Transcript Electric Potential

Electromagnetism
Last Time
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Electromagnetic induction: The process by which current is
generated by moving a conductor through a magnetic field
or a magnetic field through a conductor.
Electromotive Force: When a wire moves through a
magnetic field, a force is exerted on these charges causing
them to flow as current.
Magnetic Flux: The strength of a magnetic field is
determined by the amount of magnetic field lines crossing
perpendicular to a surface.
Electric Generators: Convert mechanical power into
electrical power.
Lenz’s Law: The induced EMF resulting from a changing
magnetic flux has a polarity that leads to an induced
current whose direction is such that the induced magnetic
field opposes the original flux change.
Last Time
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Self-Inductance: When a current is induced in a coil, an
EMF will be induced which opposes the increase in current.
Back EMF: The EMF developed to oppose the increasing
current in the windings of a solenoid.
Transformers: Increase or decrease AC voltage very
efficiently with minimal loss of power.
What You Will Learn About
JJ Thompson – Determining the
mass of an electron (CRT)
 How Electric and Magnetic Fields
Interact
 Mass Spectrometer
 Electromagnetic Radiation
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JJ Thompson’s Experiment
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Determine the mass of an electron
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Cannot be done directly – too small
Instead, measure the charge to mass ratio
How did he do it?
JJ Thompson’s Experiment
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If magnetic and electric fields are
oriented at 90o angles to one
another, the deflection of the
electrons can be controlled.
Crossed Fields in the CRT
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How do we make a charged particle go
straight if the magnetic field is going to
make it go in circles?
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Use a velocity selector that incorporates the
use of electric and magnetic fields.
Applications for a velocity selector:
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Cathode ray tubes (TV, Computer monitor)
Mass Spectrometer
Velocity Selector
Crossed Fields
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v
B out of page
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F•E
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F•B
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v
E
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v
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E and B fields are balanced to control the
trajectory of the charged particle.
FB = FE
qvB = qE
v = E/B
Phosphor
Coated
Screen
Determining the Charge to
Mass Ratio
Newton’s Second Law:
F = ma
qvB = mv2/R
q/m = v/BR
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R
• Experiment was repeated for other ions to
calculate their charge to weight ratio, thus
allowing an estimate of the mass of the
particle.
Fc
v
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• Magnetism:
Lorentz Force: FB = qv x B
x
Determining the Charge to
Mass Ratio (cont.)
• Electricity:
–
+
For 2 parallel plates:
 FE = qE
 V = Ed = W/q = ½mv2
q
 v = 2qV
m
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F•E
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E
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Substitute v in the equation for the radius of the circle
traversed by a charged particle in a magnetic field.
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 R = mv = m 2qV = 1 2Vm
qB
qB m
B
q
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q =
m
2V
B2r2
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Mass Spectrometer
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Thompson noticed that he sometimes had more
than one dot on the screen. This was the first
time that isotopes were seen experimentally.
Mass to charge ratio of positively charged ions
can be used to identify molecules in the mass
spectrometer.
Mass Spectrometer – How
does it work?
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Sample is heated into a gaseous state.
Sample is ionized into positive ions by
knocking off electrons with high energy
electrons.
Sample is accelerated between two charged
plates.
Sample proceeds through a velocity selector
using crossed fields.
Sample proceeds into a magnetic field.
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The more massive the ion, the less it will be deflected
in the magnetic field.
Sample passes through a detector where the
signal is amplified and processed by a
computer.
Mass Spectrometer
Mass Spectrometer Applications
-Paleoceanography: Determine relative
abundances of isotopes (they decay at
different rates - geological age)
-Space exploration: Determine what’s on
the moon, Mars, composition of the solar
wind, etc. Check for spacecraft leaks.
-Detect chemical and biol. weapons (nerve
gas, anthrax, etc.).
-Blood doping: steroid and drug use.
Mass Spectrometer
Electromagnetic Waves
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Let’s assume that we have electric fields
without a charged body. Can it happen?
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1860 – Years after Faraday and Oersted made
their discoveries – James Maxwell
hypothesized that electric fields changing in
time would create magnetic fields and viceversa.
Maxwell further predicted that either
accelerating charges (changing current) or
changing magnetic fields would produce
electric and magnetic fields that would move
through space (Electromagnetic Wave).
Electromagnetic Waves (cont.)
Electromagnetic Wave
www.hyperphysics.com
Characteristics of
Electromagnetic Waves
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They are transverse waves.
When the electric field is at a maximum, the magnetic field
is also at a maximum.
Use RHR to determine the direction of B relative E.
Normandale Community College
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The electric and magnetic fields are always perpendicular
to one another.
They are sinusoidal.
EM Radiation travels at the speed of light in a vacuum.
Transmitting Radio Waves
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Produced by alternating the potential back and forth on an
antenna.
AM = Amplitude Modulation where information is
imbedded into the wave by changing its amplitude or
power.
FM = Frequency Modulation where information is
imbedded into the wave by changing its frequency.
Receiving Radio Waves
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Process of receiving a radio signal is reverse that
of transmitting.
The electric field will cause electrons in the
antenna to oscillate back and forth in the
conductor, which in this case is an antenna.
This changing current can be electronically
manipulated to convert it into sound at your
speakers.
Note: Antenna needs to be oriented in the same
direction (parallel) to that producing the wave in
order to optimally receive the signal, i.e. if one is
vertical, then so should the other.
Electromagnetic Spectrum
www.Purdue.edu
Speed of Light
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Speed of Light: c = 3.00 x 108 m/s
c
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1
 o o
The relationship between o and o support James
Maxwell’s hypothesis that electromagnetic radiation is
composed of changing E and B fields.
The relationship between the speed of a wave, its
frequency and its wavelength is determined by:
v = f
Where: f = frequency
 = wavelength
Energy of Electromagnetic
Radiation
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Elect. Energy Density = Elect. Energy/Volume
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Elect. Energy Density = ½oE2
Mag. Energy Density = Mag. Energy/Volume
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Mag. Energy Density = 1
B2
2o
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Total Energy Density = Elect. Energy Density +
Mag. Energy Density
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=1
1
oE2 +
B2
2
2o
Energy of Electromagnetic
Radiation
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Since the electric and magnetic fields contain the
same amount of energy:
 = oE2
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Therefore:
1 2
=
B
o
E2
=
1
o o
E = cB
B2
The Doppler Effect
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What you already know: Sound waves exhibit the Doppler
Effect – source of sound moving in relation to observer.
vrel =
fo’ + fs
2fs
Where:
fo’ = Observed wave frequency
fs = Emitted wave frequency
vrel = relative speed of source
and observer
Note: If the source and observer are moving closer together
then the equation will have a plus sign (blue shifted). If
they are moving apart, then then it will be a minus sign
(red shifted).
Light Polarization
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Light is generally emitted from its source
with the electric field oscillating in various
directions.
Polarizers eliminate the oscillations in all
directions but one.
Polarized light has only half the energy of
the incident beam.
www.mic-d.com
Light Polarization
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Light is generally emitted from its source with
the electric field oscillating in various
directions.
Polarizers eliminate the electric field
oscillations in all directions but one.
Polarized light has only half the energy of the
incident beam.
Note: polarizers can
only work on transverse
waves such as light.
They don’t work on
longitudinal waves such
as sound waves.
www.mic-d.com
Light Polarization in Nature
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Light incident upon the molecules
in the atmosphere will excite
electrons in the atoms to oscillate
in a direction 90o from the incident
beam.
Oscillating electrons act as
antennas that re-emit the light that
is now polarized.
Over 50% of the light that reaches
the surface of the earth is
polarized!
www.mic-d.com
Key Ideas
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Electromagnetic waves consist of electric
and magnetic fields oscillating together.
Electromagnetic waves are transverse
waves.
The electromagnetic spectrum consists of
radio waves (long wavelength) to gamma
waves (short wavelength).
Energy Density: energy of wave is equal
to a sum of both the magnetic field and
electric field intensity.
Key Ideas
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Doppler Effect: When two objects are
moving further apart they are called redshifted while they are considered blueshifted if moving closer together.
Polarization: The process by which the
electric field component of EM radiation is
limited to only one direction.