2. Magnetism1 Magnetism A Whole New Topic October 23, 2006

3. Magnetism2 This Week Today we begin magnetism – a topic that will occupy us for most of the remainder of the semester. Today we begin magnetism – a topic that will occupy us for most of the remainder of the semester. Wednesday – Examination #2 Wednesday – Examination #2 Potential, Capacitors, Resisters and DC Circuits.Potential, Capacitors, Resisters and DC Circuits. There is a new, SHORT WebAssign on board on RC. (2 problems) There is a new, SHORT WebAssign on board on RC. (2 problems) No quiz on Friday. We continue with Magnetism. No quiz on Friday. We continue with Magnetism. Watch for new WA popping up after the exam. Watch for new WA popping up after the exam.

4. Magnetism3 What did you think about the quiz on Friday? Both answers = 3 points. It was fair. It was fair. It was unfair. It was unfair.

5. Magnetism4 Magnetism was known long ago.

6. Magnetism5 Lodestone (Mineral) Lodestones attracted iron filings. Lodestones seemed to attract each other. Used as a compass. –One end always pointed north. –Called the “North Pole” Lodestone is a natural magnet.

7. Magnetism6 Refrigerators are attracted to magnets!

8. Magnetism7 Where is Magnetism Used?? Motors Navigation – Compass Magnetic Tapes –Music, Data Television –Beam deflection Coil Magnetic Resonance Imaging High Energy Physics Research

9. Magnetism8 Magnet Demo – Compare to Electrostatics NSNS Pivot Magnet What Happens??

10. Magnetism9 Results - Magnets Like Poles Repel Opposite Poles Attract Magnetic Poles are only found in pairs. –No magnetic monopoles have ever been observed. Shaded End is NORTH Pole Shaded End of a compass points to the NORTH. S N

11. Magnetism10 Bring a magnet to a wooden rod The wooden rod is attracted to the magnet. The wooden rod is repelled by the magnet. Nothing happens.

12. Magnetism11 Bring a magnet to an aluminum rod. Nothing happens. The magnet attracts the rod. The magnet repels the rod. It depends on whether the N or S pole is closest to the rod. Nothing happens.

13. Magnetism12 Bring a neutral Teflon rod to a magnet… The rod attracts the magnet. The rod repels the magnet. Nothing happens.

14. Magnetism13 Bring a charged Teflon rod to a magnet.. It will attract the NORTH pole and repel the SOUTH pole. It will repel the NORTH pole and will attract the SOUTH pole. It will repel both poles. It will attract both poles. Nothing will happen.

15. Magnetism14 Observations Bring a magnet to an electrically charged object and the observed attraction will be a result of charge induction. Magnetic poles do not interact with stationary electric charges. Bring a magnet near some metals (Co, Fe, Ni …) and it will be attracted to the magnet. –The metal will be attracted to both the N and S poles independently. –Some metals are not attracted at all. (Al, Cu, Ag, Au) –Wood is NOT attracted to a magnet. –Neither is water. A magnet will force a compass needle to align with it. (No big Surprise.)

16. Magnetism15 Magnets Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles. Magnetic Field

17. Magnetism16 Consider a Permanent Magnet NS

18. Magnetism17 Introduce Another Permanent Magnet NS N S The bar magnet (a magnetic dipole) wants to align with the B-field. pivot

19. Magnetism18 The south pole of the small bar magnet is attracted towards the north pole of the big magnet. The North pole of the small magnet is repelled by the north pole of the large magnet. The South pole pf the large magnet creates a smaller force on the small magnet than does the North pole. DISTANCE effect. The field attracts and exerts a torque on the small magnet. Field of a Permanent Magnet NS N S

20. Magnetism19 Field of a Permanent Magnet NS NS The bar magnet (a magnetic dipole) wants to align with the B-field.

21. Magnetism20 The Magnetic Field Similar to Electric Field … exists in space. –Has Magnitude AND Direction. The “stronger” this field, the greater is the ability of the field to interact with a magnet.

22. Magnetism21 Convention For Magnetic Fields X  Field INTO Paper Field OUT of Paper B

23. Magnetism22 Experiments with Magnets Show Current carrying wire produces a circular magnetic field around it. Force on Compass Needle (or magnet) increases with current.

