Electromagnetic Waves

1
Chapter 34

• Electromagnetic Waves

2
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

3
Maxwells Equations Conceptual

• Electric field lines originate/terminate on
  charges or are created by changing magnetic flux
  (Gauss and Faraday Laws).
• Magnetic field lines are created by moving
  charges or changing electric flux. No magnetic
  charges. (Magnetic Gauss and Maxwell/Ampere Law)

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Maxwells Equations Mathematical
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Maxwells Prediction of EM Waves

• Using the previous equations with no sources
  (qI0) it is possible to arrive at (see text end
  of 34.2)
• And
• These are partial differential equations called
  wave equations

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Maxwells Prediction of EM Waves II

• The speed can be read off of these equations and
  is
• Simple sinusoidal solutions are of the form
• Where
• These waves travel in the x direction. For x
  direction argument becomes kx?t

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Maxwells Prediction of EM Waves III

• EM waves have speed
• The amplitudes satisfy
• The waves satisfy superposition principle
• The waves are triply traverse ?

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Fig 34-3, p.1071
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Quiz!!!

• What is the phase difference (in degrees) between
  the sinusoidal E and B fields from the previous
  slide?
• (a) 180 (b) 90 (c) 0 (d) need more info

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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 inductor and capacitor form the transmitter
• DEMO (radio faraday cage or mini-radio station)

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Energy carried by EM waves Flux

• EM waves carry energy. The rate of flow is given
  by the Poynting vector (do example of cross
  product)
• Units of S ? J/(s m2)W/ m2
• Time/Space dependent magnitude
• Intensity I Save
• Time average of cos2 (kx-?t) sin2 (kx- ?t) 1/2

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Energy carried by EM waves Density

• The instantaneous energy density in the E and B
  fields is
• Note E and B energies are on equal footing in EM
  waves
• The total energy density is
• Usually only the average is important
• Intensity is energy density X speed

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QUIZ!!!

• An EM propagates in the y direction. The E
  field is at some time in x. The magnetic field
  at that instant is (a) x (b) y (c) z (d)
  z (e) none of the above
• Which of the following are constant?
• (a) Magnitude of Poynting vector (b) uE (c) uB
  (d) ISave

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Momentum carried by EM Waves

• Since EM waves carry energy they should also
  carry momentum
• This is the momentum transferred to the surface
  for total absorption
• If there is momentum there is pressure
• For reflection double both of the above

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Radiation Pressure

• For radiation at oblique angle ? the pressure is
  modified by cos? and pressure by cos2 ? (because
  of the area factor).
• Radiation pressure is usually small (laser point
  10-6 N/m2)
• QUIZ!!! How does one maximize radiation pressure?
  (a)light on black surface (b) light on mirror
  (c)no difference

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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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Electromagnetic Waves Produced by an Antenna

• When a charged particle undergoes an
  acceleration, it must radiate energy
• If currents in an ac circuit change rapidly, some
  energy is lost in the form of em waves
• EM waves are radiated by any circuit carrying
  alternating current
• An alternating voltage applied to the wires of an
  antenna forces the electric charge in the antenna
  to oscillate

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EM Waves by an Antenna, cont

• Two rods are connected to an ac 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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Charges and Fields, Summary

• Stationary charges produce only electric fields
• Charges in uniform motion (constant velocity)
  produce electric and magnetic fields
• Charges that are accelerated produce electric and
  magnetic fields and electromagnetic waves

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The Spectrum of EM Waves

• Forms of electromagnetic waves exist that are
  distinguished by their frequencies and
  wavelengths
• c ƒ??/k
• Wavelengths for visible light range from 400 nm
  to 700 nm
• There is no sharp division between one kind of
  EM wave and the next

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The EMSpectrum

• Note the overlap between types of waves
• Visible light is a small portion of the spectrum
• Types are distinguished by frequency or wavelength

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Notes on The EM Spectrum

• Radio Waves
• Used in radio and television communication
  systems
• Microwaves
• Wavelengths from about 1 mm to 30 cm
• Well suited for radar systems
• Microwave ovens are an application

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Notes on the EM Spectrum, 2

• Infrared waves
• Produced by hot objects and molecules
• Readily absorbed by most materials
• Visible light
• Part of the spectrum detected by the human eye
• Most sensitive at about 560 nm (yellow-green)

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Notes on the EM Spectrum, 3

• Ultraviolet light
• Covers about 400 nm to 0.6 nm
• Sun is an important source of uv light
• Most uv light from the sun is absorbed in the
  stratosphere by ozone
• X-rays
• Most common source is acceleration of high-energy
  electrons striking a metal target
• Used as a diagnostic tool in medicine

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Notes on the EM Spectrum, final

• Gamma rays
• Emitted by radioactive nuclei
• Highly penetrating and cause serious damage when
  absorbed by living tissue
• Looking at objects in different portions of the
  spectrum can produce different information

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Doppler Effect and EM Waves

• A Doppler Effect occurs for em waves, but differs
  from that of sound waves
• For sound waves, motion relative to a medium is
  most important
• For light waves, the medium plays no role since
  the light waves do not require a medium for
  propagation
• The speed of sound depends on its frame of
  reference
• The speed of em waves is the same in all
  coordinate systems that are at rest or moving
  with a constant velocity with respect to each
  other

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Doppler Equation for EM Waves

• The Doppler effect for em waves
• fo is the observed frequency
• fs is the frequency emitted by the source
• u is the relative speed between the source and
  the observer
• The equation is valid only when u is much smaller
  than c

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Doppler Equation, cont

• The positive sign is used when the object and
  source are moving toward each other
• The negative sign is used when the object and
  source are moving away from each other
• Astronomers refer to a red shift when objects are
  moving away from the earth since the wavelengths
  are shifted toward the red end of the spectrum