Class 21: OutlineLast Time:Faraday’s LawFaraday’s Law of InductionWhat can change?Magnet Falling Through a RingExample: Magnitude of B Magnet Falling Through a RingMoving Towards DipoleMoving Over DipoleMoving Over DipoleFive PRS Questions:Predictions for Experiment 9 Faraday’s LawExperiment 9: Faraday’s Law of InductionFour PRS Questions:Force on A Loop Below Magnet Moving Upward;Moving Rail;Moving Rectangle near Wire;Generator.BrakesMagnet Falling Through a RingEddy Current BrakingEddy Current BrakingDemonstration:Eddy Current BrakingEddy Current BrakingEddy Current BrakingDemonstration:Levitating Magnet Superconductor & MagnetPRS Questions:Loop in Uniform FieldMutual InductanceMutual InductanceDemonstration: Remote SpeakerTransformerDemonstrations: One Turn Secondary:Nail Many Turn Secondary:Jacob’s LadderTransmission of Electric PowerExample: Transmission linesMagnetic MaterialsRecall Polar DielectricsPara/FerromagnetismPara/FerromagnetismPara/FerromagnetismMagnetization VectorHysteresis in Ferromagnets1P21-Class 21: OutlineHour 1:Expt. 9: Faraday’s LawHour 2:Faraday’s LawTransformersMagnetic Materials2P21-Last Time:Faraday’s Law3P21-Faraday’s Law of InductionBdNdtεΦ=−Changing magnetic flux induces an EMFLenz: Induction opposes change4P21-What can change? ()cosdNBAdtθε=−Quantities which can vary with time:• Magnitude of B• Area A enclosed by the loop•Angle θ between B and loop normal5P21-Magnet Falling Through a Ringhttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/faraday/07-FallingMagnetResistive/07-FallMAgRes_f54_320.htmlFalling magnet slows as it approaches a copper ring which has been immersed in liquid nitrogen.6P21-Example: Magnitude of B Magnet Falling Through a RingFalling magnet approaches a copper ringor Copper Ring approaches Magnet7P21-Moving Towards DipoleMove ring downAs ring approaches, what happens to flux?It increases8P21-Moving Over DipoleMove downFluxFlux increases then decreasesNote we have arbitrarily assigned dAup9P21-Moving Over DipoleCurrentCWCCWMove downCurrent first goes in one direction, then otherIt ALWAYS opposes the changing flux10P21-Five PRS Questions:Predictions for Experiment 9 Faraday’s Law11P21-Experiment 9:Faraday’s Law of Induction12P21-CURRENTFLUXImperfectcurrent 013P21-Four PRS Questions:Force on A Loop Below Magnet Moving Upward;Moving Rail;Moving Rectangle near Wire;Generator.14P21-Brakes15P21-Magnet Falling Through a RingWhat happened to kinetic energy of magnet?16P21-Eddy Current Brakinghttp://demoroom.physics.ncsu.edu/html/demos/163.htmlWhat happened to kinetic energy of pendulum?17P21-Eddy Current Brakinghttp://demoroom.physics.ncsu.edu/multimedia/video/5K20.22.1.MOVWhat happened to kinetic energy of disk?18P21-Demonstration:Eddy Current Braking19P21-Eddy Current BrakingThe magnet induces currents in the metal that dissipate the energy through Joule heating:ω1. Current is induced counter-clockwise (out from center)2. Force is opposing motion (creates slowing torque)XXXX20P21-Eddy Current BrakingThe magnet induces currents in the metal that dissipate the energy through Joule heating:ω1. Current is induced clockwise (out from center)2. Force is opposing motion (creates slowing torque)3. EMF proportional to ω4. .2RFε∝XXXX21P21-Demonstration:Levitating Magnet Superconductor & Magnethttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/faraday/16-superconductor/16-12_wmv320.html22P21-PRS Questions:Loop in Uniform Field23P21-Mutual Inductance24P21-Mutual Inductance112 122 112122NMINMIΦ≡Φ→=212 12dIdtMε≡ −12 21MMM==A current I2in coil 2, induces some magnetic flux Φ12in coil 1. We define the flux in terms of a “mutual inductance” M12:25P21-Demonstration:Remote Speaker26P21-TransformerStep-up transformerBssdNdtεΦ=BppdNdtεΦ=ssppNNεε=Ns> Np: step-up transformerNs< Np: step-down transformer27P21-Demonstrations:One Turn Secondary:NailMany Turn Secondary:Jacob’s Ladder28P21-Transmission of Electric PowerPower loss can be greatly reduced if transmitted at high voltage29P21-Example: Transmission linesAn average of 120 kW of electric power is sent from a power plant. The transmission lines have a total resistance of 0.40 Ω. Calculate the power loss if the power is sent at (a) 240 V, and (b) 24,000 V.521.2 105002.4 10PWIAVV×== =×(a) 83% loss!!22(500 ) (0.40 ) 100LPIR A kW== Ω=541.2 105.02.4 10PWIAVV×== =×(b)0.0083% loss22(5.0 ) (0.40 ) 10LPIR A W== Ω=30P21-Magnetic Materials31P21-Recall Polar DielectricsDielectric polarization decreases Electric Field!32P21-Para/FerromagnetismApplied external field B0tends to align the atomic magnetic moments33P21-Para/FerromagnetismThe aligned moments tend to increase the B field0mκ=BBGGEκ=0EEGGCompare to:34P21-Para/FerromagnetismParamagnet: Turn off B0, everything disordersFerromagnet: Turn off B0, remains (partially) orderedThis is why some items you can pick up with a magnet even though they don’t pick up other items35P21-Magnetization VectorM=0 M>0Useful to define “Magnetization” of material:11NiiVV===∑µMµGGG00µ=+BB MGGG36P21-Hysteresis in FerromagnetsThe magnetization M of a ferromagnetic material depends on the history of the substanceMagnetization remains even with B0off
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