24 4 heinrich rudolf hertz
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24.4 Heinrich Rudolf Hertz. 1857 – 1894 The first person generated and received the EM waves 1887 His experiment shows that the EM waves follow the wave phenomena. Hertz’s Experiment. An induction coil is connected to a transmitter

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24 4 heinrich rudolf hertz
24.4 Heinrich Rudolf Hertz
  • 1857 – 1894
  • The first person generated and received the EM waves
    • 1887
  • His experiment shows that the EM waves follow the wave phenomena
hertz s experiment
Hertz’s Experiment
  • An induction coil is connected to a transmitter
  • The transmitter consists of two spherical electrodes separated by a narrow gap to form a capacitor
  • The oscillations of the charges on the transmitter produce the EM waves.
  • A second circuit with a receiver, which also consists of two electrodes, is a single loop in several meters away from the transmitter.
hertz s experiment cont
Hertz’s Experiment, cont
  • The coil provides short voltage surges to the electrodes
  • As the air in the gap is ionized, it becomes a better conductor
  • The discharge between the electrodes exhibits an oscillatory behavior at a very high frequency
  • From a circuit viewpoint, this is equivalent to an LC circuit
hertz s experiment final
Hertz’s Experiment, final
  • Hertz found that when the frequency of the receiver was adjusted to match that of the transmitter, the energy was being sent from the transmitter to the receiver
  • Hertz’s experiment is analogous to the resonance phenomenon between a tuning fork and another one.
  • Hertz also showed that the radiation generated by this equipment exhibited wave properties
    • Interference, diffraction, reflection, refraction and polarization
  • He also measured the speed of the radiation
24 5 energy density in em waves
24.5 Energy Density in EM Waves
  • The energy density, u, is the energy per unit volume
  • For the electric field, uE= ½ eoE2
  • For the magnetic field, uB = B2 / 2mo
  • Since B = E/c and
energy density cont
Energy Density, cont
  • The instantaneous energy density associated with the magnetic field of an EM wave equals the instantaneous energy density associated with the electric field
    • In a given volume, the energy is shared equally by the two fields
energy density final
Energy Density, final
  • The total instantaneous energy density in an EM wave is the sum of the energy densities associated with each field
    • u =uE + uB = eoE2 = B2 / mo
  • When this is averaged over one or more cycles, the total average becomes
    • uav = eo (Eavg)2 = ½ eoE2max = B2max / 2mo
energy carried by em waves
Energy carried by EM Waves
  • Electromagnetic waves carry energy
  • As they propagate through space, they can transfer energy to objects in their path
  • The rate of flow of energy in an EM wave is described by a vector called the Poynting vector
poynting vector
Poynting Vector
  • The Poynting Vector is defined as
  • Its direction is the direction of propagation
  • This is time dependent
    • Its magnitude varies in time
    • Its magnitude reaches a maximum at the same instant as the fields
poynting vector final
Poynting Vector, final
  • The magnitude of the vector represents the rate at which energy flows through a unit surface area perpendicular to the direction of the wave propagation
    • This is the power per unit area
  • The SI units of the Poynting vector are J/s.m2 = W/m2
  • The wave intensity, I, is the time average of S (the Poynting vector) over one or more cycles
  • When the average is taken, the time average of cos2(kx-wt) equals half
  • I = Savg = c uavg
    • The intensity of an EM wave equals the average energy density multiplied by the speed of light
24 6 momentum and radiation pressure of em waves
24.6 Momentum and Radiation Pressure of EM Waves
  • EM waves transport momentum as well as energy
  • As this momentum is absorbed by some surface, pressure is exerted on the surface
  • Assuming the EM wave transports a total energy U to the surface in a time interval Dt, the total momentum is p = U / c for complete absorption
measuring radiation pressure
Measuring Radiation Pressure
  • This is an apparatus for measuring radiation pressure
  • In practice, the system is contained in a high vacuum
  • The pressure is determined by the angle through which the horizontal connecting rod rotates
    • For complete absorption
    • An absorbing surface for which all the incident energy is absorbed is called a black body
pressure and momentum
Pressure and Momentum
  • Pressure, P, is defined as the force per unit area
  • But the magnitude of the Poynting vector is (dU/dt)/A and so P = S / c
pressure and momentum cont
Pressure and Momentum, cont
  • For a perfectly reflecting surface,

p = 2 U / c and P = 2 S / c

  • For a surface with a reflectivity somewhere between a perfect reflector and a perfect absorber, the momentum delivered to the surface will be somewhere in between U/c and 2U/c
  • For direct sunlight, the radiation pressure is about 5 x 10-6 N/m2