Physics 1202: Lecture 15 Tday s Agenda Annuncements: Team prblems tday Team 7: Cailin Catarina, Matthew Canapetti, Kervin Vincent Team 8: Natalie Kasir, Adam Antunes, Quincy Alexander Team 9: Garrett Schlegel, Jyce Nieh, Matthew Lmbard Hmewrk #7: due Mnday Midterm 1: Average = 70% Office hurs if needed (M-2:30-3:30 r TH 3:00-4:00) Chapter 25: E&M waves: Prductin/prperties Spectra Pwer & pressure Plarizatin Chap. 25 f( x f( x) x x z y 1
25-1: Generating E-M Waves Tw rds are cnnected t an ac surce, charges scillate between the rds (a) As scillatins cntinue, the rds becme less charged, the field near the charges decreases and the field prduced at t = 0 mves away frm the rd (b) The charges and field reverse (c) The scillatins cntinue (d) Because the scillating charges in the rd prduce a current, there is als a magnetic field generated As the current changes, the magnetic field spreads ut frm the antenna The magnetic field is perpendicular t the electric field Electrmagnetic Waves are Transverse Waves The E and B fields are perpendicular t each ther Bth fields are perpendicular t the directin f mtin Therefre, em waves are transverse waves The rati f the electric field t the magnetic field is equal t the speed f light 2
E & B in Electrmagnetic Wave Plane Harmnic Wave: where: y x z Nte: the directin f prpagatin is given by the crss prduct where are the unit vectrs in the (E,B) directins. Nthing special abut (E y,b z ); eg culd have (E y,-b x ) Nte cyclical relatin: Diple radiatin pattern prprtinal t sin(wt) scillating electric diple generates e-m radiatin that is plarized in the directin f the diple radiatin pattern is dughnut shaped & utward traveling zer amplitude directly abve and belw diple maximum amplitude in-plane 3
E & B Fields in EM wave Hw it lks like Receiving E-M Radiatin receiving antenna y x Speaker z One way t receive an EM signal is t use the same srt f antenna. Receiving antenna has charges which are accelerated by the E field f the EM wave. The acceleratin f charges is the same thing as an EMF. Thus a vltage signal is created. 4
Receiving E-M Radiatin Using LRC circuit Tune w fr a specific statin Fr that w, current is maximum: resnance Lp Antennas Magnetic Diple Antennas The electric diple antenna makes use f the basic electric frce n a charged particle Nte that yu can calculate the related magnetic field using Ampere s Law. We can als make an antenna that prduces magnetic fields that lk like a magnetic diple, i.e. a lp f wire. This lp can receive signals by expliting Faraday s Law. Fr a changing B field thrugh a fixed lp f area A: F B = A B 5
Review f Waves frm 1201 The ne-dimensinal wave equatin: has a general slutin f the frm: where h 1 represents a wave traveling in the +x directin and h 2 represents a wave traveling in the -x directin. A specific slutin fr harmnic waves traveling in the +x directin is: h l A A = amplitude l = wavelength f = frequency v = speed k = wave number x E & B in Electrmagnetic Wave Plane Harmnic Wave: where: y x z Frm general prperties f waves : Þ 6
25-2 The Prpagatin f EM Waves All electrmagnetic waves prpagate thrugh a vacuum at the same rate: In materials, such as air and water, light slws dwn, but at mst t abut half the abve speed Using tricks f quantum mechanics Can stp light in matter Mre when we talk abut mdern physics! Hw can yu determine c??? Determining c c is s large: very hard t measure first measurements in the late 1676 Danish astrnmer Ole R mer (1644 1710) while wrking at the Ryal Observatry in Paris timing the eclipses f the Jupiter mn I Lking at when I ges thrugh Jupiter s shadw 7
