Exam Review MTE3Phys208MTE 3 Wed Nov 28 5:30-7pm Ch 2103!Alternate exams: Wed 6:30-8:00pm in Ch 2103 and Thu 5:30-7:00pm in the Lab room!Contents:!Ampere’s Law (32.6)!Faraday’s Law (ch 33, no Inductors 33.8, no LC Circuits 33.9, LR Circuits 33.10)!Maxwell equations (ch 34, no 34.2)!EM waves (34.6-7)!Polarization (34.8)!Photoelectric effect (38.1-2-3)!Matter waves and De Broglie wavelength (38.4)!Atom (37.6, 37.8, 38.5-7)!Wave function and uncertainty (Ch 39)23Ampere’s law! B • ds"=µoIExample: field produced by an infinitelylong wire! B " ds = B2#a =µ0I$Example: infinite solenoidlBdsBdd1path 1path=! ! !="=" sBsBNIBdoµ==!" lsBRemember last lecture Faraday’s Law4! "= E • ds#= $ddt%B= $ddtB#• dAMagnetic flux through surface bounded by pathIntegral over closed pathE is not conservative!!! ! E • dsLenz lawIf N loops with same area:! "= #Nd$Bdtchanging the magnetic flux51) Magnetic flux change: the magnitude of B changes in time2) the area crossed by B lines changes with t (motional emf)3) The angle ! between B and normal to loop changes with tflux increasesflux decreases12/09/2002 U. Wisconsin, Physics 208, Fall 2006 6AnswerCode:123Ampere’s / Faraday’s & Lenz’s lawsX BB flux increasessince B = µ0I/(2"r)and the loop goes towards smaller rvaluesLoop moving in a B-field and Lenz law7http://physics.bu.edu/~duffy/semester2/c19_quiz.htmlA rectangular loop of wire is pulled at a constant velocity from a region of zero magnetic field into a region of a uniform magnetic field. When the loop enters the field region the current induced in the wire A) will be zeroB) will be ccw C) will be cw vIindx! I ="R=d#Bdt= BLdxdt= BLvL12/09/2002 U. Wisconsin, Physics 208, Fall 2006 8Ampere-Maxwell’s lawABCBE9The 4 Maxwell’s Equations! E " dA =q#0S$ (Gauss' Law) B " dA = 0S$ E " ds = %d&Bdt (Faraday - Henry) B" dsL$=µ0I + L$µ0#0d&Edt (Ampere - Maxwell law)!Currents create a magnetic field!A changing electric field can create a magnetic fieldcharged particles create an electric field An electric field can be created by a changing magnetic fieldConsequence: induced currentThere are no magnetic monopolesLorentz force! F = q(E + v " B)• E and B are perpendicular oscillating vectors•The direction of propagation is perpendicular to E and B#Facts on EM waves!EM waves are solutions of Maxwell’s equations.! In empty space: sinusoidal wave propagating along x with velocity!E = Emax cos (kx – $t) !B = Bmax cos (kx – $t)E ! B = 0E x B direction of cTransverse wavesIn many kitchens, a microwave oven is used to cook food. The frequency of the microwaves is of the order of 1010 Hz. The wavelengths of these microwaves are on the order of (a) kilometers (b) meters (c) centimeters (d) micrometersQuick Quiz on EM spectrum! "= c / f =3 #108m / s1010/ s= 3cmE-B relationship (important!)!You measure the amplitude of the electric field for an electromagnetic plane wave to be E1, and the amplitude of the magnetic field to be B1. If the wave is adjusted so that the amplitude of the electric field is now 2E1, the amplitude you will measure for the magnetic field will be !a) 2B1, !b) 4B1, !c) B1/2, !d) B1/4, !e) the amplitude of the magnetic field is independent of the amplitude of the electric field. 12!(a). The amplitude of the magnetic and electric field are related through this equation: (Emax/Bmax) = c. Therefore, if the electric field amplitude increases by a factor of two, so must the magnetic field amplitude since c is constant.Quick Quiz on EM wavesxzycEBEnergy carried by EM waves! uE=12"0E2= uB=B22µ0=E22c2µ0!Total instantaneous energy density of EM waves u =uE + uB = 1/2 %oE2 + B2 /(2µo)!Since B = E/c andIn a given volume, the energy is shared equally by the two fields! uE= uB! Pav=Uav"t=uavAL"t= uavAcRadiation properties!This is the power per unit area (J/s.m2 = W/m2)! Iav=PavA= uavcI & E2E/B=c! prad=FA=Power / Ac=Ic!Complete absorption on a surface: total transported energy U in time interval 't ( total momentum p = U / c and prad=Sav/c!Perfectly reflecting surface: momentum of incoming and reflected light p = U/c ( total transferred momentum p = 2U/c and prad = 2Sav/cWhich of the following is constant for a plane electromagnetic wave? (a) magnitude of the Poynting vector (b) energy density uE (c) energy density uB (d) wave intensityQuick Quiz on Poynting vectorAnswer: (d). The first three choices are instantaneous values and vary in time. The wave intensity is an average over a full cycle. ! uE=12"0E2! uB=B22µ0! S =EBµ0=E2cµ0Measuring Radiation Pressure: QuizHigh vacuumIn the apparatus in the figure, suppose the black disk is replaced by one with half the radius. Which of the following are different after the disk is replaced? (a) radiation pressure on the disk; (b) radiation force on the disk; (c) radiation momentum delivered to the disk in a given time interval.Answer:A. (a)B. (b)C. (b),(c)D. NoneAnswer!(b), (c). !(a) The radiation pressure P = S / c does not change because pressure is force per unit area. !(b) the smaller disk absorbs less radiation, resulting in a smaller force (F = P x A)!(c) For the same reason, the momentum delivered to the disk in 't is reduced.! F ="p"tPolarization by selective absorptiontransmission axisPolaroid sheetLong-chain hydrocarbon moleculesIf linearly polarized light of intensity I0 passes through a polarizing filter with transmission axis at an angle ! along yEinc = E0sin! i + E0 cos! jAfter the polarizer Etransm = E0cos! jSo the intensity transmitted isItransm = E02 cos2! = )0cos2!yx!E0cos!If upolarized light of intensity I0 passes through it the intensity becomes I0/2Question on PolarizationCircularly polarized light of amplitude Ei crosses 3 polarizers.What is the ratio If/Ii?Polarizer 1 passes the component along the transmission axis that has amplitude Ei. In the region between 1 and 2 the field oscillates up and down along the first polarizer axis and it is linearly polarized.After 2 only the component Eicos($2-$1) and after 3:Eicos($2-$1) cos($3-$2)) => If/Ii =1/2 cos2($2-$1) cos2($3-$2)What happens if light were linearly polarized initially?How many green photons are in a flash of 't =1 ms of power P = 4x10-14 Watt?Green photons: # = 500 nm, E = hc/# = 2.5 eV A. 10 photonsB. 100 photonsC. 1,000 photonsD. 10,000 photonsNumber of photons and Intensity•The intensity of the beam can be increased by increasing the number of photons/second.•Photons/second = energy/second
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