Slide 1CalenderSlide 3Field Patterns From Last TimeMaxwell’s EquationsA puzzlement ..Consider the poor little capacitor…Slide 8In the gap… DISPLACEMENT CURRENTSlide 10NEXTSlide 12The Coil and the MagnetMagnetic Flux FMWhat’s Happening Here??ObservationDown the HatchDown the HatchHEY BINDELL – WAIT A SECOND …….Slide 20REMEMBER when I said E Fields start and end on CHARGES???The truthWhy do you STILL think I am a liar?Slide 24The POTENTIAL between two pointsSo, consider the following:THEREFORE WHAT WILL A VOLTMETER READ FROM A to A?Slide 28Q: Which way does E point?Slide 30Faraday’s ExperimentsInsert Magnet into CoilRemove Coil from Field RegionThat’s Strange …..Slide 35Slide 36Magnetic FluxSlide 38Slide 39W13D3 More PatternsFields, Patterns, Maxwell’s Equations and Begin Induction/Faraday’s Law2049SCALE-UPEASY!CalenderMonday Wednesday Friday Saturday14Chapter 22Gauss16 (Read rest of chapter)2 WebAssignsChapter 22Gauss18QUIZChapter 22Lentz & More21Chapter 23Faraday23QUIZChapter 23Faraday HOLIDAY28Chapter 23Faraday30Chapter 24EM2Chapter 24 EMOptional Exam (22-24)3FINAL EXAMTHE EVAN SHOWField Patterns From Last Time“Curly Field”No diverging sourceDiverging FieldPoint SourcesElectrostatic Fields Magnetic FieldsMaxwell’s Equations00 .0 ? =Faraday's Law of Induction - Next Topic (One additional term)insideinside pathqdAdAdd Iem� ==� =� =������E nB • nE lB l����A puzzlement ..enclosedid0-sBLet’s apply this to the gap of a capacitor.Consider the poor little capacitor…iiCHARGING OR DISCHARGING …. HOW CAN CURRENTFLOW THROUGH THE GAPIn a FIELD description???Through Which Surface Do we measure the current for Ampere’s Law?I=0Huh??In the gap… DISPLACEMENT CURRENTdtddtdqIntDisplacemeIdtdqLetdtdqdtdqEAEddEE0002Current gap)(in 1S through FLUX ELECTRIC TheFixes the Problem!00 . 00 ? =Faraday's Law of Induction - Next Topic( + ) insideEinside pat hqdAdAddd Idtem e� ==� =F� =������E nB • nE lB l����NEXTFix the Last Maxwell Equati on ? =Faraday's Law of Induction - d� =�E l�First, Let's DO the Demo !The Coil and the MagnetCoilCoilGalvanometerGalvanometerMagnetic Flux FMIntegral over a SURFACEWhat’s Happening Here??AObservationMeter DeflectsThere must be an emf around the loops!VariablesDirectionPolarityPitchVelocityDown the HatchAluminum PipeAluminum PipeDown the HatchBBAluminum PipeAluminum PipeNSInduced CurrentNREPEL!!There must bean Electric Fieldin the metal thatis pushing the current!!You said that there is a conducting loop.You said that there is therefore a current induced around the loop if the flux through the loop changes.But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop?Or a current???‘tis a puzzlement!HEY BINDELL – WAIT A SECOND …….REMEMBER when I said E Fields start and end on CHARGES???DID I LIE??Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously.Electric Fields created by changing magnetic fields (NON-Coulombic) can actually be shaped in loops.The truthBUT WAIT, YOU STILL LIE!Why do you STILL think I am a liar?Because you said that an emf is a voltage so if I put a voltmeter from one point on the loop around to the same point, I will get ZERO volts, won’t I? How can there be a current??Yes … butthis doesn’t makeme a liar!Let Me Explain.Is the WORK that an external agent has to do to move a unit charge from one point to another.But we also have (neglecting the sign):The POTENTIAL between two points sEVDsSo, consider the following:EConductorx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xze roREemfsEsEemf2THEREFORE WHAT WILL A VOLTMETER READ FROM A to A?EConductorx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xAA The emfB ZeroC Can’t tellHow Big is the emf?temflooptheThrou gh Faraday’s LawMichael Faraday (1791-1867)MINUS????Q: Which way does E point?A: The way that you don’t want it to point! (Lenz’s Law).Lenz’s Law Explains the (-) sign!Push a magnet into a coil of two wires and a current is produced via an emf.In this case, 2 coils, each have the SAME emf so we add..Ohm’s Law still works, socoilRemfitNemfFaraday’s Experiments??Insert Magnet into CoilRemove Coil from Field RegionThat’s Strange …..These two coils are perpendicular to each otherAll Involve Changing The MagneticFlux through the LoopsRemember the Definition of TOTAL ELECTRIC FLUX through a CLOSED surface:-dAis surface aLEAVING FieldElectric theofFlux TotaloutEsurfaceEEdnEMagnetic FluxApplies to an OPEN SURFACE only.“Quantity” of magnetism that goes through a surface.- AB dBsurfaceIn the figure below a 120-turn coil of radius 1.8 cm and resistance 6.8 W is coaxial with a solenoid with 209 turns/cm and diameter 3.2 cm. The solenoid current drops from 1.5 A to zero in time interval Δt = 25 ms. What current is induced in the coil during Δt? 0.0224
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