VIII. Magnetic Induction

1. VIII. Magnetic Induction Dr. Bill Pezzaglia Updated 2014Mar

2. 2 VIII. Magnetic Induction • Dynamos & Generators • Faraday’s Law • Inductance

3. 3 Michael Faraday (1791 - 1867) • 1821 Creates first motor • 1831 Creates “dynamo”, a DC generator • 1831 Law of induction • 1846 Discovers Diamagnetism

4. 4 A. Dynamos & Generators • Dynamo Rule • Motional EMF • Mechanical to Electric Power

5. 5 1. Dynamo Rule (a) Faraday (1831) • Move a wire so that it “cuts” magnetic field lines will generate current • Recall • Positive charges in wire will move one direction, negative the other

6. 6 1.(a).ii Planetary Dynamos Moon Io moving orbiting through Jupiters magnetic field generates BIG current

7. 7 1.(a).iii Planetary Dynamos The electric currents generate so much heat the moon has active volcanoes!

8. 8 - + (b) Magnetohydrodynamic Generators (MHD) 1832 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).

9. 9 (b).ii MHD Generators

10. 10 I (c). Faraday’s Disk Dynamo (1831) This was the first practical DC generator. It gives high current, but low voltage.

11. 11 2. EMF (Electromotive Force) (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”

12. 12 2.(b). Motional EMF • Magnetic (“Dynamo”) Work done by moving a length “L” wire through magnetic field “B” with velocity “v” generates an EMF • General Result, only the partof velocity, magnetic field andwire path which are mutuallyperpendicular will contribute.

13. 13 2.(c). AC Generator 1892 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. http://www.youtube.com/v/i-j-1j2gD28

14. 14 2.(c).ii AC Generator Details • Rectangle area: A=ab • Velocity: • EMF:

15. 15 3. Mechanical to Electric Power • Electric Power Output: • Current created will experience force from magnetic field, which is in opposite direction as “v” • Mechanical Work: by Newton’s 3rd law, we must PUSH the wire through with force F, or power:

16. 16 B. Faraday’s Law • Magnetic Flux • Faraday’s Law • Lenz’s Law

17. 17 1831 Faraday’s Three Experiments 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 He explained all of these effects with one single law

18. 18 1. Magnetic Flux • Definition: • Magnetic Flux is the Magnetic Field “B” (aka “Magnetic Intensity Vector”) times area it “flows” through • Units: Weber=Teslam2 Greek Letter: “phi”  or 

19. 44 (b) Lambert’s Law (Orientation matters!) Lambert’s Law (1760)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) Sunlight coming in at a low altitude angle will have its energy spread out over more area.

20. 20 (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.

21. 21 2. Faraday’s Law of Induction (1831) • Possibly done 1830 by Henry (unpublished) • The EMF generated in a loop of wire is equal to the change in magnetic flux through the loop (with respect to time) • You can get a change of flux in 2 ways

22. 22 (a) Change the Area of Loop • Consider sliding wire in constant magnetic field • This is equivalent to Dynamo Rule (motional emf)

23. 23 (b) Or, change the orientation of loop • Consider AC generator, where we twist the loop • This is equivalent to Dynamo Rule (motional emf)

24. 24 (c) Change Magnetic Field • You can NOT explain this one by dynamo rule, as no wires move! • 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!

25. 25 3. Lenz’s Law (1834) (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 Heinrich Lenz1804-1864

26. 26 (b). Eddy Currents • 1824, François Arago discovers when conductor is exposed to changing magnetic field, small circular “eddy currents” (also known as Foucault currents) are generated. • 1855, 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) http://www.youtube.com/watch?v=sPLawCXvKmg http://www.magnet.fsu.edu/education/community/slideshows/eddycurrents/index.html

27. 27 (c). Magnetic Levitation • Lenz’s law is usually demonstrated by “Elihu Thomson's jumping ring” (1887? 1897?). • The induced current in the metal ring creates an electromagnetic that opposes the applied field, lifting the ring. Jumping Ring: http://www.youtube.com/watch?v=Pl7KyVIJ1iE

