Chapters 34,36: Electromagnetic Induction Topics Reading Quiz 1Reading Quiz 2Reading Quiz 3Reading Quiz 4Reading Quiz 5Electromagnetic InductionExperimental Observation of InductionMagnetic FluxFaraday’s Law of InductionFaraday’s Law & Flux ChangeFaraday’s Law of InductionComment on Lenz’s LawDirection of Induced CurrentConcepTest: Lenz’s Law ConcepTest: Induced Currents ConcepTest: Induced Currents ConcepTest: Lenz’s Law Induced currents ConcepTest: Induced Currents ConcepTest: Induced Currents ConcepTest: Lenz’s Law ConcepTest: Induced CurrentsMotional EMFForce and Motional EMFPower and Motional EMFExampleElectric GeneratorsElectric GeneratorsConcepTest: GeneratorsInduction in Stationary CircuitInductanceSelf - InductanceInductance of SolenoidLR CircuitsAnalysis of LR CircuitCurrent vs Time in RL Circuit (Initially Zero Current in Inductor)L-R Circuits (2)Current vs Time in RL Circuit (For Initial Current imax in Inductor)Exponential BehaviorConcepTest: Generators and MotorsElectric MotorsMotorEnergy Stored in Magnetic FieldEnergy of an InductorEnergy in Magnetic Field (2)Energy Calculation ExamplesWeb SitesGigajoule Magnet at CERNCMS Experiment MagnetCMS Articles and PicturesPHY2061: Chapter 34-351Chapters 34,36: Electromagnetic InductionPHY2061: Chapter 34-352TopicsÎElectromagnetic Induction Magnetic flux Induced emf Faraday’s Law Lenz’s Law Motional emf Magnetic energy Inductance RL circuits Generators and transformersPHY2061: Chapter 34-353Reading Quiz 1ÎMagnetic flux through a wire loop depends on: 1) thickness of the wire 2) resistivity of the wire 3) geometrical layout of the wire 4) material that the wire is made of 5) none of the aboveFlux depends only on geometrical properties BAdΦ= ⋅∫BAPHY2061: Chapter 34-354Reading Quiz 2ÎAn induced emf produced in a motionless circuit is due to 1) a static (steady) magnetic field 2) a changing magnetic field 3) a strong magnetic field 4) the Earth’s magnetic field 5) a zero magnetic fieldFaraday’s lawPHY2061: Chapter 34-355Reading Quiz 3ÎMotional emf relates to an induced emf in a conductor which is: 1) long 2) sad 3) stationary 4) insulated 5) movingPotential difference proportional to velocityPHY2061: Chapter 34-356Reading Quiz 4ÎFaraday’s law says that a) an emf is induced in a loop when it moves through an electric field b) the induced emf produces a current whose magnetic field opposes the original change c) the induced emf is proportional to the rate of change of magnetic fluxFaraday’s lawPHY2061: Chapter 34-357Reading Quiz 5ÎA generator is a device that: a) transforms mechanical into electrical energy b) transforms electrical into mechanical energy c) transforms low voltage to high voltagePHY2061: Chapter 34-358Electromagnetic InductionÎFaraday discovered that a changing magnetic flux leads to a voltage in a wire loop Induced voltage (emf) causes a current to flow !!ÎSymmetry: electricity magnetism electric current magnetic field magnetic field electric currentÎWe can express this symmetry directly in terms of fields Changing E field B field (“displacement current”) Changing B field E field (Faraday’s law)ÎThese & other relations expressed in Maxwell’s 4 equations (Other 2 are Gauss’ law for E fields and B fields) Summarizes all of electromagnetism See Chapter 32PHY2061: Chapter 34-359This effect can be quantified by Faraday’s LawExperimental Observation of InductionPHY2061: Chapter 34-3510Magnetic FluxÎ Define magnetic flux ΦB θ is angle between B and the normal to the plane Flux units are T-m2= “webers”Î When B field is not constant or area is not flat Integrate over areacosBBAθΦ=⋅ =BABAdΦ= ⋅∫BAPHY2061: Chapter 34-35110BΦ=12BBAΦ=BBAΦ=cosBBAθΦ=⋅ =BAPHY2061: Chapter 34-3512Faraday’s Law of Inductioninducedemfnumber of loopsrate of changeof flux with time¾ The faster the change, the larger the induced emf¾ Flux change caused by changing B, area, or orientation¾ The induced emf is a voltageBdENdtΦ=−PHY2061: Chapter 34-3513Faraday’s Law & Flux ChangeÎ Rotating coil φBis maximum when coilfaces up E is maximum when coilfaces sidewaysÎ Stretched coil B constant, θ constant Area shrinks ⇒ Flux decreasescosBBAtωΦ=sinBdEN NBA tdtωωΦ=− =PHY2061: Chapter 34-3514Faraday’s Law of Inductioninducedemfnumber of loopsrate of changeof flux with time¾ Minus sign from Lenz’s Law:¾ Induced current produces a magnetic field which opposesthe original change in fluxBdENdtΦ=−PHY2061: Chapter 34-3515Comment on Lenz’s LawÎWhy does the induced current oppose the change in flux?ÎConsider the alternative If the induced current reinforced the change, then the change would get bigger, which would then induce a larger current, and then the change would get even bigger, and so on . . . This leads to a clear violation of conservation of energy!!PHY2061: Chapter 34-3516Bar magnet moves through coil¾ Current induced in coilReverse pole¾ Induced current changes signCoil moves past fixed bar magnet¾ Current induced in coil as in (A)Bar magnet stationary inside coil¾ No current induced in coilDirection of Induced CurrentSNvSNvNSSNABCDvPHY2061: Chapter 34-3517ConcepTest: Lenz’s Law ÎIf a North pole moves towards the loop from above the page, in what direction is the induced current? (a) clockwise (b) counter-clockwise (c) no induced currentMust counter flux change indownward direction with upward B fieldPHY2061: Chapter 34-3518ConcepTest: Induced Currents ÎA wire loop is being pulled through a uniform magnetic field. What is the direction of the induced current? (a) clockwise (b) counter-clockwise (c) no induced currentx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xNo change in flux, no induced currentPHY2061: Chapter 34-3519ConcepTest: Induced Currents In each of the 3 cases above, what is the direction of the induced current?(Magnetic field is into the page and has no boundaries)x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x
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