1. General Physics (PHY 2140) Lecture 12 Electricity and Magnetism
AC circuits and EM waves
The Electromagnetic Spectrum
The Doppler Effect
Modern Physics
Relativity
Galilean Relativity
Speed of Light
The Aether
Chapter 21, 26
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2. Lightning Review Last lecture: AC circuits Resonance in RLC circuits
Transformers
Electromagnetic Waves
Magnetic field in coil increases with iron, so coil resists change with a back emf -> total voltage on bulb is less ->
Review Problem: The light bulb has a resistance R, and the emf drives the circuit with a frequency w.
The light bulb glows most brightly at
1. very low frequencies.
2. very high frequencies.
3. the frequency
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Recall:

3. Resonance in an AC Circuit
Resonance occurs at the frequency, ƒo, where the current has its maximum value
To achieve maximum current, the impedance must have a minimum value
This occurs when XL = XC
Resonance when Z=0
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4. An RLC circuit is used to tune a radio to an FM station broadcasting at 88.9 MHz. The resistance in the circuit is 12.0 Ω and the capacitance is 1.40 pF. What inductance should be present in the circuit?
Given:
RLC circuit
f0=88.9 Hz
R = 12.0 W
C = 1.40 pF
Find:
L=?
The resonance frequency of the circuit should be chosen to match that of the radio station
This is sufficient information for a solution, as we know all of the quantities on the right hand side
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5. Electromagnetic Waves, Summary
A changing magnetic field produces an electric field
A changing electric field produces a magnetic field
These fields are in phase
At any point, both fields reach their maximum value at the same time
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6. Electromagnetic Waves are Transverse Waves
The E and B fields are perpendicular to each other
Both fields are perpendicular to the direction of motion
Therefore, em waves are transverse waves
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7. Properties of EM Waves Electromagnetic waves are transverse waves
Electromagnetic waves travel at the speed of light
Because em waves travel at a speed that is precisely the speed of light, light is an electromagnetic wave
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8. Question
The sun is about 1.5x1011 m from the earth.  How long does it take light to
get here?
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9. Properties of EM Waves, 2
The ratio of the electric field to the magnetic field is equal to the speed of light
Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path
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10. Properties of EM Waves, 3
Energy carried by em waves is shared equally by the electric and magnetic fields
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11. Properties of EM Waves, final
Electromagnetic waves transport linear momentum as well as energy
For complete absorption of energy U, p=U/c
For complete reflection of energy U, p=(2U)/c
Radiation pressures can be determined experimentally
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12. Determining Radiation Pressure
This is an apparatus for measuring radiation pressure
In practice, the system is contained in a vacuum
The pressure is determined by the angle at which equilibrium occurs
p=(2U)/c
p=U/c
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13. Example: Solar Sail Spacecraft
What would have been the radiation pressure exerted on the recently (unsuccessfully) launched Cosmos 1 spacecraft?
Cosmos1:
30 m diameter sail
100 kg mass
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14. Solar Sail Spacecraft - continued
Radiation pressure:
At earth =1370 W/m2
Thus
Multiply by area:
Net force:
Divide by mass gives acceleration :
In 24 hours (86400 s) speed:
In one year ( s):
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15. The Spectrum of EM Waves
Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths
c = ƒλ
Wavelengths for visible light range from 400 nm to 700 nm
There is no sharp division between one kind of em wave and the next
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16. The EM Spectrum Note the overlap between types of waves
Visible light is a small portion of the spectrum
Types are distinguished by frequency or wavelength
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17. Notes on The EM Spectrum
Radio Waves
Used in radio and television communication systems
Microwaves
Wavelengths from about 1 mm to 30 cm
Well suited for radar systems
Microwave ovens are an application
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18. Notes on the EM Spectrum, 2
Infrared waves
Incorrectly called “heat waves”
Produced by hot objects and molecules
Readily absorbed by most materials
Visible light
Part of the spectrum detected by the human eye
Most sensitive at about 560 nm (yellow-green)
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19. Notes on the EM Spectrum, 3
Ultraviolet light
Covers about 400 nm to 0.6 nm
Sun is an important source of uv light
Most uv light from the sun is absorbed in the stratosphere by ozone
X-rays
Most common source is acceleration of high-energy electrons striking a metal target
Used as a diagnostic tool in medicine
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20. Notes on the EM Spectrum, final
Gamma rays
Emitted by radioactive nuclei
Highly penetrating and cause serious damage when absorbed by living tissue
Looking at objects in different portions of the spectrum can produce different information
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21. Example: talking to a submarine
The U.S. Navy has long proposed the construction of extremely low-frequency (ELF) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this?
