General Physics (PHY 2140) Lecture 12 Electricity and Magnetism 1. AC circuits and EM waves The Electromagnetic Spectrum The Doppler Effect 6/20/2007 Modern Physics 1. Relativity Galilean Relativity Speed of Light The Aether http://www.physics.wayne.edu/~alan/2140website/main.htm Chapter 21, 26 1
Lightning Review Last lecture: 1. AC circuits Resonance in RLC circuits Transformers Electromagnetic Waves N Δ V = ΔV 2 2 1 N1 o o f 0 1 = 2π LC 1 c= = 2.99792 10 με 8 m s Review Problem: The light bulb has a resistance R, and the emf drives the circuit with a frequency ω. The light bulb glows most brightly at 1. very low frequencies. 2. very high frequencies. 3. the frequency ω = 1 LC 6/20/2007 Recall: X C = 1 ωc X L = ωl 2
Resonance in an AC Circuit Resonance occurs at the frequency, ƒ o, where the current has its maximum value To achieve maximum current, the impedance must have a minimum value This occurs when X L = X C ƒ o = 2π 1 LC 6/20/2007 3
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 f 0 =88.9 Hz R = 12.0 Ω C = 1.40 pf Find: L=? The resonance frequency of the circuit should be chosen to match that of the radio station f 1 1 = or L= f C 0 2 2 2π LC 4π 0 This is sufficient information for a solution, as we know all of the quantities on the right hand side 1 L= = 2.29 10 2 3 12 4π 88.9 10 1.40 10 2 ( Hz) ( F ) 6 H 6/20/2007 4
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 6/20/2007 5
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 6/20/2007 6
Properties of EM Waves Electromagnetic waves are transverse waves Electromagnetic waves travel at the speed of light c 1 = = 2.99792 10 με o o Because em waves travel at a speed that is precisely the speed of light, light is an electromagnetic wave 8 m s 6/20/2007 7
Question The sun is about 1.5x10 11 m from the earth. How long does it take light to get here? v = distance/time, so 11 distance 1.5 10 m t = = = 500 sec = 8.3 min 8 c 3 10 ms 6/20/2007 8
Properties of EM Waves, 2 The ratio of the electric field to the magnetic field is equal to the speed of light E c = B Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path 6/20/2007 9
Properties of EM Waves, 3 Energy carried by em waves is shared equally by the electric and magnetic fields Average power E B 2μ max o max = E 2μ 2 max o c per = unit cb 2μ 2 max o area = 6/20/2007 10
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 6/20/2007 11
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=u/c p=(2u)/c 6/20/2007 12
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 6/20/2007 13
Solar Sail Spacecraft - continued P Radiation pressure: At earth Φ=1370 W/m 2 Thus P Multiply by area: A Net force: i Divide by mass gives acceleration : In 24 hours (86400 s) speed: v In one year (31557600 s): = 2 Φ / 6/20/2007 14 c = 9.13 10 N/m = π r = 707m 3 F = P A= 6.46 10 N 6.46 10 m/s = at = 5.6 m/s 2039 m/s 6 2 2 2 5 2 2 2
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 6/20/2007 15
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 6/20/2007 16
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 6/20/2007 17
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) 6/20/2007 18
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 6/20/2007 19
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 6/20/2007 20
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 te 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? 6/20/2007 21
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 al is this? Given: ¼ wavelength antenna f 0 =75 Hz First determine the wavelength, a forth of which will give us the length of an antenna 8 v 3.00 10 m s λ = = = m= f 75Hz 6 4.00 10 4000 km The required length of antenna is then a quarter of this Find: L=? λ 4000km L= = = 1000km 4 4 6/20/2007 22
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 6/20/2007 23
Doppler Equation for EM Waves The Doppler effect for em waves f ' = f 1 u ± c 1 ± u/ c 2 2 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 6/20/2007 24 f ' = f 1 u / c
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 6/20/2007 25
Relativity Chapter 26 6/20/2007 26
A Brief Overview of Modern Physics 20 th Century revolution 1900 Max Planck Basic ideas leading to Quantum theory 1905 Einstein Special Theory of Relativity 21 st Century Story is still incomplete 6/20/2007 27
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 s Theory of Special Relativity When speeds are much less than the speed of light 6/20/2007 28
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 s Laws are valid Objects subjected to no forces will move in straight lines 6/20/2007 29
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 6/20/2007 30
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 6/20/2007 31
Galilean Relativity Example, conclusion The two observers disagree on the shape of the ball s s path Both agree that the motion obeys the law of gravity and Newton s 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 6/20/2007 32
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 6/20/2007 33
Luminiferous Ether 19 th 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 6/20/2007 34
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 6/20/2007 35
Michelson-Morley 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 6/20/2007 36
Michelson-Morley 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 6/20/2007 37
Michelson-Morley Morley Equipment 6/20/2007 38
Michelson-Morley 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 6/20/2007 39