Mutual Induction and Transformer

1 P21-Class 21: OutlineHour 1:Expt. 9: Faraday’s LawHour 2:Faraday’s LawTransformersMagnetic Materials2 P21-Last Time:Faraday’s Law3 P21-Faraday’s Law of InductionBdNdtεΦ=−Changing magnetic flux inducesan EMFLenz: Induction opposeschange4 P21-What can change? ()cosdNBAdtθε=−Quantities which can vary with time:•Magnitude of B•Area A enclosed by the loop•Angle θbetween B and loop normal 5 P21-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.6 P21-Example: Magnitude of B Magnet Falling Through a RingFalling magnet approaches a copper ringorCopper Ring approaches Magnet7 P21-Moving Towards DipoleMove ring downAs ring approaches, what happens to flux?It increases8 P21-Moving Over DipoleMove downFluxFlux increases then decreasesNote we have arbitrarily assigned dA up9 P21-Moving Over DipoleCurrentCWCCWMove downCurrent first goes in one direction, then otherIt ALWAYS opposes the changing flux10 P21-Five PRS Questions:Predictions for Experiment 9 Faraday’s Law11 P21-Experiment 9:Faraday’s Law of Induction12 P21-CURRENTFLUXImperfectcurrent 013 P21-Four PRS Questions:Force on A Loop Below Magnet Moving Upward;Moving Rail;Moving Rectangle near Wire;Generator.14 P21-Brakes 15 P21-Magnet Falling Through a RingWhat happened to kinetic energy of magnet?16 P21-Eddy Current Brakinghttp://demoroom.physics.ncsu.edu/html/demos/163.htmlWhat happened to kinetic energy of pendulum?17 P21-Eddy Current Brakinghttp://demoroom.physics.ncsu.edu/multimedia/video/5K20.22.1.MOVWhat happened to kinetic energy of disk?18 P21-Demonstration:Eddy Current Braking 19 P21-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)XXXX20 P21-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∝XXXX21 P21-Demonstration:Levitating Magnet Superconductor & Magnethttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/faraday/16-superconductor/16-12_wmv320.html22 P21-PRS Questions:Loop in Uniform Field23 P21-Mutual Inductance24 P21-Mutual Inductance112122 112122NMINMIΦ≡Φ→=21212dIdtMε≡−1221MMM==A current I2in coil 2, induces some magnetic flux Φ12in coil 1. We define the flux in terms of a “mutual inductance” M12:25 P21-Demonstration:Remote Speaker26 P21-TransformerStep-up transformerBssdNdtεΦ=BppdNdtεΦ=ssppNNεε=Ns> Np: step-up transformerNs< Np: step-down transformer27 P21-Demonstrations:One Turn Secondary:NailMany Turn Secondary:Jacob’s Ladder28 P21-Transmission of Electric PowerPower loss can be greatly reduced if transmitted at high voltage29 P21-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.521.2105002.410PWIAVV×===×(a) 83% loss!!22(500)(0.40)100LPIRAkW==Ω=541.2105.02.410PWIAVV×===×(b)0.0083% loss22(5.0)(0.40)10LPIRAW==Ω=30 P21-Magnetic Materials31 P21-Recall Polar DielectricsDielectric polarization decreasesElectric Field!32 P21-Para/FerromagnetismApplied external field B0tends to alignthe atomic magnetic moments33 P21-Para/FerromagnetismThe aligned moments tend to increasethe B field0mκ=BB􀁇􀁇Eκ=0EE􀁇􀁇Compare to:34 P21-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 items35 P21-Magnetization VectorM=0M>0Useful to define “Magnetization”of material:11NiiVV===∑µMµ􀁇􀁇􀁇00µ=+BBM􀁇􀁇􀁇36 P21-Hysteresisin FerromagnetsThe magnetization Mof a ferromagnetic material depends on the historyof the substanceMagnetization remains even with B0off !!!