Physics 7C, Lecture 6

1. Physics 7C, Lecture 6 Magnetic Forces, Induced Currents, Induced EMFs, & Induction Winter Quarter -- 2007 Professor Robin Erbacher 343 Phy/Geo erbacher@physics.ucdavis.edu

2. Announcements • Course syllabus (policy, philosophy) on the web: • http://physics7.ucdavis.edu • Unit 9 continues today: DLMs 8 -14. • No quiz today, Demos on magnetism and induction. • Quizzes every other lecture, ~20 minutes each, • average of 4 best = 45% (or 20)% of grade. • Turn off cell phones and pagers during lecture.

3. B The Magnetic Field B We have now deduced the existence of a magnetic field B in the presence of moving charges (or current) I: Magnitude of magnetic field: Ampere’s Law: What does B depend on? 1/r (or similar, depending on charge configuration and Ampere’s law… …and current I What units does it have? Teslas In which direction does it point?

4. Electric and Magnetic Field Maps

5. Fundamentally, magnetism is an interaction between two moving charges… always.

6. Forces due to magnetic fields (a.k.a. B fields)

7. exerts force exerts force Object A Object B creates field Object B Object A field Recall: Force Models Recall our discussion about contact forces, used when direct action occurs between 2 bodies. We called this: Direct Model of Forces But when we considered questions of indirect forces: How does Earth exert its gravitational force on the ball while in mid-air? This was an example of action-at-a-distance, leading to Field Model of Forces

8. exerts force Direct Model of Forces Object A Object B exerts force Object A field field Object B creates Magnetic Fields and Forces Analogy to Gravity/Electric fields:Magnetic Fields We can think about moving charge I (current) exerting a force on a moving charge qv. Field Model of Forces

9. Field model for magnetism A charge creates a field, that then puts a force on other charges. Moving qB fieldforce on other moving charges, qv Moving charge, or a current of moving charge, creates a field that places a force on another moving charge. This is a different field than the static E-Field and creates a different type of force. All charges create E-fields but only moving charges create B fields!

10. F into the screen v x B B q Force due to a B Field Right-hand rule 2 (for a positive charge): The force on a moving charge works like this: Your thumb points in the direction of the moving charge, B is along your index finger, and F is the middle finger. Very BadFinger We’ve stepped into 3-D physics. F = qvBsinq, where q is the angle between B and v

11. The force on a moving charge due to a B field is: The Hall Effect (1897) More on Magnetic Forces What direction is the resulting force?(What is this cross-product thing?) Right-hand rule 2!

12. Force due to a B Field

13. Finding Magnetic Force PRS question: What direction is the force F on a charge +q with velocity v at point N? 1) Into the screen 2) Out of the screen 3) Towards the wire 4) Away from the wire 5) Points down 6) Points up 7) Another direction v +q  N  P  W I

14. Which direction is the force due to the B Field?

15. Some rules of thumb (so to speak)… PRS questions: True or False? There is no magnetic force on a charge at rest.

16. Some rules of thumb (so to speak)… PRS questions: True or False? There is no magnetic force on a charge at rest. There is no force on a charge moving parallel or anti-parallel to B.

17. Some rules of thumb (so to speak)… PRS questions: True or False? There is no magnetic force on a charge at rest. There is no force on a charge moving parallel or anti-parallel to B. Force is never perpendicular to the v - B plane.

18. Some rules of thumb (so to speak)… PRS questions: True or False? There is no magnetic force on a charge at rest. There is no force on a charge moving parallel or anti-parallel to B. Force is never perpendicular to the v - B plane. The force on a positive charge is in the exact opposite direction of RHR2.

19. Some rules of thumb (so to speak)… PRS questions: True or False? There is no magnetic force on a charge at rest. There is no force on a charge moving parallel or anti-parallel to B. Force is never perpendicular to the v - B plane. The force on a positive charge is in the exact opposite direction of RHR2. The B-field creating a force on a test charge is created by a source which is not the moving test charge itself which is feeling the force.

20. Some rules of thumb to study… The correct answers: • There is no force on a charge at rest. • There is no force on a charge moving parallel or anti-parallel to B. • Force is always perpendicular to the v - B plane. • The force on a negative charge is in the exact opposite direction of RHR2. • The B-field is created by a source which is not the moving charge feeling the force.

21. Microscopic model of magnetism

22. Intrinsic magnetism Electrons have an inherit electrical property – their charge. They also have an inherent magnetic property and act like tiny bar magnets. This is called the magnetic moment.

23. E B The electron is a source of both e- e- an electric field (due to its e e ﾐ ﾐ negative charge) and a magnetic field (due to its "spin") Hund’s Rules for electron shell levels: Electrons pair up and cancel out magnetic Properties. Leftover electrons can give More magnetic properties, like with Fe2+. 4 3d 4s 2 3p 6 3s 2 6 2p 2 2s 1s 2 2+ Hund's Rules for Fe B Fields from Particles • We know that moving electric charges cause magnetic fields.Another source of magnetism can be “spin”. • Electrons orbiting nuclei create current loops • Protons and electrons themselves have rotation:Spin!

