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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