarity, they interact
much like masses interact gravitationally.
• Force is along the line joining the
—
particles.
The force between two electrons is 10-10. The
distance between the electrons is doubled.
The force is now
A.
B.
C.
D.
Electrostatic force: FE = k Q1 Q 2 /r2
k = 9x109 Nm2/C2
Gravitational force: FG=GM1M 2/ r2
0.5 x 10-10 N
0.25 x 10-10 N
1 x 10-10 N
2 x 10-10 N
G=6.7x10-11 Nm2/kg2
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• Electrostatic force between proton and electron
in a hydrogen atom
+
F
16
Electrical machines
Electrostatic force is strong
Qp=1.6x10-19 C
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Qe = -1.6x10-19 C
-
r = 1x10-10 m
FE = (9x109)(1.6x10-19)(1.6x10-19)/(10-10)2 = 2.3x10-8 N
• Can mechanize the
rubbing process to
continually separate
charge.
• This charge can then
be transferred to
other objects.
• Gravitational force between proton and electron
FG = (6.7x10-11)(1.7x10-27)(9.1x10-31)/(10-10) 2 = 2.3x10-28 N
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3
The van de Graf machine
Charge transfer
and forces
+ +
+ +
-
-
+ +
+ +
• Ben Franklin’s ‘door bell’.
• Announced presence of
lightning so knew to go
out and do his
experiments!
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• The van de Graf machine
continually transfers charge
to the ‘dome’ via a moving
belt.
• Charge on the dome can be
transferred to other objects.
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Sparks
Van de Graaf
The sphere gives the girl a large negative
charge. Each strand of hair is trying to:
A. Get away from the charged sphere.
B. Get away from the ground.
C. Get away from the other strands of hair.
• If we separate enough charge, strong attractive/repulsive
forces can tear electrons from air atoms
• Charged particles flow from one electrode to the other
• This flow of charged particles is an electric current.
Like charges attached to the hair strands repel,
causing them to get away from each other.
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Producing EM Waves
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Hertz wave generator
Accelerating electrical current
generates a wave that travels through space.
Lightning / spark produces electromagnetic wave.
Wave consists of oscillating electric and magnetic fields.
But still haven’t said what electric/magnetic fields are
+
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4
Resonators again!
Eventually transatlantic signals!
Capacitor
banks
Induction
coils
Spark gap
• Transmitter
Transmitter
Receiver
The balls and rods formed an
electrically resonant circuit
Resonantly tuned to pick up
the transmitted signal
Spark initiated oscillations at
resonant freuquency ~ 1 MHz
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Gulgielmo Marconi’s transatlantic transmitter
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The idea of electric fields
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Why bother?
• EM wave made up of
oscillating electric and magnetic fields.
• Why invent fields - why not just use forces?
• But what is an electric field?
• Think of the EM wave. A spark is an accelerating
current flow, producing the wave.
• Electric field is a way to describe the force
on a charged particle due to other charges
around it.
• The wave continues to propagate
even when the spark is gone.
• Force = charge × electric field
• No charges anywhere,
but oscillating fields are still present.
• The direction of the force is the direction of
the electric field.
• This is an extension of the basic idea of fields.
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Electric field lines
• Faraday invented the idea of field lines
following the force to
visualize the electric field.
Field lines emanate from
positive charge and terminate
on negative charge.
Local electric field is same
direction as field lines.
Force is parallel or antiparallel
to field lines.
Charged particle will move
along these field lines.
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