28. 28 (d). Magnetic Levitation • Meissner Effect (1933) 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: http://www.youtube.com/watch?v=94-Z2QgHl-s&feature=related Train: http://www.youtube.com/watch?v=GHtAwQXVsuk

29. 29 C. Inductance • Mutual Induction (Transformers) • Self Inductance & RL circuits • Energy in Inductors

30. 30 1. Mutual Induction (a) 1831 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=ohmsec) • If first coil is solenoid, then can show

31. 31 (a).ii Coefficient of Coupling [DETAILS] • 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. • 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)

32. 32 (b) Ruhmkorff Induction Coil • Probably first invented by invented by Nicholas Callan in 1836. • 1851 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 • BIG voltage is generated in secondary by Faraday’s law • This was how early Cathode Ray, X-ray and “neon signs” were powered. https://www.youtube.com/watch?v=1C4lOAPBu7A

33. 33 (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. • 1884 “Closed Flux Transformer” invented: the flux through both coils is the same: Divide the equations to get the transformer rule: Note that power is conserved!

34. 34 2. Self Inductance (a) Probably done first by Joseph Henry 1830, 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 :

35. 35 b. Inductor Combinations • Rules for networks of inductors is similar to resistors (hence opposite of capacitors) • In Series: Inductors ADD • In Parallel: Inductors combine: or

36. 36 (c) Inductor Behavior • 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! Demo of Back EMF: http://www.youtube.com/watch?v=aSmMFog10D0

37. 37 (c) RL Circuits (incomplete) • No notes here, see section 26.5 in book • In brief, RL circuits behave complementary to RC circuits. Inductors try to keep the current flowing, so if there is an abrupt loss of current, inductors will attempt to supply any voltage necessary to keep the current flowing, the current will decay exponentially with time constant: • Complementary, the RC circuit: capacitors try to keep the voltage the same, so if there is an abrupt loss of voltage, the capacitor will attempt supply any current necessary to keep the voltage up. The voltage will decay exponentially with time.

38. 38 3. Energy Stored in Inductor • Energy in Inductor: • You can think of it as “kinetic energy of current” stored in the inductor (whereas a capacitor stores “potential energy” of charge) • Using the equations for magnetic field and inductance of a solenoid coil, you can show:

39. 39 b. Energy Density • Divide by volume (of a solenoid coil) • In other words, the energy of an inductor is stored in the magnetic field itself! [Whereas for a capacitor its stored in the electric field] • This energy creates a “magnetic pressure” that tries to push a coil apart

40. 40 c. Forces on Cores etc. • If you insert a core, you increase the inductance by factor Km: • Hence, increase the energy. Hence inductors will want to push cores out (doorbell or induction gun). • By inserting core, you change inductance, so more correct formula for voltage (with possible sign errors):

41. 41 References • 1831 Faraday Law of Induction • Neat video: http://www.youtube.com/watch?v=yahQtxBV5vA&feature=related • http://www.youtube.com/watch?v=VPxdl1zpcC8&feature=related • Magnetic flux and orientation: http://www.youtube.com/watch?v=KXFXUrBWp-c&feature=related • AC generator http://www.youtube.com/watch?v=gqA3WoOunEA&feature=related • Even better AC generator: http://www.youtube.com/watch?v=i-j-1j2gD28&NR=1 • Variable AC generator: http://www.youtube.com/watch?v=mCvXa_VVFh4&feature=related • Simulations: http://www.esjd.pt/recursos_educativos/phet1.0/new/simulations/index1057.html?cat=All_Sims

42. 42 Schedules/Reading In Knight “College Physics” (2nded) • Faraday’s Law, Chapter 25.1-25.4 • Transformer 26.2 • RL circuit 26.5, and lab notes. • Skip 25.5-25.8 for now (Maxwell’s Equations)