Electromagnetic Waves

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Chapter 21

• Electromagnetic Waves

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Exam II
Curve 30
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Electromagnetic Waves Ch 21, Secs 812
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James Clerk Maxwell

• 1831 1879
• Electricity and magnetism were originally thought
  to be unrelated
• In 1865, James Clerk Maxwell provided a
  mathematical theory that showed a close
  relationship between all electric and magnetic
  phenomena
• Electromagnetic theory of light

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Maxwells Starting Points

• Electric field lines originate on positive
  charges and terminate on negative charges

• Magnetic field lines always form closed loops
  they do not begin or end anywhere

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Can electric fields form closed loops?

1. Yes
2. No

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21 22 23 24 25 26 27 28 29 30
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Maxwells Starting Points

• A varying magnetic field induces an emf and hence
  an electric field (Faradays Law)

• Magnetic fields are generated by moving charges
  or currents (Ampères Law)

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Maxwells Hypothesis

• Turning Faradays Law upside down, Maxwell
  hypothesized that a changing electric field would
  produce a magnetic field (Maxwell-Ampères Law)

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Maxwell Equations
closed surface enclosed charge
closed surface no mag. charge
closed loop linked current flux
closed loop linked flux

• Conservation of energy

• Conservation of charge

Lorentz force law
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Maxwells Predictions

• Maxwell concluded that visible light and all
  other electromagnetic (EM) waves consist of
  fluctuating electric and magnetic fields, with
  each varying field inducing the other
• Accelerating charges generate these time varying
  E and B fields
• Maxwell calculated the speed at which these
  electromagnetic waves travel in a vacuum speed
  of light c 3.00 x 108 m/s

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Hertzs Confirmation of Maxwells Predictions

• 1857 1894
• First to generate and detect electromagnetic
  waves in a laboratory setting
• Showed radio waves could be reflected, refracted
  and diffracted
• The unit Hz is named for him

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Hertzs Experimental Apparatus

• An induction coil is connected to two large
  spheres forming a capacitor
• Oscillations are initiated by short voltage
  pulses
• The oscillating current (accelerating charges)
  generates EM waves

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Hertzs Experiment

• Several meters away from the transmitter is the
  receiver
• This consisted of a single loop of wire connected
  to two spheres

• When the oscillation frequency of the transmitter
  and receiver matched, energy transfer occurred
  between them

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Hertzs Conclusions

• Hertz hypothesized the energy transfer was in the
  form of waves
• These are now known to be electromagnetic waves
• Hertz confirmed Maxwells theory by showing the
  waves existed and had all the properties of light
  waves (e.g., reflection, refraction, diffraction)
• They had different frequencies and wavelengths
  which obeyed the relationship v f ? for waves
• v was very close to 3 x 108 m/s, the known speed
  of light

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EM Waves by an Antenna

• Two rods are connected to an oscillating source,
  charges oscillate between the rods (a)
• As oscillations continue, the rods become less
  charged, the field near the charges decreases and
  the field produced at t 0 moves away from the
  rod (b)
• The charges and field reverse (c) the
  oscillations continue (d)

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EM Waves by an Antenna, final

• Because the oscillating charges in the rod
  produce a current, there is also a magnetic field
  generated
• As the current changes, the magnetic field
  spreads out from the antenna
• The magnetic field is perpendicular to the
  electric field

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Electromagnetic Waves, Summary

• A changing magnetic field produces an electric
  field
• A changing electric field produces a magnetic
  field
• These fields are in phase
• At any point, both fields reach their maximum
  value at the same time

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Electromagnetic Waves are Transverse Waves

• The and fields are perpendicular to each
  other
• Both fields are perpendicular to the direction of
  motion
• Therefore, EM waves are transverse waves

Active Figure A Transverse Electromagnetic Wave
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Properties of EM Waves

• Electromagnetic waves are transverse waves
• They travel at the speed of light
• This supports the fact that light is an EM wave

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Properties of EM Waves, 2

• The ratio of the electric field to the magnetic
  field is equal to the speed of light
• Electromagnetic waves carry energy as they travel
  through space, and this energy can be transferred
  to objects placed in their path

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Properties of EM Waves, 3

• Energy carried by EM waves is shared equally by
  the electric and magnetic fields
• Average power per unit area

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Properties of EM Waves, final

• Electromagnetic waves transport linear momentum
  as well as energy
• For complete absorption of energy U
• p U/c ? F Pave/c
• For complete reflection of energy U
• p (2U)/c ? F 2Pave/c
• Radiation pressures (forces) can be determined
  experimentally

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Determining Radiation Pressure

• This is an apparatus for measuring radiation
  pressure
• In practice, the system is contained in a vacuum
• The pressure is determined by the angle at which
  equilibrium occurs

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Summary of Properties ofElectromagnetic (EM)
Waves

• They travel at the speed of light
• They are transverse waves
• E, B perpendicular to each other and velocity
• Ratio of E and B field magnitudes E/Bc
• Electric and magnetic fields carry equal energy
• They carry both energy and momentum
• Can deliver U and p to a surface

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The Spectrum of EM Waves

• Forms of electromagnetic waves exist that are
  distinguished by their frequency and wavelength
• c ƒ?
• Wavelengths for visible light range from 400700
  nm
• a small portion of the spectrum
• Wavelengths
• 1 km 10-3 m (radio) electronic
• 1 ?m 10-6 m (visible, IR)
• 1 nm 10-9 m (UV, X-ray)
• 1 Å 10-10 m (X-ray) atomic
• 1 fm 10-15 m (?-ray) nuclear