Magnetic Induction. VIII. Magnetic Induction. 1. Dynamo Rule. A. Dynamos & Generators. B. Faraday s Law. C. Inductance. A. Dynamos & Generators

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1 Magnetic Induction VIII. Magnetic Induction A. Dynamos & Generators Dr. Bill Pezzaglia B. Faraday s Law C. Inductance Updated 03Aug5 Michael Faraday (79-867) 3 A. Dynamos & Generators 4 8 Creates first motor 83 Creates dynamo, a DC (Direct Current) generator 83 Law of induction ) Dynamo Rule ) Motional EMF 846 Discovers Diamagnetism 3) Mechanical to Electric Power. Dynamo Rule (a) Faraday (83) Move a wire so that it cuts magnetic field lines will generate current Recall F q v B Positive charges in wire will move one direction, negative the other 5.(a).ii Planetary Dynamos Moon Io moving orbiting through Jupiters magnetic field generates BIG current 6

2 .(a).iii Planetary Dynamos 7 (b) Magnetohydrodynamic Generators (MHD) 8 The electric currents generate so much heat the moon has active volcanoes! 83 Faraday s Fluid Generator experiment at Waterloo Bridge: attempts to measure current generated from velocity of Thames cutting through earth s magnetic field (didn t work too well). F q v B - + (b).ii MHD Generators 9 (c). Faraday s Disk Dynamo (83) 0 This was the first practical DC generator. It gives high current, but low voltage. I. EMF (Electromotive Force).(b). Motional EMF (a) Definition of EMF () Misnomer: its not really a force, it s a voltage (i.e. ENERGY per charge) Chemical EMF: A battery is like a pump. When charges pass through, their energy is increased. Change in voltage= EMF Work V q Magnetic ( Dynamo ) Work done by moving a length L wire through magnetic field B with velocity v generates an EMF V Work q FL ( qvb) L q q General Result, only the part of velocity, magnetic field and wire path which are mutually perpendicular will contribute V ( v B) L

3 .(c). AC Generator 3.(c).ii AC Generator Details 4 89 Tesla (working for Edison) invents AC Generator. Edison hates the idea (he is using DC dynamos), and so Tesla sells it to Westinghouse. Edison goes on a campaign to convince people AC is DANGEROUS while DC is safe. Rectangle area: A=ab Nikola Tesla Angular Velocity: f (frequency f=60 Hertz) EMF is sinusoidal: V BA sin 3. Mechanical to Electric Power 5 B. Faraday s Law 6 (a) Electric Power Output: (b) Current created will experience force from magnetic field, which is in opposite direction as v F I L B P VI (c) Mechanical Work: by Newton s 3 rd law, we must PUSH the wire through with force F, or power: P F v ( ILB) v I ( LBv) IV ) Magnetic Flux ) Faraday s Law 3) Lenz s Law 83 Faraday s Three Experiments 7. Magnetic Flux 8 Generated current by: Moving a coil in and out of a magnetic field Moving magnet in and out of coil When current turned on or off in a coil, current is generated in a nearby coil. Michael Faraday (a) Definition: Magnetic Flux is the Magnetic Field B (aka Magnetic Intensity Vector ) times area A it flows through B A Units: Weber=Teslam He explained all of these effects with one single law Greek Letter: phi or 3

4 (b) Lambert s Law (Orientation matters!) Sunlight coming in at a low altitude angle will have its energy spread out over more area. Lambert s Law (760) Intensity is reduced by cosine of angle of incidence Flux is the dot product of the electric field vector with the area vector (which is normal to the surface) B A BA cos 44 (c) Magnetic Flux is Conserved Because there are no magnetic monopoles, there are no sources of magnetic field lines. Magnetic Field Lines must be continuous (i.e. continue through magnet) Gauss s law for magnetism: total magnetic flux through a closed surface is ZERO. 0. Faraday s Law of Induction (83) (a) Change the Area of Loop [Details] Possibly done 830 by Henry (unpublished) Consider sliding wire in constant magnetic field The EMF (i.e. voltage V ) generated in a loop of wire is equal to the change in magnetic flux through the loop (with respect to time) V You can get a change of flux in ways, by changing field, or area ( B) A B ( A) A V B V ()BvL This is equivalent to Dynamo Rule (motional emf) A vl (b) Or, change the orientation of loop [Details] 3 (c) Change Magnetic Field 4 Consider AC generator, where we twist the loop BA cos V BA sin V BA sin This is equivalent to Dynamo Rule (motional emf) Most Important: You can NOT explain this one by dynamo rule, as no wires move! B V A However, it makes perfect sense because motion is relative. Whether you think the magnet is moving with the coil still, or the magnet still with the coil moving merely depends upon the motion of the observer! 4

