Chapter 23 Electromagnetic Waves Lecture 14

Transcription

1 Chapter 23 Electrmagnetic Waves Lecture The Discvery f Electrmagnetic Waves 23.2 Prperties f Electrmagnetic Waves 23.3 Electrmagnetic Waves Carry Energy and Mmentum 23.4 Types f Electrmagnetic Radiatin: The Electrmagnetic Spectrum 23.5 Generatin and Prpagatin f Electrmagnetic Wave 23.6 Plarizatin 23.7 Dppler Effect

2 Electrmagnetic Thery Theretical understanding f electricity and magnetism Seemed cmplete by arund 1850 Culmb s Law and Gauss Law explained electric fields and frces Ampère s Law and Faraday s Law explained magnetic fields and frces The laws were verified in many experiments Intrductin

3 Unanswered Questins What was the nature f electric and magnetic fields? What is the idea f actin at a distance? Hw fast d the field lines assciated with a charge react t a mvement in the charge? James Clerk Maxwell studied sme f these questins in the mid-1800 s His wrk led t the discvery f electrmagnetic waves Intrductin

4 Discvery f EM Waves A time-varying magnetic field gives rise t an electric field A magnetic field can prduce an electric field Maxwell prpsed a mdificatin t Ampère s Law A time-varying electric field prduces a magnetic field This gives a new way t create a magnetic field Als gives equatins f electrmagnetism a symmetry clsed path B L I enclsed Sectin 23.1

5 Symmetry f E and B The crrect frm f Ampère s Law (due t Maxwell) says that a changing electric flux prduced a magnetic field. Since a changing electric flux can be caused by a changing E, there was an indicatin that a changing electric field prduces a magnetic field Faraday s Law says that a changing magnetic flux prduces an induced emf, and an emf is always assciated with an electric field Since a changing magnetic flux can be caused by a changing B, we can als say that a changing magnetic field prduces an electric field Sectin 23.1

6 Symmetry f E and B, cnt. Sectin 23.1

7 Electrmagnetic Waves Self-sustaining scillatins invlving E and B are pssible The scillatins are an electrmagnetic wave Electrmagnetic waves are als referred t as electrmagnetic radiatin Bth the electric and magnetic fields must be changing with time Althugh Maxwell wrked ut the details f em waves in great mathematical detail (Maxwell equatins), experimental prf f the existence f the waves wasn t carried ut until 1887 Sectin 23.1

8 Perpendicular Fields Accrding t Faraday s Law, a changing magnetic flux thrugh a given area prduces an electric field The directin f the electric field is perpendicular t the magnetic field that prduced it Similarly, the magnetic field induced by a changing electric field is perpendicular t the electric field that prduced it Sectin 23.1

9 Prperties f EM Waves An electrmagnetic wave invlves bth an electric field and a magnetic field These fields are perpendicular t each ther The prpagatin directin f the wave is perpendicular t bth the electric field and the magnetic field Sectin 23.1

10 EM Waves are Transverse Waves Imagine a snapsht f the electrmagnetic (em) wave The electric field is alng the x-axis The wave travels in the z-directin Determined by the right-hand rule #2 The magnetic field is alng the y-directin Because bth fields are perpendicular t the directin f prpagatin, the wave is a transverse wave Sectin 23.2

11 Light is an EM Wave Maxwell fund the speed f an em wave can be expressed in terms f tw universal cnstants (frm the Maxwell equatins) Permittivity f free space, ε Magnetic permeability f free space, μ The speed f an em wave is dented by c (frm the Maxwell equatins) Inserting the values f ε and μ, we btain c = 3.00 x 10 8 m/s! The value f the speed f an electrmagnetic wave is the same as the speed f light c Maxwell answered the questin f the nature f light it is an electrmagnetic wave He als shwed that the equatins f electricity and magnetism prvide the thery f light 1 Sectin 23.2

12 EM Waves in a Vacuum Remember that mechanical waves need a medium t travel thrugh Many physicists searched fr a medium fr em waves t travel thrugh EM waves can travel thrugh many materials, but they can als travel thrugh a vacuum All em waves travel with speed c thrugh a vacuum The frequency and wavelength are determined by the way the wave is prduced Sectin 23.2

13 EM Waves in Material Substances When an em wave travels thrugh a material substance, its speed depends n the prperties f the substance The speed f the wave is always less than c The speed f the wave depends n the wave s frequency Sectin 23.2

14 EM Waves Carry Energy An em wave carries energy in the electric and magnetic fields assciated with the wave Assume a wave interacts with a charged particle The particle will experience an electric frce Sectin 23.3

15 EM Waves Carry Energy, cnt. As the electric field scillates, s will the frce The electric frce will d wrk n the charge The charge s kinetic energy will increase Energy is transferred frm the wave t the particle The wave carries energy The ttal energy per unit vlume is the sum f its electric and magnetic energies u ttal = u elec + u mag 1 2 uelec E, Eq and umag B, Eq Sectin 23.3

16 EM Waves Carry Energy, final As the wave prpagates, the energies per unit vlume scillate It turns ut that the electric and magnetic energies are equal, and this leads t the prprtinality between the peak electric and magnetic fields u 1 1 E 2 2 E elect 2 2 u c B mag B c 1 2 uelec E, Eq and umag B, Eq Sectin 23.3

