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UW-Madison PHYSICS 107 - PHYSICS 107 Lecture Notes

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From Last Time…The electric force and fieldWork and VoltageMagnetic fields are from currentsCurrents in a permanent magnetMagnetic ForceFaraday’s law of induction and Lenz’s LawAmperes Law and LightMaxwell’s unificationProperties of EM WavesTypes of EM wavesSizes of EM wavesQuestionProducing EM WavesResonatorsEventually transatlantic signals!But wait… there’s moreApplications: Magnets for MRILarge scale applicationsWave effects in EM radiationEM version of Doppler shift: the red shiftInterference: Key IdeaInterference RequirementsInterference of light wavesDestructive interferenceInterference: secondary maximaResulting diffraction patternHertz’s measurement: the speed of electromagnetic wavesPhy107 Fall 20061From Last Time…•Charges and currents•Electric and magnetic forces•Work, potential energy and voltageToday…Electric fields, magnetic fields, and their unification and lightPhy107 Fall 20062The electric force and field++Force on this charge……due to this charge+++Q1Q2€ F =kq1q2r2€ E =kQr2•Charge q1 can exert a force on any number of charges. Would like to understand just the part from q1.€ F = EqPhy107 Fall 20063Work and Voltage+€ KE =12mv2•The work we do to move charge q2 from far away to near charge q1 can converted to kinetic energy++€ W =kq1q2r€ V =kQr€ W → PE → KE•We may want to do the same exercise with many charges. For instance a flow of charges that then go to your house to provide energy.€ W = qV → KEPhy107 Fall 20064Magnetic fields are from currentsIron filings align with magnetic field linesField direction follows right-hand-rulePhy107 Fall 20065Currents in a permanent magnet•Magnetic field from a permanent magnet arises from microscopic circulating currents.•Primarily from spinning electronsPhy107 Fall 20066Magnetic Force•What does the magnetic force act on?–Electric field is from a charge and exerts a force on other charges–Magnetic field is from a moving charge and exerts a force on other moving charges!•Magnetic field B•Magnetic force F = qvB–F perpendicular to both v and BPhy107 Fall 20067Faraday’s law of inductionand Lenz’s Law•A changing(moving) magnetic field causes a current in a metal. However, electric fields are what causes electrons to move in a metal•Changing magnetic fields produce electric fields•The current produces a magnetic field, which repels the bar magnetPhy107 Fall 20068Amperes Law and Light•Finally: Changing electric fields cause magnetic fields!•Electric fields are from charges•Magnetic fields are from moving charges•Changing Magnetic fields cause Electric fields•Changing Electric fields cause Magnetic fields•All this was expressed in Maxwell’s equations•Maxwell and others realized that a changing magnetic/electric field could cause a changing magnetic/ electric field. The condition for one to cause the other and vice-versa was for the two to change in a sin wave pattern and move at the velocity of light!Phy107 Fall 20069Maxwell’s unification•Intimate connection between electricity and magnetism•Time-varying magnetic field induces an electric field (Faraday’s Law)•Time-varying electric field generates a magnetic fieldThis is the basis of Maxwell’s unification of electricity and magnetism into Electromagnetism € r ∇ ×r E = −1c∂r B ∂tr ∇ ×r B = 1c∂r E ∂tIn vacuum:Phy107 Fall 200610Properties of EM Waves•Has all properties of a wave: wavelength, frequency, speed•At a fixed location, electric and magnetic fields oscillate in time. •Electric and magnetic fields in the wave propagate in empty space at the wave speed.•Electric and magnetic fields are perpendicular to propagation direction: a transverse wave.•Propagation speed c = 3 x 108 m/s (186,000 miles/second!)Phy107 Fall 200611Types of EM wavesWe are familiar with many different wavelengths of EM wavesAll are the same phenomenaPhy107 Fall 200612Sizes of EM waves•Visible light has a typical wavelength of500 nm = 500 x 10-9 m = 0.5 x 10-6 m = 0.5 microns (µm)•A human hair is roughly 50 µm diameter–100 wavelengths of visible light fit in human hair•A typical AM radio wave has a wavelength of 300 meters!•It’s vibration frequency is f = c / = 3x108 m/s / 300 m = 1,000,000 cycles/s = 1 MHz•AM 1310, your badger radio network, has a vibration frequency of 1310 KHz = 1.31 MHzPhy107 Fall 200613QuestionAM 1310, your badger radio network, has a vibration frequency of 1310 KHz = 1310 x 103 Hz = 1.31 x 106 HzIt travels at 3 x 108 m / s. What is it’s wavelength?A. 230 metersB. 2.3 metersC. 0.0043 metersD. 4.3 metersPhy107 Fall 200614Producing EM Waves+- Accelerating electrical current generates a wave that travels through space.Lightning / spark produces electromagnetic wave.Wave consists of oscillating electric and magnetic fields.Phy107 Fall 200615Resonators•TransmitterTransmitterThe balls and rods formed an electrically resonant circuitSpark initiated oscillations at resonant freuquency ~ 1 MHzReceiverResonantly tuned to pick up the transmitted signalPhy107 Fall 200616Eventually transatlantic signals!Gulgielmo Marconi’s transatlantic transmitterCapacitor banksInduction coilsSpark gapPhy107 Fall 200617But wait… there’s more•Energy can be stored in the field. •Energy density proportional to(Electric field)2(Magnetic field)2•Makes sense since light clearly has some energy in it. Light can heat things up. Also using a solar sail(sail to catch all the light that hits it) you can be sped up by absorbing the momentum of the light.•Finally electromagnetism propagates at the speed of light. Light seems to be what causes electric and magnetic fields!Phy107 Fall 200618Applications: Magnets for MRI•Magnetic Resonance Imaging typically done at 1.5 T•Superconducting magnet to provides static magnetic field•Detects a small magnetic field from Hydrogen atoms in water that align with the field.Phy107 Fall 200619Large scale applicationsProposed ITER fusion test reactorSuperconducting magnetPlasma confinement torusPhy107 Fall 200620Wave effects in EM radiation•Same properties as sound waves: common to all waves.•Doppler shift: change in light frequency due to motion of source or observer•Interference: superposition of light waves can result in either increase or decrease in brightness.Phy107 Fall 200621EM version of Doppler shift:the red shift•If a star is moving away from us, the light from that star will be shifted to


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UW-Madison PHYSICS 107 - PHYSICS 107 Lecture Notes

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