1. 1 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

2. 2 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.

3. 3 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

4. 4 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

5. 5 LC circuit

6. 6 24.5 Energy Density in EM Waves The energy density, u, is the energy per unit volume For the electric field, u E = ½  o E 2 For the magnetic field, u B = B 2 / 2  o Since B = E/c and

7. 7 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

8. 8 Energy Density, final The total instantaneous energy density in an EM wave is the sum of the energy densities associated with each field u =u E + u B =  o E 2 = B 2 /  o When this is averaged over one or more cycles, the total average becomes u av =  o (E avg ) 2 = ½  o E 2 max = B 2 max / 2  o

9. 9 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

10. 10 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

11. 11 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. m 2 = W/m 2

12. 12 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 cos 2 (kx-  t) equals half I = S avg = c u avg The intensity of an EM wave equals the average energy density multiplied by the speed of light

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16. 16 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  t, the total momentum is p = U / c for complete absorption

17. 17 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

18. 18 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

19. 19 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/m 2

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