24. Magnetism23 Current Carrying Wire Current into the page. B Right hand Rule- Thumb in direction of the current Fingers curl in the direction of B

25. Magnetism24 Current Carrying Wire B field is created at ALL POINTS in space surrounding the wire. The B field has magnitude and direction. Force on a magnet increases with the current. Force is found to vary as ~(1/d) from the wire.

26. Magnetism25 Compass and B Field Observations –North Pole of magnets tend to move toward the direction of B while S pole goes the other way. –Field exerts a TORQUE on a compass needle. –Compass needle is a magnetic dipole. –North Pole of compass points toward the NORTH.

27. Magnetism26 Planet Earth

28. Magnetism27 Inside it all. 8000 Miles

29. Magnetism28 On the surface it looks like this..

30. Magnetism29 Inside: Warmer than Floriduh

31. Magnetism30 Much Warmer than Floriduh

32. Magnetism31 Finally

33. Magnetism32 In Between The molten iron core exists in a magnetic field that had been created from other sources (sun…). The molten iron core exists in a magnetic field that had been created from other sources (sun…). The fluid is rotating in this field. The fluid is rotating in this field. This motion causes a current in the molten metal. This motion causes a current in the molten metal. The current causes a magnetic field. The current causes a magnetic field. The process is self-sustaining. The process is self-sustaining. The driving force is the heat (energy) that is generated in the core of the planet. The driving force is the heat (energy) that is generated in the core of the planet.

34. Magnetism33 After molten lava emerges from a volcano, it solidifies to a rock. In most cases it is a black rock known as basalt, which is faintly magnetic, like iron emerging from a melt. Its magnetization is in the direction of the local magnetic force at the time when it cools down. Instruments can measure the magnetization of basalt. Therefore, if a volcano has produced many lava flows over a past period, scientists can analyze the magnetizations of the various flows and from them get an idea on how the direction of the local Earth's field varied in the past. Surprisingly, this procedure suggested that times existed when the magnetization had the opposite direction from today's. All sorts of explanation were proposed, but in the end the only one which passed all tests was that in the distant past, indeed, the magnetic polarity of the Earth was sometimes reversed.

35. Magnetism34 Ancient Navigation

36. Magnetism35 This planet is really screwed up! NORTH POLE SOUTH POLE

37. Magnetism36 Compass Direction Repeat Navigation DIRECTION N S If N direction is pointed to by the NORTH pole of the Compass Needle, then the pole at the NORTH of our planet must be a SOUTH MAGNETIC POLE! Navigation DIRECTION S N And it REVERSES from time to time.

38. Magnetism37 Rowland’s Experiment Rotating INSULATING Disk which is CHARGED + or – on exterior. xxx xxx B xxx Field is created by any moving charge. Increases with charge on the disk. Increases with angular velocity of the disk. Electrical curent is a moving charge. ++ + + ++

39. Magnetism38 So much for the observations. Let’s do the physics!

40. Magnetism39 A Look at the Physics q There is NO force on a charge placed into a magnetic field if the charge is NOT moving. q If the charge is moving, there is a force on the charge, perpendicular to both v and B. F = q v x B There is no force if the charge moves parallel to the field.

41. Magnetism40 WHAT THE HECK IS THAT??? A WHAT PRODUCT? A CROSS PRODUCT – Like an angry one?? Alas, yes …. F=qv X B

42. Magnetism41 The Lorentz Force This can be summarized as: v F B q m or:  is the angle between B and V

43. Magnetism42 Nicer Picture

44. Magnetism43 VECTOR CALCULATIONS

45. Magnetism44 Note See proof of previous approach on the website.

46. Magnetism45 Practice Which way is the Force??? B and v are parallel. Crossproduct is zero. So is the force.

47. Magnetism46 Units

48. Magnetism47 t e s l a s are

49. Magnetism48 The Magnetic Force is Different From the Electric Force. Whereas the electric force acts in the same direction as the field: The magnetic force acts in a direction orthogonal to the field: And --- the charge must be moving !! (Use “Right-Hand” Rule to determine direction of F)

50. Magnetism49 So… A moving charge can create a magnetic field. A moving charge is acted upon by a magnetic field. In Magnetism, things move. In the Electric Field, forces and the field can be created by stationary charges.