17 Intensity f an EM Wave The strength f an em wave is usually measured in terms f its intensity SI unit is W/m 2 Intensity is the amunt f energy transprted per unit time acrss a surface f unit area Intensity als equals the energy density multiplied by the speed f the wave I = u ttal c = ½ ε c E 2 Since E = c B, the intensity is als prprtinal t the square f the magnetic field amplitude I u E B ttal c ce cb c E c B Sectin 23.3

18 Slar Cells The intensity f sunlight n a typical sunny day is abut 1000 W/m² A slar cell cnverts the energy frm sunlight int electrical energy Current phtvltaic cells capture nly abut 15% f the energy that strikes them Als must accunt fr nights and cludy days Making better and mre practical slar cells is an imprtant engineering challenge Sectin 23.3

19 EM Waves Carry Mmentum An electrmagnetic wave has n mass, but it des carry mmentum Cnsider the cllisin shwn The mmentum is carried by the wave befre the cllisin and by the particle after the cllisin Sectin 23.3

20 EM Waves Carry Mmentum, cnt. The absrptin f the wave ccurs thrugh the electric and magnetic frces n charges in the bject When the charge absrbs an electrmagnetic wave, there is a frce n the charge in the directin f prpagatin f the riginal wave The frce n the charge is related t the charge s change in mmentum: F B = Δp / Δt Accrding t cnservatin f mmentum, the final mmentum n the charge must equal the initial mmentum f the electrmagnetic wave The mmentum f the wave is p = E ttal / c Sectin 23.3

21 Radiatin Pressure When an electrmagnetic wave is absrbed by an bject, it exerts a frce n the bject The ttal frce n the bject is prprtinal t its expsed area Radiatin pressure is the electrmagnetic frce divided by the area radiatin This can als be expressed P in terms f the intensity P radiatin F A F A P F F L radiatin Wrk uttal I A A L Vlume c I c I uttal c Sectin 23.3

22 Electrmagnetic Spectrum All em waves travel thrugh a vacuum at the speed c c = x 10 8 m/s ~ 3.00 x 10 8 m/s c is defined t have this value and the value f a meter is derived frm this speed Electrmagnetic waves are classified accrding t their frequency and wavelength The wave equatin is true fr em waves: c = ƒ λ The range f all pssible electrmagnetic waves is called the electrmagnetic spectrum Sectin 23.4

23 Light is an Electrmagnetic Wave f c Figure 23-8 p797

24 Radi Waves Frequencies frm a few hertz up t abut 10 9 hertz Crrespnding wavelengths are frm abut 10 8 meters t a few centimeters Parallel wires can act as an antenna The AC current in the antenna is prduced by time-varying electric fields in the antenna This then prduces a time-varying magnetic field and the em wave As the current scillates with time, the charge is accelerated In general, when an electric charge is accelerated, it prduces electrmagnetic radiatin Sectin 23.4

25 Micrwaves Micrwaves have frequencies between abut 10 9 Hz and Hz Crrespnding wavelengths are frm a few cm t a few tenths f a mm Micrwave vens generate radiatin with a frequency near 2.5 x 10 9 Hz The micrwave energy is transferred t water mlecules in the fd, heating the fd Sectin 23.4

26 Infrared Infrared radiatin has frequencies frm abut Hz t 4 x Hz Wavelengths frm a few tenths f a mm t a few micrns We sense this radiatin as heat Als useful fr mnitring the Earth s atmsphere Sectin 23.4

27 Visible Light Frequencies frm abut 4 x10 14 Hz t 8 x10 14 Hz Wavelengths frm abut 750 nm t 400 nm The clr f the light varies with the frequency Lw frequency; high wavelength red High frequency; lw wavelength blue The speed f light inside a medium depends n the frequency f the radiatin The effect is called dispersin White light is separated int different clrs Sectin 23.4

28 Dispersin Example Sectin 23.4

29 Ultravilet Ultravilet (UV) light has frequencies frm abut 8 x Hz t Hz Crrespnding wavelengths are abut 3 nm t 400 nm UV radiatin stimulates the prductin f vitamin D in the bdy Excessive expsures t UV light can cause sunburn, skin cancer and cataracts Sectin 23.4

30 X-Rays Frequencies frm abut Hz t abut Hz Discvered by Wilhelm Röntgen in 1895 X-rays are weakly absrbed by skin and ther sft tissue and strngly absrbed by dense material such as bne, teeth, and metal In the 1970 s CT (CAT) scans were develped Sectin 23.4

31 X-Ray Example Sectin 23.4

32 CT Scan With a single X-ray image, there will always be parts f the persn s bdy that are bscured Images can be taken frm different angles A CT scan takes many X- ray images at many different angles Cmputer analysis is used t cmbine the images int a three-dimensinal representatin f the bject Sectin 23.4

33 Gamma Rays Gamma rays are the highest frequency electrmagnetic waves, with frequencies abve Hz Wavelengths are less than m Gamma rays are prduced by prcesses inside atmic nuclei They are prduced in nuclear pwer plants and in the Sun Gamma rays als reach us frm utside the slar system Sectin 23.4

34 Astrnmy and EM Radiatin Different applicatins generally use different wavelengths f em radiatin Astrnmy uses virtually all types f em radiatin The pictures shw the Crab Nebula at varius wavelengths Clrs indicate intensity at each wavelength Sectin 23.4