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Lecture PowerPoints

Chapter 22 Physics: Principles with Applications, 7th edition

Giancoli

Chapter 22 Electromagnetic Waves


Contents of Chapter 22

•  Changing Electric Fields Produce Magnetic Fields; Maxwell’s Equations

•  Production of Electromagnetic Waves •  Light as an Electromagnetic Wave and the Electromagnetic

Spectrum

•  Measuring the Speed of Light

•  Energy in EM Waves

•  Momentum Transfer and Radiation Pressure •  Radio and Television; Wireless Communication


22-1 Changing Electric Fields Produce Magnetic Fields; Maxwell’s Equations

Maxwell’s equations are the basic equations of electromagnetism. They involve calculus; here is a summary:

1.  Gauss’s law relates electric field to charge: Flux of the electric field through the closed surface is equal to the sum of all electric charges enclosed by this surface divided by ε0.

2.  A law stating there are no magnetic “charges”: Flux of the magnetic field through the closed surface is equal to zero.

3.  A changing electric field produces a magnetic field and vice versa.

4.  A magnetic field is produced by an electric current, and also by a changing electric field.



Only one part of this is new—that a changing electric field produces a magnetic field.

Ampère’s law relates the magnetic field around a current to the current through a surface.



In order for Ampère’s law to hold, it can’t matter which surface we choose. But look at a discharging capacitor; there is a current through surface 1 but none through surface 2:



Therefore, Ampère’s law is modified to include the creation of a magnetic field by a changing electric field—the field between the plates of the capacitor in this example.


22-2 Production of Electromagnetic Waves

Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created they can propagate on their own.

These propagating fields are called electromagnetic waves.



Oscillating charges will produce electromagnetic waves:



Far from the source, the waves are plane waves:



The electric and magnetic waves are perpendicular to each other, and to the direction of propagation.



When Maxwell calculated the speed of propagation of electromagnetic waves, he found:

Using the known values of ε0 and µ0 gives c = 3.00 x 108 m/s.

This is the speed of light in a vacuum.


(22-3)

22-3 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

Light was known to be a wave. The production and measurement of electromagnetic waves of other frequencies confirmed that light was an electromagnetic wave as well.

The frequency of an electromagnetic wave is related to its wavelength:


(22-4)

22-3 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

Electromagnetic waves can have any wavelength; we have given different names to different parts of the electromagnetic spectrum.


Example 1

•  Electromagnetic waves and sound waves can have the same frequency. (a) What is the wavelength of a 1 kHz electromagnetic wave? (b) What is the wavelength of a 1 kHz sound wave? The speed of sound in air is 341 m/s.

•  Solution: •  a)

•  b)


€

c = λf ⇒ λ =cf

=3⋅ 108m / s103Hz

= 3⋅ 105m

€

v = λf ⇒ λ =vf

=341m / s103Hz

= 0.341m

Example 2

•  Pulsed lasers used for science and medicine produce very brief bursts of electromagnetic energy. If the laser light wavelength is 1062 nm, and the pulse lasts for 34 picoseconds, how many wavelengths are found within the laser pulse?

•  Solution: The length of the pulse is L =c.t. So the number of wavelengths can be found as a ratio of L and λ.


€

N =c⋅ tλ

=3⋅ 108m / s⋅ 34⋅ 10−12 s

1062⋅ 10−9m= 9600

22-4 Measuring the Speed of Light

The speed of light was known to be very large, although careful studies of the orbits of Jupiter’s moons showed that it is finite.

One important measurement, by Michelson, used a rotating mirror:


22-4 Measuring the Speed of Light

Over the years, measurements have become more and more precise; now the speed of light is defined to be:

c = 2.99792458 × 108 m/s

This is then used to define the meter.


22-5 Energy in EM Waves

Energy is stored in both electric and magnetic fields, giving the total energy density of an electromagnetic wave:

Each field contributes half the total energy density.


(22-5)

(22-6a)


This energy is transported by the wave.



The energy transported through a unit area per unit time is called the intensity:

Its average value is given by:


(22-7)

(22-8)

€

I =ΔUAΔt

=ε 0E

2( ) AcΔt( )AΔt

= ε 0cE2

Example

•  A radio transmitter is operating at an average power of 4 kW and is radiating uniformly in all directions. What is the average intensity of the signal 8 km from the transmitter?

•  Answer: 4.97 µW/m2

•  Solution: Power is defined as energy divided by time. Intensity is defined as energy divided by area and by time. Area in this case is area of the sphere with radius of 8 km.


€

I =ΔUAΔt

=PA

=4⋅ 103W

4π⋅ 8⋅ 103m( )2= 4.97⋅ 10−6W / m2

22-6 Momentum Transfer and Radiation Pressure

In addition to carrying energy, electromagnetic waves also carry momentum. This means that a force will be exerted by the wave.

