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24.4 Heinrich Rudolf HertzPowerPoint Presentation

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
- 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

- 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 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

- 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

- 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

- 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

- 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

- 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

- 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

Intensity

- 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

- 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

- 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, 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

- 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

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