electromagnetic waves chapter 4. 21.11 introduction: maxwell’s equations electricity and magnetism...

Electromagnetic WavesElectromagnetic Waves

Chapter 4Chapter 4

21.11 Introduction: 21.11 Introduction: Maxwell’s equationsMaxwell’s equations

Electricity and Electricity and magnetism were magnetism were originally thought to originally thought to be unrelatedbe unrelated

in 1865, James Clerk in 1865, James Clerk Maxwell provided a Maxwell provided a mathematical theory mathematical theory that showed a close that showed a close relationship between relationship between all electric and all electric and magnetic phenomenamagnetic phenomena

Maxwell’s Equations and Hertz’s

Discoveries

the line integral of the magnetic field around any closed path is the sum of μ0 times the net current through that path and μ0ε0 times the rate of change of electric flux through any surface bounded by that path.

Maxwell’s predictionsMaxwell’s predictions Electric field lines originate on positive charges and terminate on negative Electric field lines originate on positive charges and terminate on negative

chargescharges ElectricElectric field is produced by field is produced by chargescharges

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

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!!!

Maxwell’s PredictionsMaxwell’s Predictions If magnetic field can create electric field and vice versa, there is If magnetic field can create electric field and vice versa, there is

a very interesting phenomenon to be observeda very interesting 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 which in turn produces changing electric one (but: energy

conservation)conservation) … … which in turn produces changing magnetic field…which in turn produces changing magnetic field…

Maxwell concluded that visible light and all other Maxwell concluded that visible light and all other electromagnetic waves consist of fluctuating electric and electromagnetic waves consist of fluctuating electric and magnetic fields, with each varying field inducing the othermagnetic fields, with each varying field inducing the other

Maxwell calculated the speed of light to be 3x10Maxwell calculated the speed of light to be 3x1088 m/s m/s

Note: Charges and FieldsNote: Charges and Fields

StationaryStationary charges produce only charges produce only electric fieldselectric fields ChargesCharges in in uniform motionuniform motion (constant velocity) (constant velocity)

produce produce electricelectric and and magnetic fieldsmagnetic fields ChargesCharges 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 At any point, both fields reach their maximum

value at the same timevalue at the same time

Electromagnetic WavesElectromagnetic WavesEM 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.

Electromagnetic Waves are Electromagnetic Waves are Transverse WavesTransverse 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

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?

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

Properties of EM WavesProperties of EM Waves Electromagnetic waves are transverse wavesElectromagnetic waves are transverse waves Electromagnetic 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 Because em waves travel at a speed that is precisely the speed of light, of light, light is an electromagneticlight is an electromagnetic wave wave

812.99792 10

o o

c m s

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

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

B

Ec

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

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

o

2max

o

2max

o

maxmax

2

Bc

c2

E

2

BE

areaunitperpowerAverage

Properties of EM Waves, Properties of EM Waves, finalfinal

Electromagnetic waves transport Electromagnetic waves transport linear momentum as well as energylinear momentum as well 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 Radiation pressures can be

determined experimentallydetermined experimentally

The Spectrum of EM WavesThe Spectrum of EM Waves Forms of electromagnetic waves exist that Forms of electromagnetic waves exist that

are distinguished by their frequencies and are distinguished by their frequencies and wavelengthswavelengths

c = ƒλc = ƒλ

Wavelengths for visible light range from Wavelengths for visible light range from 400 nm to 700 nm400 nm to 700 nm

There 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

The EMThe EMSpectrumSpectrum

Note the overlap Note the overlap between types of between types of waveswaves

Visible light is a Visible light is a small portion of small portion of the spectrumthe spectrum

Types are Types are distinguished by distinguished by frequency or frequency or wavelengthwavelength

Notes on The EM SpectrumNotes on The EM Spectrum

Radio WavesRadio Waves Used in radio and television Used in radio and television

communication systemscommunication 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

Notes on the EM Spectrum, Notes on the EM Spectrum, 22

Infrared wavesInfrared waves Incorrectly called “heat waves”Incorrectly called “heat waves” Produced by hot objects and Produced by hot objects and

moleculesmolecules Readily absorbed by most materialsReadily absorbed by most materials

Visible lightVisible light Part of the spectrum detected by the Part of the spectrum detected by the

human eyehuman eye Most sensitive at about 560 nm Most sensitive at about 560 nm

(yellow-green)(yellow-green)

Notes on the EM Spectrum, Notes on the EM Spectrum, 33

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 Most uv light from the sun is absorbed in the

stratosphere by ozonestratosphere by ozone X-raysX-rays

Most common source is acceleration of high-Most common source is acceleration of high-energy electrons striking a metal targetenergy electrons striking a metal target

Used as a diagnostic tool in medicineUsed as a diagnostic tool in medicine

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

Gamma raysGamma rays Emitted by radioactive nucleiEmitted by radioactive nuclei Highly 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 Looking at objects in different

portions of the spectrum can produce portions of the spectrum can produce different informationdifferent information

Example: talking to a Example: talking to a submarinesubmarine

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?

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