Determining c By timing the eclipses f the Jupiter mn I I takes 42.5 hurs t rbit Jupiter Rømer estimated that light wuld take abut 16 minutes t travel a distance equal t the diameter f Earth s rbit arund the Sun This wuld give light a velcity ~ 225,000 km/s Apprximate: need t accunt fr mtin f Jupiter as well but 1 st determinatin f finite speed fr light! Hipplyte Fizeau experiment 23 September 1819 18 September 1896 First labratry measurement f c In 1849, using a ray f light passing (r nt) thrugh a wheel with 720 ntches (turning up t 100 rev/sec.) Light reflected frm mirrr (8 km away) Fund c ~ 3.13 X 10 6 m/s (5% t large) 8
c? Q+++ - - - C i L Recall LC Circuits The energy is cnserved LC: current scillates When the capacitr is fully charged: i When the current is at maximum (I ): 0 t The maximum energy stred in the capacitr and in the inductr are the same: Energy is Stred in fields The energy density fr a parallel plate capacitr: The Electric field is given by: Þ A + + + + - - - - - d The energy density u in the field is given by: The energy density fr a lng slenid: The inductance L is: Energy U: l r N turns The energy density 9
Links between E & B In LC, maximum energy in C and L are equal If C and L have the same vlume: u E = u B E & B are related : Units: e 0 = 8.885 10 12 C 2 /Nm 2 µ 0 = 12.566 10 7 N/A 2 Mre abut c Units: e 0 = 8.885 10 12 C 2 /Nm 2 µ 0 = 12.566 10 7 N/A 2 [e 0 µ 0 ] = (C 2 /Nm 2 ) (N/A 2 )=(C 2 /m 2 ) (s 2 /C 2 )= s 2 / m 2 S [e 0 µ 0 ] = [1/v 2 ] We have Using values abve: c=299,276,596 m/s ~ 3X10 8 m/s and r 10
Velcity f Electrmagnetic Waves The wave equatin fr E x : (derived frm Maxwell s Eqn) Therefre, we nw knw the velcity f electrmagnetic waves in free space: Putting in the measured values fr µ 0 & e 0, we get: This value is identical t the measured speed f light! We identify light as an electrmagnetic wave. Dppler effect Like fr any ther wave Applies t electrmagnetic waves The speed f the waves in vacuum des nt change but as the bserver and surce mve with respect t ne anther, the frequency des change. 11
25-3: The EM Spectrum These EM waves can take n any wavelength frm angstrms t miles (and beynd). We give these waves different names depending n the wavelength. Gamma Rays X Rays Ultravilet Visible Light Infrared Micrwaves Shrt Wave Radi TV and FM Radi AM Radi Lng Radi Waves 10-14 10-10 10-6 10-2 1 10 2 10 6 10 10 Wavelength [m] The EM Spectrum Frms f EM waves exist that are distinguished by their frequencies and wavelengths c = ƒλ Wavelengths fr visible light range frm 400 nm t 700 nm There is n sharp divisin between ne kind f em wave and the next 12
Visible 33-1 Electrmagnetic Spectrum Waves Ntes n The EM Spectrum Radi Waves Used in radi and televisin cmmunicatin systems Generated by charges accelerating in cnducting wires Micrwaves Wavelengths frm abut 1 mm t 30 cm Generated by electrnic devices Well suited fr radar systems Micrwave vens are an applicatin Infrared waves Incrrectly called heat waves Prduced by ht bjects and mlecules Readily absrbed by mst materials Visible light Part f the spectrum detected by the human eye Mst sensitive at abut 560 nm (yellw-green) Prduced by rearrangement f electrns in atms and mlecules 13
Mre n the EM Spectrum Ultravilet light Cvers abut 400 nm t 0.6 nm Sun is an imprtant surce f uv light Mst uv light frm the sun is absrbed in the stratsphere by zne X-rays Mst cmmn surce is acceleratin f highenergy electrns striking a metal target Used as a diagnstic tl in medicine Gamma rays Emitted by radiactive nuclei Highly penetrating and cause serius damage when absrbed by living tissue Lking at bjects in different prtins f the spectrum can prduce different infrmatin Lecture 15, ACT 1 Cnsider yur favrite radi statin. I will assume that it is at 100 n yur FM dial. That means that it transmits radi waves with a frequency f=100 MHz. What is the wavelength f the signal? A) 3 cm B) 3 m C) ~0.5 m D) ~500 m 14