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22. The required length of antenna is then a quarter of this
The U.S. Navy has long proposed the construction of extremely low-frequency (ELF) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this?
Given:
¼ wavelength
antenna
f0=75 Hz
Find:
L=?
First determine the wavelength, a forth of which will give us the length of an antenna
The required length of antenna is then a quarter of this
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23. Doppler Effect and EM Waves
A Doppler Effect occurs for em waves, but differs from that of sound waves
For sound waves, motion relative to a medium is most important
For light waves, the medium plays no role since the light waves do not require a medium for propagation
The speed of sound depends on its frame of reference
The speed of em waves is the same in all coordinate systems that are at rest or moving with a constant velocity with respect to each other
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24. Doppler Equation for EM Waves
The Doppler effect for em waves
f’ is the observed frequency
f is the frequency emitted by the source
u is the relative speed between the source and the observer
The equation is valid only when u is much smaller than c
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25. Doppler Equation, cont
The positive sign is used when the object and source are moving toward each other
The negative sign is used when the object and source are moving away from each other
Astronomers refer to a red shift when objects are moving away from the earth since the wavelengths are shifted toward the red end of the spectrum
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26. Relativity
Chapter 26
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27. A Brief Overview of Modern Physics
20th Century revolution
1900 Max Planck
Basic ideas leading to Quantum theory
1905 Einstein
Special Theory of Relativity
21st Century
Story is still incomplete
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28. Basic Problems
The speed of every particle in the universe always remains less than the speed of light
Newtonian Mechanics is a limited theory
It places no upper limit on speed
It is contrary to modern experimental results
Newtonian Mechanics becomes a specialized case of Einstein’s Theory of Special Relativity
When speeds are much less than the speed of light
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29. Galilean Relativity Choose a frame of reference
Necessary to describe a physical event
According to Galilean Relativity, the laws of mechanics are the same in all inertial frames of reference
An inertial frame of reference is one in which Newton’s Laws are valid
Objects subjected to no forces will move in straight lines
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30. Galilean Relativity – Example
A passenger in an airplane throws a ball straight up
It appears to move in a vertical path
The law of gravity and equations of motion under uniform acceleration are obeyed
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31. Galilean Relativity – Example, cont
There is a stationary observer on the ground
Views the path of the ball thrown to be a parabola
The ball has a velocity to the right equal to the velocity of the plane
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32. Galilean Relativity – Example, conclusion
The two observers disagree on the shape of the ball’s path
Both agree that the motion obeys the law of gravity and Newton’s laws of motion
Both agree on how long the ball was in the air
Conclusion: There is no preferred frame of reference for describing the laws of mechanics
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33. Galilean Relativity – Limitations
Galilean Relativity does not apply to experiments in electricity, magnetism, optics, and other areas
Results do not agree with experiments
The observer should measure the speed of the pulse as v+c
Actually measures the speed as c
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34. Luminiferous Ether
19th Century physicists compared electromagnetic waves to mechanical waves
Mechanical waves need a medium to support the disturbance
The luminiferous ether was proposed as the medium required (and present) for light waves to propagate
Present everywhere, even in space
Massless, but rigid medium
Could have no effect on the motion of planets or other objects
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35. Verifying the Luminiferous Ether
Associated with an ether was an absolute frame where the laws of e & m take on their simplest form
Since the earth moves through the ether, there should be an “ether wind” blowing
If v is the speed of the ether relative to the earth, the speed of light should have minimum or maximum values depending on its orientation to the “wind”
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36. Michelson-Morley Experiment
First performed in 1881 by Michelson
Repeated under various conditions by Michelson and Morley
Designed to detect small changes in the speed of light
By determining the velocity of the earth relative to the ether
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37. Michelson-Morley Equipment
Used the Michelson Interferometer
Arm 2 is aligned along the direction of the earth’s motion through space
The interference pattern was observed while the interferometer was rotated through 90°
The effect should have been to show small, but measurable, shifts in the fringe pattern
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38. Michelson-Morley Equipment
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39. Michelson-Morley Results
Measurements failed to show any change in the fringe pattern
No fringe shift of the magnitude required was ever observed
Light is now understood to be an electromagnetic wave, which requires no medium for its propagation
The idea of an ether was discarded
The laws of electricity and magnetism are the same in all inertial frames
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