The radiation pressure is related to the average intensity. It is a minimum if the wave is fully absorbed:

and a maximum if it is fully reflected:


(22-10a)

(22-10b)

Example: A solar sail

•  Proposals have been made to use the radiation pressure from the Sun to help propel spacecraft around the solar system. Intensity is 1000 W/m2.

–  (a) About how much force would be applied on a 1km x 1km highly reflective sail when about the same distance from the Sun as the Earth is? Answer: 10 N

–  (b) By how much this increase the speed of a 5000-kg spacecraft in 1 year? Answer: about 200,000 km/h

–  (C) If the spacecraft started from rest, about hw far would it travel in a year?


Radio and Television

•  The 1800s: Earliest Broadcasting –  Maxwell (Theorized the existence of electromagnetic waves as

“luminous ether.”) –  Bell (Transmitting sounds by telegraph in 1877.) –  Hertz (Invented the “spark-gap detector” which verified the existence of

electromagnetic waves.) –  Marconi (Invented radio in 1895. First radio company in London,

1897.)


Generation of Radio Waves

•  Accelerating charges radiate EM energy •  If charges oscillate back and forth, get time-varying fields

E

+ + +

- - -

+

-

-

+

- - -

+ + +

Generation of Radio Waves

If charges oscillate back and forth, get time-varying magnetic fields too. Note that the magnetic fields are perpendicular to the electric field vectors

B

+ + +

- - -

+

-

-

+

- - -

+ + +

Polarization of Radio Waves

E Transmitting antenna

Reception of Radio Waves

Receiving antenna works best when ‘tuned’ to the wavelength of the signal,

and has proper polarization

Electrons in antenna are “jiggled” by passage of electromagnetic wave

E

Optimum antenna length is λ/4: one-quarter wavelength

22-7 Radio and Television; Wireless Communication

This figure illustrates the process by which a radio station transmits information. The audio signal is combined with a carrier wave:


Encoding Information on Radio Waves

•  What quantities characterize a radio wave? •  Two common ways to carry analog information with radio

waves –  Amplitude Modulation (AM) –  Frequency Modulation (FM): “static free”

UCSD: Physics 8; 2006

AM Radio •  Amplitude Modulation (AM) uses changes in the signal strength to convey information

pressure modulation (sound)

electromagnetic wave modulation

AM Radio in Practice

•  Uses frequency range from 530 kHz to 1700 kHz –  each station uses 9 kHz –  spacing is 10 kHz (a little breathing room) → 117 channels –  9 kHz of bandwidth means 4.5 kHz is highest audio frequency that can

be encoded •  falls short of 20 kHz capability of human ear

•  Previous diagram is exaggerated: –  audio signal changes slowly with respect to radio carrier

•  typical speech sound of 500 Hz varies 1000 times slower than carrier •  thus will see 1000 cycles of carrier to every one cycle of audio

FM Radio •  Frequency Modulation (FM) uses changes in the wave’s frequency to convey information

pressure modulation (sound)

electromagnetic wave modulation

FM Radio in Practice •  Spans 87.8 MHz to 108.0 MHz in 200 kHz intervals

–  101 possible stations –  example: 91X runs from 91.0–91.2 MHz (centered at 91.1)

•  Nominally uses 150 kHz around center –  75 kHz on each side –  30 kHz for L + R (mono) → 15 kHz audio capability –  30 kHz offset for stereo difference signal (L - R)

•  Again: figure exaggerated –  75 kHz from band center, modulation is > 1000 times slower than

carrier, so many cycles go by before frequency noticeably changes

AM vs. FM

•  FM is not inherently higher frequency than AM –  these are just choices –  aviation band is 108–136 MHz uses AM technique

•  Besides the greater bandwidth (leading to stereo and higher audio frequencies), FM is superior in immunity to environmental influences

–  there are lots of ways to mess with an EM-wave’s amplitude •  pass under a bridge •  re-orient the antenna

–  no natural processes mess with the frequency •  FM still works in the face of amplitude foolery

Spring 2006 37

Frequency Allocation

38

Converting back to sound: AM

•  AM is easy: just pass the AC signal from the antenna into a diode

–  or better yet, a diode bridge –  then use capacitor to smooth out bumps

•  but not so much as to smooth out audio bumps

B

D

radio signal

amplifier/ speaker


At the receiving end, the wave is received, demodulated, amplified, and sent to a loudspeaker:



The receiving antenna is bathed in waves of many frequencies; a tuner is used to select the desired one:


Summary of Chapter 22

•  Maxwell’s equations are the basic equations of electromagnetism

•  Electromagnetic waves are produced by accelerating charges; the propagation speed is given by:

•  The fields are perpendicular to each other and to the direction of propagation.

•  The wavelength and frequency of EM waves are related:

•  The electromagnetic spectrum includes all wavelengths, from radio waves through visible light to gamma rays.


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Lecture PowerPoints Chapter 22 Physics: Principles …hep0.okstate.edu/flera/phys1214/Ch22_Giancoli7e.pdf · Lecture PowerPoints Chapter 22 Physics: Principles with ... Physics 8;