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General Physics (PHY 2140)

Lecture 22Lecture 22 Electricity and Magnetism

Electromagnetic wavesPropertiesSpectrum

Chapter 21

http://www.physics.wayne.edu/~apetrov/PHY2140/

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Lightning ReviewLightning Review

Last lecture:

1.1. AC circuitsAC circuits Resistors, capacitors, inductors in ac circuitsResistors, capacitors, inductors in ac circuits Power in an AC circuitPower in an AC circuit Resonance in a RLC circuitResonance in a RLC circuit

Review Problem: The light bulb has a resistance R, and the emf drives the circuit with a frequency .The light bulb glows most brightly at

1. very low frequencies.2. very high frequencies.3. the frequency

22L CZ R X X

tan L CX X

R

0

1

2f

LC

1, 2

2C LX X fLfC

1 LC

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Reminder (for those who don’t read Reminder (for those who don’t read syllabussyllabus))

Reading Quizzes (bonus 5%):

It is important for you to come to class prepared, i.e. be familiar with the material to be presented. To test your preparedness, a simple five-minute quiz, testing your qualitative familiarity with the material to be discussed in class, will be given at the beginning of some of the classes. No make-up reading quizzes will be given.

There could be one today… … but then again…

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21.11 Introduction: Maxwell’s equations21.11 Introduction: Maxwell’s equations

Electricity and magnetism Electricity and magnetism were originally thought to be were originally thought to be unrelatedunrelatedin 1865, James Clerk Maxwell in 1865, James Clerk Maxwell provided a mathematical provided a mathematical theory that showed a close theory that showed a close relationship between all relationship between all electric and magnetic electric and magnetic phenomenaphenomena

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Maxwell’s predictionsMaxwell’s predictions

Electric field lines originate on positive charges and terminate on Electric field lines originate on positive charges and terminate on negative chargesnegative charges

ElectricElectric field is produced by field is produced by chargescharges

Magnetic field lines always form closed loops – they do not begin or Magnetic field lines always form closed loops – they do not begin or end anywhereend anywhere

MagneticMagnetic filed is produced by currents ( filed is produced by currents (moving chargesmoving charges))

A varying magnetic field induces an emf and hence an electric field A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)(Faraday’s Law)

ElectricElectric field is also produced by field is also produced by changing magnetic fieldchanging magnetic field

Magnetic Magnetic field is also produced byfield is also produced by changing electric field. changing electric field.

Question:Question: is there a is there a symmetrysymmetry between electric and magnetic fields, between electric and magnetic fields, i.e. can i.e. can magnetic fieldmagnetic field be produced by be produced by changing electric fieldchanging electric field??????

Maxwell: YES!!!

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Maxwell’s PredictionsMaxwell’s Predictions

If magnetic field can create electric field and vice versa, there is a very If magnetic field can create electric field and vice versa, there is a very interesting phenomenon to be observedinteresting phenomenon to be observed

Changing electric field produces magnetic field…Changing electric field produces magnetic field… … … which in turn produces changing electric one (but: energy conservation)which in turn produces changing electric one (but: energy conservation) … … which in turn produces changing magnetic field…which in turn produces changing magnetic field…

Maxwell concluded that visible light and all other electromagnetic Maxwell concluded that visible light and all other electromagnetic waves consist of fluctuating electric and magnetic fields, with each waves consist of fluctuating electric and magnetic fields, with each varying field inducing the othervarying field inducing the otherMaxwell calculated the speed of light to be 3x10Maxwell calculated the speed of light to be 3x1088 m/s m/s

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Note: Charges and FieldsNote: Charges and Fields

StationaryStationary charges produce only charges produce only electric fieldselectric fieldsChargesCharges in in uniform motionuniform motion (constant velocity) produce (constant velocity) produce electricelectric and and magnetic fieldsmagnetic fieldsChargesCharges that are that are acceleratedaccelerated produce produce electric and electric and magnetic fields and electromagnetic wavesmagnetic fields and electromagnetic waves

These fields are These fields are in phasein phase At any point, both fields reach their maximum value at the same At any point, both fields reach their maximum value at the same

timetime

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Electromagnetic WavesElectromagnetic Waves

EM waves can be produced by an antenna, which is just some kind of wire that is connected to an ac source.  The ac source produces oscillating + and - charges which set up electric field (due to the separation of charge) and a magnetic field (due to the current in the wire).

Note that the electric and magnetic fields are perpendicular to each other.  This field begins to move away from the antenna and in a little while the ac source has caused the situation to reverse.

