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

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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.

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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

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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

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LC circuit

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24.5 Energy Density in EM Waves The energy density, u, is the energy per

unit volume For the electric field, uE= ½ oE2

For the magnetic field, uB = B2 / 2o

Since B = E/c and oo1c 2

212 2B E o

o

Bu u E

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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

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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 = oE2 = B2 / o

When this is averaged over one or more cycles, the total average becomes uav = o (Eavg)2 = ½ oE2

max = B2max / 2o

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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

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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

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o S E B

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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

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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-t) equals half

I = Savg = c uavg

The intensity of an EM wave equals the average energy density multiplied by the speed of light

2 2max max max max

2 2 2avgo o o

E B E c BI Sc

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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

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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

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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

1 1F dp dU dtPA A dt c A

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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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