PHY2049: Chapter 301Chapter 30: Electromagnetic InductionPHY2049: Chapter 302TopicsÎElectromagnetic Induction Magnetic flux Induced emf Faraday’s Law Lenz’s Law Motional emf Magnetic energy Inductance RL circuits Generators and transformersPHY2049: Chapter 303Reading 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= ⋅∫BAPHY2049: Chapter 304Reading 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 lawPHY2049: Chapter 305Reading 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 velocityPHY2049: Chapter 306Reading 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 lawPHY2049: Chapter 307Reading 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 voltagePHY2049: Chapter 308Electromagnetic 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 32PHY2049: Chapter 309This effect can be quantified by Faraday’s LawExperimental Observation of InductionPHY2049: Chapter 3010Magnetic 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= ⋅∫BAPHY2049: Chapter 30110BΦ=12BBAΦ=BBAΦ=cosBBAθΦ=⋅ =BAPHY2049: Chapter 3012Faraday’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=−PHY2049: Chapter 3013Faraday’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=− =PHY2049: Chapter 3014Faraday’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=−PHY2049: Chapter 3015Comment 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!!PHY2049: Chapter 3016Bar 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 CurrentSNvSNvNSSNABCDvPHY2049: Chapter 3017ConcepTest: 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 fieldPHY2049: Chapter 3018ConcepTest: 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 currentPHY2049: Chapter 3019ConcepTest: 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)(a) clockwise (b) counter-clockwise (c) no induced currentx 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 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 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 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 x123Counter NoneNone (max flux,so not changing)PHY2049: Chapter 3020ConcepTest: Lenz’s Law ÎIf a coil is shrinking in a B field pointing into the page, in what direction is the induced current? (a) clockwise (b) counter-clockwise (c) no induced currentDownward flux is decreasing,so need to create downwardB fieldPHY2049: Chapter 3021Induced currents ÎA circular loop in the plane of the paper lies in a 3.0 T magnetic field pointing into the paper. The loop’s diameter changes from 100 cm to 60 cm in 0.5 s What is the magnitude of the average induced emf? What is the direction of the induced current? If the coil resistance is 0.05Ω , what is the average induced current? Direction = clockwise (Lenz’s law) Current = 3.016 / 0.05 = 60.3 A1()220.3
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