Electromagnetism

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Electromagnetism
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Last Time

• 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.
• Lenzs 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.

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Last Time

• 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.

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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 Thompsons Experiment

• Determine the mass of an electron
• Cannot be done directly too small
• Instead, measure the charge to mass ratio
• How did he do it?

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JJ Thompsons Experiment

• If magnetic and electric fields are oriented at
  90o angles to one another, the deflection of the
  electrons can be controlled.

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Crossed Fields in the CRT

• How do we make a charged particle go straight if
  the magnetic field is going to make it go in
  circles?
• Use a velocity selector that incorporates the use
  of electric and magnetic fields.
• Applications for a velocity selector
• Cathode ray tubes (TV, Computer monitor)
• Mass Spectrometer
• Velocity Selector

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Crossed Fields



FE
FB
E
- - - - -
B out of page

• E and B fields are balanced to control the
  trajectory of the charged particle.
• FB FE
• qvB qE
• v E/B

Phosphor Coated Screen
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Determining the Charge to Mass Ratio
x x x x x x x x x
x x x x x x x x
x x x x x x x

• Magnetism
• Lorentz Force FB qv x B
• Newtons Second Law
• F ma
• qvB mv2/R
• q/m v/BR
• Experiment was repeated for other ions to
  calculate their charge to weight ratio, thus
  allowing an estimate of the mass of the particle.

R
v
Fc
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Determining the Charge to Mass Ratio (cont.)

• Electricity
• For 2 parallel plates
• FE qE
• V Ed W/q ½mv2
• q
• v 2qV
• m
• Substitute v in the equation for the radius of
  the circle traversed by a charged particle in a
  magnetic field.
• mv m 2qV 1 2Vm q
  2V
• qB qB m B q m B2r2

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Mass Spectrometer

• 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.

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Mass Spectrometer How does it work?

• 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.
• 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.

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Mass Spectrometer
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Mass Spectrometer - Applications

• -Paleoceanography Determine relative abundances
  of isotopes (they decay at different rates -
  geological age)
• -Space exploration Determine whats 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

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Electromagnetic Waves

• Lets assume that we have electric fields without
  a charged body. Can it happen?
• 1860 Years after Faraday and Oersted made their
  discoveries James Maxwell hypothesized that
  electric fields changing in time would create
  magnetic fields and vice-versa.
• 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).

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Electromagnetic Waves (cont.)
www.hyperphysics.com
Electromagnetic Wave
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Characteristics of Electromagnetic Waves

• 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.
• 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.

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Transmitting Radio Waves

• 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.

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Receiving Radio Waves

• 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.

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Electromagnetic Spectrum
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Speed of Light

• Speed of Light c 3.00 x 108 m/s
• The relationship between ?o and ?o support James
  Maxwells 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

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Energy of Electromagnetic Radiation

• Elect. Energy Density Elect. Energy/Volume
• Elect. Energy Density ½?oE2
• Mag. Energy Density Mag. Energy/Volume
• Mag. Energy Density 1
• 2?o
• Total Energy Density Elect. Energy Density
  Mag. Energy Density
• ? 1 1
• 2 2?o

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Energy of Electromagnetic Radiation

• Since the electric and magnetic fields contain
  the same amount of energy
• ? ?oE2
• ? B2
• Therefore
• 1
• ?o ?o
• E cB

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The Doppler Effect

• What you already know Sound waves exhibit the
  Doppler Effect source of sound moving in
  relation to observer.
• 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).

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Light Polarization

• 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.

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Light Polarization

• 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 dont work on
• longitudinal waves such
• as sound waves.

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Light Polarization in Nature

• 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!

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Key Ideas

• 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.

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Key Ideas

• Doppler Effect When two objects are moving
  further apart they are called red-shifted while
  they are considered blue-shifted if moving closer
  together.
• Polarization The process by which the electric
  field component of EM radiation is limited to
  only one direction.