Lightning ReviewReview 1: right hand ruleReview 2: EMF polarity and current direction20.4 Lenz’s law revisitedLenz’s law: energy conservationExample: direction of the currentApplications of Magnetic Induction20.5 GeneratorsAC generatorAC generator (cont)DC generatorMotorsExample: coil in magnetic field20.6 Eddy currents (application)1110/10/200310/10/2003General Physics (PHY 2140)Lecture 17Lecture 17¾ Electricity and Magnetism9Induced voltages and induction9Lenz’s law9Generators and motorsChapter 20http://www.physics.wayne.edu/~apetrov/PHY2140/2210/10/200310/10/2003Lightning ReviewLightning Review0BnIµ=Last lecture:1.1.Induced voltages and inductionInduced voltages and induction99Induced EMFInduced EMF99Faraday’s lawFaraday’s law99Motional EMFcosBAθΦ=Nt∆Φ=−∆EMotional EMFBlv=EReview Problem: A long, straight wire carries a steady current I. A rectangular conducting loop lies in the same plane as the wire, with two sides parallel to the wire and two sides perpendicular. Suppose the loop is pushed toward the wire as shown. Given the direction of I, the induced current in the loop is1. clockwise.2. counterclockwise.3. need more information3310/10/200310/10/2003Review 1: right hand ruleReview 1: right hand rule4410/10/200310/10/2003Review 2: EMF polarity and current directionReview 2: EMF polarity and current direction-+Current flows from + to Current flows from + to ––terminal of the battery (source of EMF)terminal of the battery (source of EMF)Electrons move in the opposite direction.5510/10/200310/10/200320.4 Lenz’s law revisited20.4 Lenz’s law revisitedApplication of Lenz's law will tell Application of Lenz's law will tell us the direction of induced us the direction of induced currents, the direction of currents, the direction of applied or produced forces, applied or produced forces, and the polarity of induced and the polarity of induced emf'semf's..Lenz's law says that the induced current will produce Lenz's law says that the induced current will produce magnetic flux magnetic flux opposing this changeopposing this change. To oppose an . To oppose an increase into the page, it generates magnetic field which increase into the page, it generates magnetic field which points out of the page, at least in the interior of the loop. points out of the page, at least in the interior of the loop. Such a magnetic field is produced by a Such a magnetic field is produced by a counterclockwisecounterclockwisecurrent (use the right hand rule to verify). current (use the right hand rule to verify).6610/10/200310/10/2003Lenz’s law: energy conservationLenz’s law: energy conservationWe arrive at the same conclusion from We arrive at the same conclusion from energy conservation point of viewenergy conservation point of viewThe preceding analysis found that the The preceding analysis found that the current is moving current is moving ccwccw. Suppose that this . Suppose that this is not so.is not so.If the current If the current I I is is cwcw, the direction of the , the direction of the magnetic force, magnetic force, BlIBlI, on the sliding bar , on the sliding bar would be would be rightright..This would accelerate the bar to the right, This would accelerate the bar to the right, increasing the area of the loop even more.increasing the area of the loop even more.This would produce even greater force This would produce even greater force and so on.and so on.In effect, this would generate energy out of In effect, this would generate energy out of nothing violating the law of conservation of nothing violating the law of conservation of energy. Our original Our original assertion that the assertion that the current is current is cwcwis is not right, so the not right, so the current is current is ccwccw!energy. !7710/10/200310/10/2003NSNSSSThe induced flux seeks to counteract the change.vvNchange change8810/10/200310/10/2003Example: direction of the currentExample: direction of the currentFind the direction of the current induced in the resistor at the instant the switch is closed.9910/10/200310/10/2003Applications of Magnetic InductionApplications of Magnetic InductionTape / Hard Drive / ZIP ReadoutTape / Hard Drive / ZIP ReadoutTiny coil responds to change in flux as the magnetic domains (enTiny coil responds to change in flux as the magnetic domains (encoding coding 0’s or 1’s) go by.0’s or 1’s) go by.Question: How can your VCR display an image while paused?Question: How can your VCR display an image while paused?Credit Card ReaderCredit Card ReaderMust swipe cardMust swipe cardÆÆgenerates changing fluxgenerates changing flux––Faster swipe Faster swipe ÆÆbigger signalbigger signal101010/10/200310/10/200320.5 Generators20.5 GeneratorsGenerators and motors are two of the most important Generators and motors are two of the most important applications of induced applications of induced emfemf(magnetic inductance). (magnetic inductance). A generator is something that converts mechanical A generator is something that converts mechanical energy to electrical energy. energy to electrical energy. Alternating Current (AC) generatorAlternating Current (AC) generatorDirect Current (DC) generatorDirect Current (DC) generatorA motor does the opposite, it converts electrical energy A motor does the opposite, it converts electrical energy to mechanical energy. to mechanical energy.111110/10/200310/10/2003AC generatorAC generatorCompute EMFCompute EMFIt is only generated in BC It is only generated in BC and DA wiresand DA wiresEMF generated in BC and EMF generated in BC and DA would beDA would beThus, total EMF isThus, total EMF isIf the loop is rotating with If the loop is rotating with ωABCDωvv sin θBlv⊥==BC DAEEB22sinBlv Blvθ⊥==EA2sin 2 sin2aBlv t Bl tωωω==Eas v=rω=aω/2121210/10/200310/10/2003AC generator (cont)AC generator (cont)Generalize the result to N loopsGeneralize the result to N loopswhere we also noticed that where we also noticed that A=laA=laNote: Note: is reached when is reached when ωωt=90t=90˚˚or 270or 270˚NBAω=maxsinNBA tωω=EEMF generated by the AC generatorE˚131310/10/200310/10/2003DC generatorDC generatorBy a clever change to the rings and brushes of the ac By a clever change to the rings and brushes of the ac generator, we can create a dc generator, that is, a generator, we can create a dc generator, that is, a generator where the polarity of the