ch 19-21

1. Magnetism and Induction ch 19-21

2. Magnetism • What’s a magnet? • something that reacts to other magnets • seriously? • Something that produces a magnetic field • seriously, seriously?

3. Three types of magnetic materials • Ferromagnets • permanent magnets (refrigerator, bar, etc) • iron, cobalt, rare-earth, manganese compounds • Paramagnets • weakly attracted to magnets but not permanent • 100x-1000x weaker than ferromagnets • aluminum, platinum, oxygen, ferrofluid • Diamagnets • everything else • weakly repelled by magnets

4. Magnet properties • Have two poles • north, south • Like poles repel, opposites attract • sound familiar? • don’t confuse poles with charges!!!!!! • Break a magnet • what do you get? • two magnets! • No magnetic monopoles! (AFAWK) • can isolate charges but not poles

5. Magnetic properties • Keep breaking. When do you stop getting magnets? • Also, we just said iron is a magnet. Watch me stick this iron nail to my magnetic white board! • @#$%!!! • what gives?

6. Magnetic domains • Ferromagnets are made up of atomic magnets which form domains • Macroscopic magnetism depends on domain alignment. • Not a magnet • Magnet

7. Making & breaking magnets • How do you make a magnet out of ferromagnetic material? • align the domains. but how? • use another magnet (external magnetic field) • How do you weaken/terminate a magnet • disrupt the domains. but how? • increase temperature (increase vibrations) • smack it around • ALL MAGNETISM COMES FROM MOVING ELECTRIC CHARGE

8. Another analogy to electricity • The magnetic field vector, B (like E) • aka magnetic flux density • aka magnetic induction • NOT aka magnetic field strength • B can be represented by lines of force (like E) • 1) lines never cross (like E) • 2) density of lines proportional to B (like E) • 3) ALWAYS form closed loops (no monopoles) • 4) outside of magnet, arrow points NS

9. Earth’s magnetic field • compasses point north • it’s the north end of the compass that’s attracted to the geographic north pole • so what magnetic pole is up north? • the magnetic south pole!

10. Earth’s magnetic field • why does it exist? • core of the earth • molten metals • free electrons moving • moving charge • magnet!

11. Magnetic forces • Place a charge between magnets. What does it do? • Nothing! why not? • So what could we do to make it interact? • What factors might affect the interaction? +

12. Magnetic forces & B • F = qvBsinθ • Lorentz Force • Force of magnetic push on a single particle • B = F/qvsinθ • units: N/(Cm/s) = kg/(Cs) = T (Tesla) • older: Wb/m2 -- 1T = 1 Wb/m2 • more common: G (Gauss) – 1T = 10,000G

13. Magnetic forces • We’ve got an equation for a lone moving charge. But what about a moving charge in wire? • F = qvBsinθ • F = q(L/Δt)Bsinθ • F = (q/Δt)Bsinθ • F = ILBsinθ +

14. Magnetic Forces • What direction is the force? • 1st right hand rule

15. The Hall effect (1879) • Makes engineers mad • proves negatives flow • Physicists and engineers both see this setup as proper. Voltmeter reads positive • How to discern?

16. The Hall Effect • Replace resistor with a Hall probe • a sheet of conducting metal • Place in a magnetic field • Which side becomes positive? • Connect voltmeter and interpret! x xxxx x xxxx x xxxx x xxxx x xxxx

17. Getting loopy

18. Warmup to scifi (sounding) stuff • A positive charge moving right is injected into a large, uniform magnetic field as shown. What will its path be? x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x +

19. Let’s explore that path • Moving in a circle means… • What’s providing it? • Ftot = Fmag • mac = qvBsinθ • m(v2/r) = qvBsinθ • mv/r = qBsin90 • r = mv/qB

20. How long is a lap? • v = ωr • v = ω(mv/qB) • 1 = ωm/(qB) • Recall ω = 2π/T • 1 = 2πm/(TqB) • T = 2πm/(qB) • f = 1/T = qB/(2πm) • characteristic frequency

21. So what? • The are the cyclotron equations • Cyclotrons • A type of particle accelerator • Evolution from linear accelerators

22. Cyclotrons • Uses E across “dee” electrodes to accelerate particle • A/C current flips signs appropriately • Uses B to curve particle & shoot • see Java demo

23. Limitations of cyclotrons • They’re obsolete now. Why? • Size • Cost • RELATIVITY • as you get really fast, mass increases • can’t exceed speed of light • Solutions • synchrocyclotrons – adjust f with relativity • synchrotrons – change f and B for constant r

24. Induction practice • A 200 turn/cm solenoid, diameter =3cm has at its center a 100 turn coil of diameter 2cm aligned in parallel. Current in the solenoid is changed from 1.5A to -1.5A in .05s. Find induced voltage in the coil .048 V

25. Practice • A loop of flexible wire w/ 10 turns is in a B=.2T aligned perpendicular to the orientation of the loop. In .1s, the loop is stretched from r=1cm to r=3cm. Find induced voltage and direction of current · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · .05V clockwise

26. Lenz’s Law • The induced current (caused by the induced EMF) appears in the direction that opposes the change that induced it • The induced current travels in a direction that creates a magnetic field w/ flux opposing the change in the original flux through the circuit • Induced current fights the inducer

27. Practice • A square coil with 25 turns and side length 1.8cm has total resistance .35Ω. It lies in the xz plane (flat on table) and B points down • If B changes from 0T.5T in .8s, find EMF • Find magnitude and direction of induced current EMF = -5.06E-3 V CCW I = 1.45E-2 A

28. Quantifying induction • A loop with resistor R, height L, and width (in field) of x. Find the flux enclosed by the loop. • ΦB = BLx x x x x x x x x x x x x x x x x x x x x x x x x L x

29. Quantifying induction • Now pull loop with velocity v. Find EMF • ξ = -(BLxf – BLxi)/Δt • ξ = BLv • Positive here because x decreases with time x x x x x x x x x x x x x x x x x x x x x x x x L x

30. Quantifying induction • Find the current in the loop • I = BLv/R • If the top and bottom of the loop are insulators, charges separate b/c of right hand rule. Find E. • V = EL so E = V/L = BLv/L = Bv

31. Practice • A plane with 30m wingspan flies N where the downward component of Earth’s B is 6E-5T and the northward component is 4.7E-5T. Find the voltage across the wingtips if the plane flies at 250m/s. Which wing is at higher voltage? ξ = .450V, west wing > east wing

32. Uses of induction • GFI (ground fault interruptor) on sockets • If an electrical short, B exists • induced current trips breaker • Electric guitars & record players • moving magnet (string, arm) near/through coil induces EMF, magnified by amp • Traffic light sensor • car presence changes inductance • Motors?

33. Induction and motors • Recall: motor = loop turning in B thanks to F=ILB • plus a commutator if DC motor • But as loop spins, number of B lines changes! • Induced EMF and current! • In which direction? • against “normal” current (causing the spin) • Called back-EMF • Fast-running motors are more power efficient • P = I2R

34. Utilizing back-EMF • What if rather than turning a “motor” by passing current through the loop, we just have something turn it? • hand crank, fan blades, water wheel, hamsters • We generate current • Generator! • Motors: electrical  mechanical energy • Generators: mechanical  electrical

35. Generators • Like motors, generators without commutatorsreverse • alternating current is easy to generate • A/C vs D/C • Edison vs Tesla • Tesla’s A/C advantage: OptimusPrime • transformers allow electricity to be passed at high voltage, low current • less power loss through wires: P = I2R • Edison goes on a murder spree