5 3. Lenz s Law (834) 5 (b). Eddy Currents 6 (a) The law: Direction of induced current is such as to oppose the cause producing it. It s the minus sign in Faraday s Law V Heinrich Lenz , François Arago discovers when conductor is exposed to changing magnetic field, small circular eddy currents (also known as Foucault currents) are generated. 855, J.B.L. Foucault rotates a copper disc with rim between poles of magnet and discovers that the induced eddy currents in the metal cause: Inductive Braking: the force required for the rotation of a copper disc becomes greater with magnet (even though copper is not attracted by a magnet) Inductive Heating: the disc becomes heated by the eddy current (i.e. friction ), because of resistance of metal. Braking (tubes) (c). Magnetic Levitation 7 (d). Magnetic Levitation 8 Lenz s law is usually demonstrated by Elihu Thomson's jumping ring (887? 897?). The induced current in the metal ring creates an electromagnetic that opposes the applied field, lifting the ring. Jumping Ring: Meissner Effect (933) for superconductors, the eddy currents are so strong that they become perfectly diamagnetic, cancelling the external field, inducing magnetic levitation. Application: Magnetically levitated trains! JR-Maglev EDS suspension is due to the magnetic fields induced either side of the vehicle by the passage of the vehicle's superconducting magnets. -- Wikipedia Meissner Effect: Train: C. Inductance 9. Mutual Induction 30 ) Mutual Induction (Transformers) ) Self Inductance & RL circuits 3) Energy in Inductors (a) 83 Faraday notes when current turned on or off in a coil, voltage is generated in a nearby coil. Define Mutual Inductance M (units of Henries=ohmsec) V M I V Details: If first coil is solenoid of length l, with N turns, and second coil has area A with N turns, then the mutual induction is: A M 0NN 5

6 (a).ii Coefficient of Coupling [DETAILS] 3 (b) Ruhmkorff Induction Coil 3 Loosely Coupled: if coils are far apart, not all of magnetic flux from first coil goes through the second (flux leakage). Early transformers were very inefficient because of this. Tightly Coupled: either have coils wrapped around each other, or share same iron core so that nearly all flux from one goes through other. Probably first invented by invented by Nicholas Callan in Ruhmkorff shows if secondary coil has many more windings than primary, then a BIG voltage can be generated from a small one. DC current in primary creates magnetic field Current is periodically interrupted by a vibrating switch, causing field to collapse Reciprocity: If make coils same length with same area, and tightly coupled, then mutual inductance is same both ways ( L is self inductance to be discussed in next section) BIG voltage is generated in secondary by Faraday s law This was how early Cathode Ray, X-ray and neon signs were powered. M M L L (c) Transformer Equation Nikola Tesla pioneered the idea of using AC current, transmitting power at high voltages (low current) and then using transformers to step it back down to low voltage for user. 884 Closed Flux Transformer invented: the flux through both coils is the same: V N V N Divide the equations to get the transformer rule: V N V N I I Note that power is conserved! V I VI 33. Self Inductance (a) Probably done first by Joseph Henry 830, a year before Faraday. Current in coil makes a magnetic field. Change in current changes field, which by Faraday s law creates a voltage in the coil (by Lenz law a back emf which opposes change). Definition of (self) inductance: Details: Self Inductance L is a function only of geometric (and magnetic permeability) of coil. Generally goes like square of number of turns N. For solenoid of length l and area A with iron core of permeability : L N I V L B L N I A 34 (b) Inductor Behavior 35 c. Inductors in Circuits 36 In brief, Inductors resist change in current The inductor has zero current initially, and when you close the switch, the inductor creates a back voltage to resist current trying to flow through it. Instead the current flows freely through the light bulb. Over time, the current starts to flow through the inductor and energy is stored in the magnetic field it creates. When you open the switch, the inductor try to keep the current flowing, so it will attempt to supply any voltage necessary to do so. The bulb will light until the magnetic field collapses (exponentially). However, the BIG voltage surge might burn the bulb out! Rules for networks of inductors is similar to resistors (hence opposite of capacitors) Inductors in series ADD Inductors in parallel: L L L L L L or L L L L L Demo of Back EMF: 6

7 3. Energy Stored in Inductor Energy in Inductor: U LI You can think of it as kinetic energy of current stored in the inductor (whereas a capacitor stores potential energy of charge) The energy of an inductor is stored in the magnetic field: U B volume 37 References 83 Faraday Law of Induction Neat video: Magnetic flux and orientation: AC generator Even better AC generator: Variable AC generator: Simulations: