Faraday's Law and application

1 P20-Class 20: OutlineHour 1:Faraday’s LawHour 2:Faraday’s Law: Applications2 P20-Previously:Force on Magnetic Dipole3 P20-PRS Question:Force on Magnetic Dipole4 P20-Last Time:Ampere’s Law5 P20-Ampere’s Law: .∫=⋅encId0µsB􀁇􀁇IBBLongCircularSymmetry(Infinite) Current SheetXXXXXXXXXXXXBXXXXXXXXXXXXXXXXSolenoid =2 Current SheetsTorus6 P20-Group Problem: TorusA torus (a solenoid of radius aand nturns/meter whose ends are bent around to make a donut of radius R) carries a uniform current I.Find B on what was the central axis of the solenoidIIRa7 P20-Ampere’s Law: TorusAmperian Loop:B is Constant & ParallelI PenetratesBXXXXXXXXXXXXXXXXXXXXRaPicture:Solenoid (slinky) curved around & joined end to end8 P20-This Time:Faraday’s LawFourth (Final) Maxwell’s Equation(but we still have to go back and add another term to Ampere’s Law!)Underpinning of Much Technology9 P20-Demonstration:Falling Magnet 10 P20-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.11 P20-Demonstration:Jumping Rings12 P20-Jumping RingAn aluminum ring jumps into the air when the solenoid beneath it is energized13 P20-What is Going On?It looks as though the conducting loops have current in them (they behave like magnetic dipoles) even though they aren’t hooked up14 P20-Demonstration:Induction15 P20-Electromagnetic Induction16 P20-Movie and Visualization:Inductionhttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/faraday/15-inductance/15-1_wmv320.htmlLenz’s Law says that the flux tries to remain the same, so the field lines get “hung up” at the coil. 17 P20-Faraday’s Law of InductionBdNdtεΦ=−A changing magnetic flux inducesan EMF18 P20-What is EMF?dε=⋅∫Es􀁇􀁇Looks like potential. It’s a “driving force”for current19 P20-Faraday’s Law of InductionBdNdtεΦ=−A changing magnetic flux inducesan EMF20 P20-Magnetic Flux Thru Wire LoopAnalogous to Electric Flux (Gauss’ Law)cosBBABAθ⊥Φ===⋅BA􀁇􀁇BSd=⋅∫ΦBA􀁇􀁇(1) Uniform B(2) Non-Uniform B21 P20-Faraday’s Law of InductionBdNdtεΦ=−A changing magnetic flux inducesan EMF22 P20-Minus Sign? Lenz’s LawInduced EMF is in direction that opposesthechange in flux that caused it23 P20-Three PRS Questions:Lenz’ Law24 P20-Faraday’s Law of InductionBdNdtεΦ=−A changing magnetic flux inducesan EMF25 P20-Ways to Induce EMF ()cosdNBAdtθε=−Quantities which can vary with time:•Magnitude of B•Area A enclosed by the loop•Angle θbetween B and loop normal 26 P20-Ways to Induce EMF ()cosdNBAdtθε=−Quantities which can vary with time:•Magnitude of B•Area A enclosed by the loop•Angle θbetween B and loop normal 27 P20-Group Discussion:Magnet Falling Through a RingFalling magnet slows as it approaches a copper ring which has been immersed in liquid nitrogen.28 P20-PRS Question:Force on Loop Below Magnet29 P20-Ways to Induce EMF ()cosdNBAdtθε=−Quantities which can vary with time:•Magnitude of B•Area A enclosed by the loop•Angle θbetween B and loop normal e.g. Falling Magnet30 P20-Group Problem: Changing AreaConducting rod pulled along two conducting rails in a uniform magnetic field B at constant velocity v 1.Direction of induced current?2.Direction of resultant force?3.Magnitude of EMF?4.Magnitude of current?5.Power externally supplied to move at constant v?􀁁31 P20-Ways to Induce EMF ()cosdNBAdtθε=−Quantities which can vary with time:•Magnitude of B•Area A enclosed•Angle θbetween B and loop normale.g. Moving Coil & Dipolee.g. Sliding bar32 P20-Changing Angle0BΦ=⋅=BA􀁇􀁇BBAΦ=⋅=BA􀁇􀁇33 P20-Applets that show these 3 caseshttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/faraday/13-faradayapp02/13-faradayapp02_320.html34 P20-Faraday’s LawThe last of the Maxwell’s Equations (Kind of, still need one more term in Ampere’s Law)35 P20-Maxwell’s Equations00(Gauss's Law)(Faraday's Law)0(Magnetic Gauss's Law)(Ampere's Law)inSBCSencCQddddtddIεµ⋅=Φ⋅=−⋅=⋅=∫∫∫∫∫∫Creating Electric FieldsEAEsCreating Magnetic FieldsBABs􀁇􀁇􀁇􀁇􀁇􀁇􀁇􀁇􀁷􀁶􀁷􀁶36 P20-TechnologyManyApplications of Faraday’s Law37 P20-DC Motor (magnetostatics)38 P20-Motors & GeneratorscoscosBBABAtθωΦ==(cos)sinBddNNABtNABtdtdtωωωεΦ=−=−=39 P20-Speakers & Microphones (magnetostatics)See Diagram: http://electronics.howstuffworks.com/speaker3.htm40 P20-Metal DetectorSee Animation of how VLF metal detectors work:http://home.howstuffworks.com/metal-detector2.htmInduction StovetopsGround Fault Interrupters (GFI)41 P20-Electric Guitar42 P20-Demonstration:Electric Guitar