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Electromagnetic Waves are Transverse WavesElectromagnetic Waves are Transverse Waves

TheThe E E and and BB fields are fields are perpendicularperpendicular to each other to each other

Both fields are perpendicular to Both fields are perpendicular to the direction of motionthe direction of motion

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

1 LC

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Review problem: car radioReview problem: car radio

An An RLC RLC circuit is used to tune a radio to an FM station broadcasting at 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 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? 1.40 pF. What inductance should be present in the circuit?

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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 C = 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 1or

42f L

f CLC

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

6

22 3 12

12.29 10

4 88.9 10 1.40 10L H

Hz F

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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 lightElectromagnetic waves travel at the speed of light

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

812.99792 10

o o

c m s

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The sun is about 1.5x10The sun is about 1.5x101111 m from the earth.  How long does it take light to m from the earth.  How long does it take light to get here? get here?

11

8

distance 1.5 10500 sec 8.3 min

time 3 10

mt

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

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

B

Ec

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

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

o

2max

o

2max

o

maxmax

2

Bc

c2

E

2

BE

areaunitperpowerAverage

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Properties of EM Waves, finalProperties of EM Waves, final

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

For complete absorption of energy U, For complete absorption of energy U,

p=U/cp=U/c For complete reflection of energy U, For complete reflection of energy U,

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

Radiation pressures can be determined experimentallyRadiation pressures can be determined experimentally

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Determining Radiation PressureDetermining Radiation Pressure

This is an apparatus for This is an apparatus for measuring radiation pressuremeasuring radiation pressureIn practice, the system is In practice, the system is contained in a vacuumcontained in a vacuumThe pressure is determined by The pressure is determined by the angle at which equilibrium the angle at which equilibrium occursoccurs

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The Spectrum of EM WavesThe Spectrum of EM Waves

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

c = ƒλc = ƒλ

Wavelengths for visible light range from 400 nm to 700 nmWavelengths for visible light range from 400 nm to 700 nmThere is no sharp division between one kind of em wave There is no sharp division between one kind of em wave and the nextand the next

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The EMThe EMSpectrumSpectrum

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

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Notes on The EM SpectrumNotes on The EM Spectrum

Radio WavesRadio Waves Used in radio and television communication systemsUsed in radio and television communication systems

MicrowavesMicrowaves Wavelengths from about 1 mm to 30 cmWavelengths from about 1 mm to 30 cm Well suited for radar systemsWell suited for radar systems Microwave 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 waves Incorrectly called “heat waves”Incorrectly called “heat waves” Produced by hot objects and moleculesProduced by hot objects and molecules Readily absorbed by most materialsReadily absorbed by most materials

Visible lightVisible light Part of the spectrum detected by the human eyePart of the spectrum detected by the human eye Most sensitive at about 560 nm (yellow-green)Most sensitive at about 560 nm (yellow-green)

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

Ultraviolet lightUltraviolet light Covers about 400 nm to 0.6 nmCovers about 400 nm to 0.6 nm Sun is an important source of uv lightSun is an important source of uv light Most uv light from the sun is absorbed in the stratosphere by ozoneMost uv light from the sun is absorbed in the stratosphere by ozone

X-raysX-rays Most common source is acceleration of high-energy electrons striking a Most common source is acceleration of high-energy electrons striking a

metal targetmetal target Used as a diagnostic tool in medicineUsed as a diagnostic tool in medicine

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Notes on the EM Spectrum, finalNotes on the EM Spectrum, final

Gamma raysGamma rays Emitted by radioactive nucleiEmitted by radioactive nuclei Highly penetrating and cause serious damage when absorbed Highly penetrating and cause serious damage when absorbed

by living tissueby living tissue

Looking at objects in different portions of the spectrum Looking at objects in different portions of the spectrum can produce different informationcan produce different information

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Example: talking to a submarineExample: talking to a submarine

The U.S. Navy has long proposed the construction of extremely low-The U.S. Navy has long proposed the construction of extremely low-frequency (ELF) communications systems; such waves could penetrate frequency (ELF) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency wavelength antenna for a transmitter generating ELF waves of frequency 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 low-frequency The U.S. Navy has long proposed the construction of extremely low-frequency (ELF) communications systems; such waves could penetrate the oceans to reach (ELF) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this?transmitter generating ELF waves of frequency 75 Hz. How practical 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 400075

v m sm km

f Hz

The required length of antenna is then a quarter of this

40001000

4 4

kmL km