24. Dipoles in a bar magnet

25. Wire loops: Forces on loops, current loops, induced currents, Faraday’s Law

26. Faraday’s Law of Induction Left:A close-up view of an electric guitar pickup. The pop-jazz guitarist Les Paul was the first person to use the law of induction to create an “electric guitar”. We will learn today how this device “picks up” the mechanical vibrations to produce an electric signal. Right:Shows the Prius for 2007, with the “Hybrid Synergy Drive” system. A major component of the most fuel-efficient hybrids is the use of regenerative braking, a technology that uses the law of induction.

27. Interaction of Loops, Wires, Currents, B fields

28. B Field force on wire A wire in an external B – field will feel a force on it. with current

29. x x x F x I x x x Force on a wire… There is a force on each charged particle which pulls them against the side of the wire pulling the whole wire with it. What sign are the moving charges in a current? F = ILBsinq Which is the same as before, since qv = qL/t = Lq/t = LI An external B-field

30. Homework: Prove to yourself…

31. Magnetic (B) field from current loop

32. RHR1 for current loops

33. Current loop field v. bar magnet Field due to current loop Dipole field of a bar magnet Notice the similarities between these fields. Loop attracts/repels magnets, so acts like a magnet.

34. I F F S S I B N N I F Torque on a loop Which direction will the current loop move due to the force? Up Down Flip sideways to right Flip sideways to left PRS question: We see that a current loop will experience a torque in the presence of a magnetic field.

35. Magnetic torque to get power Since a current loop will experience a torque in the presence of a magnetic field, this torque can be used to produce mechanical work to the outside world: a motor.

36. Electrical Motors An electrical motor will rotate the wire loop. Reverse current after each half turn and it will keep turning. commutator armature motor: input is electric energy the output is mechanical energy generator: has mechanical energy as the input and electrical energy as the output

37. Michael Faraday • poor English child (1 of 10) of a blacksmith • Self-educated while working as a bookbinder • Bound his ornate notes of the public lectures of famous chemist Humphrey Davy • Worked as Davy’s servant and eventually became the greater scientist by far • Very poorly understood math, so created a pictorial method (e.g. the Field) • Invented electric transformer and generator Michael Faraday 1791-1867

38. Faraday’s Experiment Magnetic Induction

39. Moving a magnet close to a loop • Moving it to the right, current flows in one direction (e.g. positive). • Holding it in place, no current. • Moving it to the left, current flows. Furthermore, it flows in opposite direction to that of (a).

40. Magnetic Flux • Flux  is maximum, all the area is presented to the field lines: • F = BA • Flux is zero, none of the field lines pass through the loop. • F=0 • Flux is reduced only the component of the area in the direction of the field lines contributes to flux • F = B A cos (q)

41. Faraday’s Law of Induction • An induced emf (i.e. an induced voltage) in a coil of wire will be produced when there is a changing magnetic flux through the wire coil. (Changing # field lines.) • The induced current (i.e. an induced voltage) in a coil of wire will be produced in a direction that opposes the change that caused it. • Lenz’s Law.

42. Faraday’s Law of Induction Faraday’s Law of Induction… Put another way: Changing the number of B field lines through a loop in a circuit causes voltage (emf), and therefore, current!

43. Bar Magnet Induction Homework Problem: • A bar magnet is moved rapidly toward a 40-turn, circular coil of wire. As the magnet moves, the average value of B cos  over the area of the coil increases from 0.0125 T to 0.450 T in 0.250 s. • If the radius of the coil is 3.05 cm, and the resistance of its wire is 3.55 W, find the magnitude of (a) the induced emf and (b) the induced current.

44. An Example: Lenz’s Law As the magnetic field decreases with time, the current in the loop flows such that it produces a magnetic field that tries to oppose the decrease.

45. Alternating Currents (AC) • As you see in DL, you induce a current by moving • a loop through a B field. The current acts to oppose a change in B field through the loop. • Lens’ Law! The current changes direction as you move in and out. Our regular household power is 110V AC. (Can get 220V, multi-phasic, etc). What does DC mean?

46. Pick-up Coil: Electric Guitar • The Pickup coil is wrapped around a magnet. • Metal string becomes magnetized. • Plucking the string makes the string oscillate. • Oscillations cause a change in flux in the coil, creating an induced current.

47. Electrical Generators • As the coil is rotated by an external source of mechanical work, it produces an emf that can be used to power an electric circuit. • Actual generators used in hydroelectric power plants are pictured on the right.

48. Regenerative Braking: Electric Cars • During acceleration, the battery gives power to the electric motor to help turn the axle. • Electric Motor, producing torque • Torquet=IAB sin(q) • During braking, the axle turns the motor gears, producing an induced emf that recharges the battery. • Electric generator.

49. Important Points • Both ends of a magnet can attract an object, e.g. steel • Magnetic poles are not the same as electric charges • Magnetic forces are distinct from electric forces • A compass needle is itself a small magnet • A magnetic field is defined to point in the direction of the compass needles north pole • A magnetic field comes out of the north pole and goes into the south pole- it doesn’t die inside • A magnet is a dipole of north and south. There is no monopole an object of containing only a north pole or only a south pole. At least, non found yet.