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Electromagnetic Waves


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Title: Electromagnetic Waves

Chapter 21
  • Electromagnetic Waves

Exam II
Curve 30
Electromagnetic Waves Ch 21, Secs 812
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
  • Electromagnetic theory of light

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

Can electric fields form closed loops?
  1. Yes
  2. No

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
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)

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

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
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

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

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

Hertzs Experiment
  • Several meters away from the transmitter is the
  • 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

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

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)

EM Waves by an Antenna, final
  • Because the oscillating charges in the rod
    produce a current, there is also a magnetic field
  • As the current changes, the magnetic field
    spreads out from the antenna
  • The magnetic field is perpendicular to the
    electric field

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

Electromagnetic Waves are Transverse Waves
  • The and fields are perpendicular to each
  • Both fields are perpendicular to the direction of
  • Therefore, EM waves are transverse waves

Active Figure A Transverse Electromagnetic Wave
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

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

Properties of EM Waves, 3
  • Energy carried by EM waves is shared equally by
    the electric and magnetic fields
  • Average power per unit area

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

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

Summary of Properties ofElectromagnetic (EM)
  • 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

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
  • 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
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