PHY2049: Chapter 302Chapter 30: Electromagnetic InductionPHY2049: Chapter 303SubjectsÎInduced emfFaraday’s law (law #3 of electricity and magnetism)Lenz’s lawMotional emfÎInductanceÎRL circuitsÎMagnetic energyÎGenerators, transformersPHY2049: Chapter 304Electric flux∫⋅= AdBΦrrB∫⋅= AdEΦrrMagnetic fluxSurface defined by a conductive loopClosed surface (Gaussian surface)(N m2/C)(T m2)Units: 1 T m2 = 1 weber = 1 WbθBAΦ cosB=if Bis uniform and surface is flat.Magnetic FluxPHY2049: Chapter 305Faraday’s Law (Law #3 of E&M)dtΦdNBε −=emfÎ To avoid errorsUse Faraday’s law to calculate only the magnitude of emfUse Lenz’s law to find the direction# of turns of the loopFlux through the loopPHY2049: Chapter 306Î Same as the negative sign in Faraday’s law Lenz’s law: Direction of induced emf is such that resulting current opposes change in ФB.Î Let’s examine three ways to change ФBthrough a coil Change B Change area of the coil (motional emf) Change angle θ of the coil with respect to B (motional emf) – principle of the generatorLenz’s LawPHY2049: Chapter 307Q1 Is the induced emf and current clockwise or counterclockwise?Q2 What does the ammeter read, when the magnet is held in place?ClockwiseZeroQ3 What happens while the magnet is being pulled back?Counterclockwise emf and currentQ4 What happens if the S pole of the magnet is pushed toward the loop?Counterclockwise emf and currentChanging BNSPHY2049: Chapter 308B field points into screen. Is induced emfclockwise or couterclockwise?Changing AreavPHY2049: Chapter 309Another ExampleÎWhat is the direction of induced emf?(a) Clockwise(b) Counterclockwise(c) No emfIpullRHR #2RHR #3 and LenzPHY2049: Chapter 3010Î Current i due to emf receives force from BÎ Force required to pull the loopÎ Power (work per time) required to pull the loopÎ Power dissipated in the wire as heat iLBF=iLBF=reqMotional emf and Energy Agrees!LvBε =||Riε ||=()()()RLvBvFFP2reqreqreqtimedistance===()RLvBRRLvBRiP222diss===FiiPHY2049: Chapter 3011Electric Power Generation… when Faraday was endeavouring to explain to Gladstone (Chancellor of the Exchequer) and several others an important new discovery in science, Gladstone's only commentary was “but, after all, what use is it?” “Why, sir,” replied Faraday, “there is every probability that you will soon be able to tax it!”W. E. H. Lecky, Democracy and Liberty (Longmans Green, London,
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