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Lecture PowerPoints
Chapter 22 Physics: Principles with Applications, 7th edition
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.
22-1 Changing Electric Fields Produce Magnetic Fields; Maxwell’s Equations
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:
22-1 Changing Electric Fields Produce Magnetic Fields; Maxwell’s Equations
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.
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.
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:
• 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.
• 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.
• 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.
• 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?
• Accelerating charges radiate EM energy • If charges oscillate back and forth, get time-varying fields
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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
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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:
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
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Frequency Allocation
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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
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radio signal
amplifier/ speaker
22-7 Radio and Television; Wireless Communication
At the receiving end, the wave is received, demodulated, amplified, and sent to a loudspeaker: