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General Physics (PHY 2140)

Lecture 12Lecture 12Electricity and Magnetism1. AC circuits and EM waves

The Electromagnetic SpectrumThe Doppler Effect

Modern Physics1. Relativity

Galilean RelativitySpeed of Light The Aether

Chapter 21, 26

http://www.physics.wayne.edu/~alan/2140Website/Main.htm

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Lightning ReviewLightning Review

Last lecture:1.1.

AC circuitsAC circuitsResonance in RLC circuitsResonance in RLC circuitsTransformersTransformersElectromagnetic WavesElectromagnetic Waves

01

2f

LCπ=

22 1

1

NV VN

Δ = Δ

81 2.99792 10o o

c m sμ ε

= = ×

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 1 LCω =

1CX Cω= LX Lω=Recall:

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Resonance in an AC CircuitResonance in an AC Circuit

ResonanceResonance occurs at the occurs at the frequency, frequency, ƒƒoo

, where the current , where the current has its maximum valuehas its maximum value

To achieve maximum current, the To achieve maximum current, the impedance must have a minimum impedance must have a minimum valuevalueThis occurs when XThis occurs when XLL = X= XCC

LC21ƒo

π=

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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 circuitf0

=88.9 HzR = 12.0 ΩC = 1.40 pF

Find:

L=?

The resonance frequency of the circuit should be chosen to match that of the radio station

0 2 20

1 1or42

f Lf CLC ππ

= =

This is sufficient information for a solution, as we know all of the quantities on the right hand side

( ) ( )6

22 3 12

1 2.29 104 88.9 10 1.40 10

L HHz Fπ

−

−= = ×

× ×

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Electromagnetic Waves, Electromagnetic Waves, SummarySummary

A changing magnetic field produces an A changing magnetic field produces an electric fieldelectric fieldA changing electric field produces a A changing electric field produces a magnetic fieldmagnetic fieldThese fields are These fields are in phasein phase

At any point, both fields reach their At any point, both fields reach their maximum value at the same timemaximum value at the same time

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Electromagnetic Waves are Electromagnetic Waves are Transverse WavesTransverse Waves

TheThe EE and and BB fields fields are perpendicular to are perpendicular to each othereach otherBoth fields are Both fields are perpendicular to the perpendicular to the direction of motiondirection of motion

Therefore, em Therefore, em waves are waves are transverse wavestransverse waves

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Properties of EM WavesProperties of EM Waves

Electromagnetic waves are transverse wavesElectromagnetic waves are transverse wavesElectromagnetic waves travel at the speed of Electromagnetic waves travel at the speed of lightlight

Because em waves travel at a speed that is Because em waves travel at a speed that is precisely the speed of light, precisely the speed of light, light is an light is an electromagnetic waveelectromagnetic wave

81 2.99792 10o o

c m sμ ε

= = ×

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The sun is about 1.5x10The sun is about 1.5x101111

m from the earth.m from the earth.

How long does it take light to How long does it take light to get here? get here?

11

8

distance/time, sodistance 1.5 10 500 sec 8.3 min

c 3 10

vmt

m s

=

×= = = =

×

QuestionQuestion

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Properties of EM Waves, 2Properties of EM Waves, 2

The ratio of the electric field to the magnetic The ratio of the electric field to the magnetic field is equal to the speed of lightfield is equal to the speed of light

Electromagnetic waves carry energy as they Electromagnetic waves carry energy as they travel through space, and this energy can be travel through space, and this energy can be transferred to objects placed in their pathtransferred to objects placed in their path

BEc =

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Properties of EM Waves, 3Properties of EM Waves, 3

Energy carried by em waves is shared Energy carried by em waves is shared equally by the electric and magnetic equally by the electric and magnetic fieldsfields

o

2max

o

2max

o

maxmax

2Bc

c2E

2BE

areaunitperpowerAverage

μ=

μ=

μ

=

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Properties of EM Waves, finalProperties of EM Waves, final

Electromagnetic waves transport linear Electromagnetic waves transport linear momentum as well as energymomentum as well as energy

For complete absorption of energy U, For complete absorption of energy U, p=U/cp=U/cFor complete reflection of energy U, For complete reflection of energy U, p=(2U)/cp=(2U)/c

Radiation pressures can be determined Radiation pressures can be determined experimentallyexperimentally

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Determining Radiation Determining Radiation PressurePressure

This is an apparatus This is an apparatus for measuring for measuring radiation pressureradiation pressureIn practice, the In practice, the system is contained system is contained in a vacuumin a vacuumThe pressure is The pressure is determined by the determined by the angle at which angle at which equilibrium occursequilibrium occurs

p=U/cp=U/c

p=(2U)/cp=(2U)/c

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Example: Solar Sail SpacecraftExample: Solar Sail Spacecraft

What would have been the radiation What would have been the radiation pressure exerted on the recently pressure exerted on the recently (unsuccessfully) launched Cosmos 1 (unsuccessfully) launched Cosmos 1 spacecraft?spacecraft?

Cosmos1:Cosmos1:30 m diameter sail30 m diameter sail100 kg mass100 kg mass

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Radiation pressure:Radiation pressure:At earth At earth ΦΦ=1370 W/m=1370 W/m22

ThusThusMultiply by area: Multiply by area: Net force:Net force:Divide by mass gives acceleration :Divide by mass gives acceleration :In 24 hours (86400 s) speed:In 24 hours (86400 s) speed:In one year (31557600 s):In one year (31557600 s):

2 /P c= Φ

2 2707mA rπ= =6 29.13 10 N/mP −= ×

Solar Sail Spacecraft Solar Sail Spacecraft --

continuedcontinued

36.46 10F P A N−= = ×i5 26.46 10 m/s−×

25.6 m/sv at= =22039 m/s

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The Spectrum of EM WavesThe Spectrum of EM Waves

Forms of electromagnetic waves exist Forms of electromagnetic waves exist that are distinguished by their that are distinguished by their frequencies and wavelengthsfrequencies and wavelengths

c = c = ƒƒλλWavelengths for visible light range from Wavelengths for visible light range from 400 nm to 700 nm400 nm to 700 nmThere is no sharp division between one There is no sharp division between one kind of em wave and the nextkind of em wave and the next

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The EMThe EM SpectrumSpectrum

Note the overlap Note the overlap between types of between types of waveswavesVisible light is a Visible light is a small portion of small portion of the spectrumthe spectrumTypes are Types are distinguished by distinguished by frequency or frequency or wavelengthwavelength

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Notes on The EM SpectrumNotes on The EM Spectrum

Radio WavesRadio WavesUsed in radio and television communication Used in radio and television communication systemssystems

MicrowavesMicrowavesWavelengths from about 1 mm to 30 cmWavelengths from about 1 mm to 30 cmWell suited for radar systemsWell suited for radar systemsMicrowave ovens are an applicationMicrowave ovens are an application

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Notes on the EM Spectrum, 2Notes on the EM Spectrum, 2

Infrared wavesInfrared wavesIncorrectly called Incorrectly called ““heat wavesheat waves””Produced by hot objects and moleculesProduced by hot objects and moleculesReadily absorbed by most materialsReadily absorbed by most materials

Visible lightVisible lightPart of the spectrum detected by the Part of the spectrum detected by the human eyehuman eyeMost sensitive at about 560 nm (yellowMost sensitive at about 560 nm (yellow--green)green)

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Notes on the EM Spectrum, 3Notes on the EM Spectrum, 3

Ultraviolet lightUltraviolet lightCovers about 400 nm to 0.6 nmCovers about 400 nm to 0.6 nmSun is an important source of uv lightSun is an important source of uv lightMost uv light from the sun is absorbed in the Most uv light from the sun is absorbed in the stratosphere by ozonestratosphere by ozone

XX--raysraysMost common source is acceleration of highMost common source is acceleration of high--energy electrons striking a metal targetenergy electrons striking a metal targetUsed as a diagnostic tool in medicineUsed as a diagnostic tool in medicine

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Notes on the EM Spectrum, Notes on the EM Spectrum, finalfinal

Gamma raysGamma raysEmitted by radioactive nucleiEmitted by radioactive nucleiHighly penetrating and cause serious Highly penetrating and cause serious damage when absorbed by living tissuedamage when absorbed by living tissue

Looking at objects in different portions Looking at objects in different portions of the spectrum can produce different of the spectrum can produce different informationinformation

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Example: talking to a Example: talking to a submarinesubmarine

The U.S. Navy has long proposed the construction of extremely loThe U.S. Navy has long proposed the construction of extremely loww--

frequency (ELF) communications systems; such waves could penetrafrequency (ELF) communications systems; such waves could penetrate te the oceans to reach distant submarines. Calculate the length of the oceans to reach distant submarines. Calculate the length of a quartera quarter--

wavelength antenna for a transmitter generating ELF waves of frewavelength antenna for a transmitter generating ELF waves of frequency quency 75 Hz. How practical is this?75 Hz. How practical is this?

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The U.S. Navy has long proposed the construction of extremely loThe U.S. Navy has long proposed the construction of extremely loww--frequency frequency (ELF) communications systems; such waves could penetrate the oce(ELF) communications systems; such waves could penetrate the oceans to reach ans to reach distant submarines. Calculate the length of a quarterdistant submarines. Calculate the length of a quarter--wavelength antenna for a wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practictransmitter generating ELF waves of frequency 75 Hz. How practical is this?al is this?

Given:

¼

wavelengthantennaf0

=75 Hz

Find:

L=?

First determine the wavelength, a forth of which will give us the length of an antenna

863.00 10 4.00 10 4000

75v m s m kmf Hz

λ ×= = = × =

The required length of antenna is then a quarter of this

4000 10004 4

kmL kmλ= = =

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Doppler Effect and EM WavesDoppler Effect and EM Waves

A Doppler Effect occurs for em waves, but A Doppler Effect occurs for em waves, but differs from that of sound wavesdiffers from that of sound waves

For sound waves, motion relative to a medium is For sound waves, motion relative to a medium is most importantmost important

For light waves, the medium plays no role since the light For light waves, the medium plays no role since the light waves do not require a medium for propagationwaves do not require a medium for propagation

The speed of sound depends on its frame of The speed of sound depends on its frame of referencereference

The speed of em waves is the same in all coordinate The speed of em waves is the same in all coordinate systems that are at rest or moving with a constant systems that are at rest or moving with a constant velocity with respect to each othervelocity with respect to each other

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Doppler Equation for EM Doppler Equation for EM WavesWaves

The Doppler effect for em wavesThe Doppler effect for em waves

ff’’ is the observed frequencyis the observed frequencyf is the frequency emitted by the sourcef is the frequency emitted by the sourceu is the u is the relative speedrelative speed between the source and the between the source and the observerobserverThe equation is valid only when u is much smaller The equation is valid only when u is much smaller than cthan c

' 1 uf fc

⎛ ⎞= ±⎜ ⎟⎝ ⎠ 2 2

1 /'1 /

u cf fu c

±=

−

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Doppler Equation, contDoppler Equation, cont

The positive sign is used when the object The positive sign is used when the object and source are moving and source are moving towardtoward each othereach otherThe negative sign is used when the object The negative sign is used when the object and source are moving and source are moving away fromaway from each each otherotherAstronomers refer to a Astronomers refer to a red shiftred shift when when objects are moving away from the earth objects are moving away from the earth since the wavelengths are shifted toward since the wavelengths are shifted toward the red end of the spectrumthe red end of the spectrum

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Chapter 26Chapter 26

RelativityRelativity

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A Brief Overview of Modern A Brief Overview of Modern PhysicsPhysics

2020thth Century revolutionCentury revolution1900 Max Planck1900 Max Planck

Basic ideas leading to Quantum theoryBasic ideas leading to Quantum theory

1905 Einstein1905 EinsteinSpecial Theory of RelativitySpecial Theory of Relativity

2121stst CenturyCenturyStory is still incompleteStory is still incomplete

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Basic ProblemsBasic Problems

The speed of every particle in the universe The speed of every particle in the universe always remains always remains less thanless than the speed of the speed of lightlightNewtonian Mechanics is a limited theoryNewtonian Mechanics is a limited theory

It places no upper limit on speedIt places no upper limit on speedIt is contrary to modern experimental resultsIt is contrary to modern experimental resultsNewtonian Mechanics becomes a specialized Newtonian Mechanics becomes a specialized case of Einsteincase of Einstein’’s Theory of Special Relativitys Theory of Special Relativity

When speeds are much less than the speed of lightWhen speeds are much less than the speed of light

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Galilean RelativityGalilean Relativity

Choose a Choose a frame of referenceframe of referenceNecessary to describe a physical eventNecessary to describe a physical event

According to Galilean Relativity, the According to Galilean Relativity, the laws of mechanics are the same in all laws of mechanics are the same in all inertial frames of referenceinertial frames of reference

An inertial frame of reference is one in An inertial frame of reference is one in which Newtonwhich Newton’’s Laws are valids Laws are validObjects subjected to no forces will move in Objects subjected to no forces will move in straight linesstraight lines

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Galilean Relativity Galilean Relativity ––

ExampleExample

A passenger in an A passenger in an airplane throws a airplane throws a ball straight upball straight up

It appears to move It appears to move in a vertical pathin a vertical pathThe law of gravity The law of gravity and equations of and equations of motion under motion under uniform acceleration uniform acceleration are obeyedare obeyed

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Galilean Relativity Galilean Relativity ––

Example, Example, contcont

There is a stationary There is a stationary observer on the observer on the groundground

Views the path of the Views the path of the ball thrown to be a ball thrown to be a parabolaparabolaThe ball has a The ball has a velocity to the right velocity to the right equal to the velocity equal to the velocity of the planeof the plane

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Galilean Relativity Galilean Relativity ––

Example, Example, conclusionconclusion

The two observers disagree on the shape of The two observers disagree on the shape of the ballthe ball’’s paths pathBoth agree that the motion obeys the law of Both agree that the motion obeys the law of gravity and Newtongravity and Newton’’s laws of motions laws of motionBoth agree on how long the ball was in the Both agree on how long the ball was in the airairConclusion:Conclusion: There is no preferred frame of There is no preferred frame of reference for describing the laws of reference for describing the laws of mechanicsmechanics

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Galilean Relativity Galilean Relativity –– LimitationsLimitations

Galilean Relativity does Galilean Relativity does notnot apply to experiments in apply to experiments in electricity, magnetism, optics, and other areaselectricity, magnetism, optics, and other areasResults do not agree with experimentsResults do not agree with experiments

The observer should measure the speed of the pulse as v+cThe observer should measure the speed of the pulse as v+cActually measures the speed as cActually measures the speed as c

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Luminiferous EtherLuminiferous Ether

1919thth Century physicists compared Century physicists compared electromagnetic waves to mechanical waveselectromagnetic waves to mechanical waves

Mechanical waves need a medium to support the Mechanical waves need a medium to support the disturbancedisturbance

The The luminiferous etherluminiferous ether was proposed as the was proposed as the medium required (and present) for light medium required (and present) for light waves to propagatewaves to propagate

Present everywhere, even in spacePresent everywhere, even in spaceMassless, but rigid mediumMassless, but rigid mediumCould have no effect on the motion of planets or Could have no effect on the motion of planets or other objectsother objects

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Verifying theVerifying the Luminiferous EtherLuminiferous Ether

Associated with an ether was Associated with an ether was an an absolute frameabsolute frame where the where the laws of e & m take on their laws of e & m take on their simplest formsimplest formSince the earth moves through Since the earth moves through the ether, there should be an the ether, there should be an ““ether windether wind”” blowingblowingIf v is the speed of the ether If v is the speed of the ether relative to the earth, the speed relative to the earth, the speed of light should have minimum of light should have minimum or maximum values depending or maximum values depending on its orientation to the on its orientation to the ““windwind””

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MichelsonMichelson--Morley ExperimentMorley Experiment

First performed in 1881 by Michelson First performed in 1881 by Michelson Repeated under various conditions by Repeated under various conditions by Michelson and MorleyMichelson and MorleyDesigned to detect small changes in the Designed to detect small changes in the speed of lightspeed of light

By determining the velocity of the earth By determining the velocity of the earth relative to the etherrelative to the ether

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MichelsonMichelson--Morley EquipmentMorley EquipmentUsed the Michelson Used the Michelson InterferometerInterferometerArm 2 is aligned along the Arm 2 is aligned along the direction of the earthdirection of the earth’’s s motion through spacemotion through spaceThe interference pattern The interference pattern was observed while the was observed while the interferometer was interferometer was rotated through 90rotated through 90°°The effect should have The effect should have been to show small, but been to show small, but measurable, shifts in the measurable, shifts in the fringe patternfringe pattern

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MichelsonMichelson--Morley EquipmentMorley Equipment

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MichelsonMichelson--Morley ResultsMorley Results

Measurements failed to show any change in Measurements failed to show any change in the fringe patternthe fringe pattern

No fringe shift of the magnitude required was ever No fringe shift of the magnitude required was ever observedobserved

Light is now understood to be an Light is now understood to be an electromagnetic wave, which requires no electromagnetic wave, which requires no medium for its propagationmedium for its propagation

The idea of an ether was discardedThe idea of an ether was discarded

The laws of electricity and magnetism are the The laws of electricity and magnetism are the same in all inertial framessame in all inertial frames