The EM Spectrum Each wavelength shws different details The EM Spectrum Each wavelength shws different details 15
Energy in EM Waves / review Electrmagnetic waves cntain energy which is stred in E and B fields: = Therefre, the ttal energy density in an e-m wave = u, where The Intensity f a wave is defined as the average pwer transmitted per unit area = average energy density times wave velcity: 25-4 Energy and Mmentum in Electrmagnetic Waves The energy a wave delivers t a unit area in a unit time is called the intensity. 16
25-4 Energy and Mmentum in Electrmagnetic Waves Substituting fr the energy density: An electrmagnetic wave als carries mmentum: Mmentum in EM Waves Electrmagnetic waves cntain mmentum: The mmentum transferred t a surface depends n the area f the surface. Thus Pressure is a mre useful quantity. If a surface cmpletely absrbs the incident light, the mmentum gained by the surface p We use the abve expressin plus Newtn s Secnd Law in the frm F=Dp/Dt t derive the fllwing expressin fr the Pressure, Þ If the surface cmpletely reflects the light, cnservatin f mmentum indicates the light pressure will be duble that fr the surface that absrbs. 17
Radiatin pressure Therefre, it exerts pressure, called the radiatin pressure: Radiatin pressure is respnsible fr the curvature f this cmet s dust tail. 25-5: Plarizatin f light Recall E&M wave y x z 22_all_imgs_in_ppt This is an example f linearly plarized light Electric field alng a fixed axis ( here y ) Mst light surce are nnplarized Electric field alng randm axis E 18
25-5 Plarizatin The plarizatin f an EM wave refers t the directin f its electric field Plarized light has its electric fields all in the same directin. Unplarized light has its electric fields in randm directins. 25-5 Plarizatin A beam f unplarized light can be plarized by passing it thrugh a plarizer It allws nly a particular cmpnent f the electric field t pass thrugh Here is a mechanical analg: 19
Plarizers Made f lng mlecules (plymers) Blck electric field alng their length Electric field perpendicular passes thrugh E E. H. Land (1909 1991): Plarid E S E after =E csq Recall that I ~ E 2 I = I 0 cs 2 q 25-5 Law f Malus Étienne-Luis Malus 23 July 1775 24 February 1812 French fficer in Naplen army Naplen Egypt expeditin: 1798 t 1801 Since the intensity f light is prprtinal t the square f the field, the intensity f the transmitted beam is given by the Law f Malus: The light exiting frm a plarizer is plarized in the directin f the plarizer. 20
25-5 Plarizatin Fr unplarized light passing thrugh a plarizer the transmitted intensity is half the initial intensity A plarizer and an analyzer can be cmbined 25-5 Plarizatin Scattering f light by atms/mlecules Unplarized light can be partially r cmpletely plarized atms/mlecules which act as small antennas If the light is already plarized, its transmissin will depend n its plarizatin. 2017 Pearsn Educatin, Inc. 21
25-5 Plarizatin This means that sunlight will be plarized, depending n the angle ur line f sight makes with the directin t the Sun. 25-5 Plarizatin Plarizatin can als ccur when light reflects frm a smth surface: 22
Recap f Tday s Tpic : Annuncements: Team prblems tday Team 7: Cailin Catarina, Matthew Canapetti, Kervin Vincent Team 8: Natalie Kasir, Adam Antunes, Quincy Alexander Team 9: Garrett Schlegel, Jyce Nieh, Matthew Lmbard Hmewrk #7: due Mnday Midterm 1: Average = 70% Office hurs if needed (M-2:30-3:30 r TH 3:00-4:00) Chapter 25: E&M waves: Prductin/prperties Spectra Pwer & pressure Plarizatin 23