51. Magnetism50 Wires A wire with a current contains moving charges. A magnetic field will apply a force to those moving charges. This results in a force on the wire itself. –The electron’s sort of PUSH on the side of the wire. F Remember: Electrons go the “other way”.

52. Magnetism51 The Wire in More Detail B out of plane of the paper Assume all electrons are moving with the same velocity v d.

53. Magnetism52 Magnetic Levitation Current = i mg Magnetic Force Where does B point????Into the paper.

54. Magnetism53 MagLev

55. Magnetism54 Motion of a charged particle in a magnetic Field

56. Magnetism55 There was a crooked man who lived in a crooked house that was wired with crooked wires

57. Magnetism56 Crooked Wire (in a plane) in a constant B field

58. Magnetism57 Case 1 The magnetic force on a curved current carrying conductor in a uniform magnetic field is the same as that of a straight conductor carrying the same current between the two points a and b.

59. Magnetism58 Case 2 The net magnetic force on a closed current carrying loop is ZERO!

60. Magnetism59 Current Loop Loop will tend to rotate due to the torque the field applies to the loop. What is force on the ends??

61. Magnetism60 The Loop pivot OBSERVATION Force on Side 2 is out of the paper and that on the opposite side is into the paper. No net force tending to rotate the loop due to either of these forces. The net force on the loop is also zero,

62. Magnetism61 An Application The Galvanometer

63. Magnetism62 The other sides  1 =F 1 (b/2)Sin(  ) =(B i a) x (b/2)Sin(  ) total torque on the loop is: 2  1 Total torque:  =(iaB) bSin(  ) =iABSin(  ) (A=Area)

64. Magnetism63 A Coil Normal to the coil RIGHT HAND RULE TO FIND NORMAL TO THE COIL: “Point or curl you’re the fingers of your right hand in the direction of the current and your thumb will point in the direction of the normal to the coil.

65. Magnetism64 Dipole Moment Definition Define the magnetic dipole moment of the coil  as:  =NiA  =  X B We can convert this to a vector with A as defined as being normal to the area as in the previous slide.

66. Magnetism65 Trajectory of Charged Particles in a Magnetic Field ++++++++++++++++++++++++++++++++++++++++ v B F ++++++++++++++++++++++++++++++++++++++++ v B F (B field points into plane of paper.)

67. Magnetism66 Trajectory of Charged Particles in a Magnetic Field ++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++ v v BB F F (B field points into plane of paper.) Magnetic Force is a centripetal force

68. Magnetism67 Review of Rotational Motion  atat arar a t = r  tangential acceleration a r = v 2 / r radial acceleration The radial acceleration changes the direction of motion, while the tangential acceleration changes the speed. r  s  = s / r  s =  r  ds/dt = d  /dt r  v =  r  = angle,  = angular speed,  = angular acceleration Uniform Circular Motion  = constant  v and a r constant but direction changes a r = v 2 /r =  2 r F = ma r = mv 2 /r = m  2 r KE = ½ mv 2 = ½ mw 2 r 2 v  arar

69. Magnetism68

70. Magnetism69 ++++++++++++++++++++++++++++++++++++++++ Radius of a Charged Particle Orbit in a Magnetic Field v B F r Centripetal Magnetic Force Force = Note: as, the magnetic force does no work!

71. Magnetism70 Cyclotron Frequency ++++++++++++++++++++++++++++++++++++++++ v B F r The time taken to complete one orbit is:

72. Magnetism71 More Circular Type Motion in a Magnetic Field

73. Magnetism72 Mass Spectrometer Smaller Mass

74. Magnetism73

75. Magnetism74 An Example A beam of electrons whose kinetic energy is K emerges from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic field B such that

76. Magnetism75 Problem Continued r

77. Magnetism76 crossed Let’s Look at the effect of crossed E and B Fields: x x x x x x q, m B v E

78. Magnetism77 What is the relation between the intensities of the electric and magnetic fields for the particle to move in a straight line ?. x x x x x x q m B v E FEFE FBFB F E = q E and F B = q v B If F E = F B the particle will move following a straight line trajectory q E = q v B v = E / B