2. Magnetism1 Magnetism A Whole New Topic

3. Magnetism2 Bad Week ….. Examination #2 on Friday Examination #2 on Friday Don’t miss the WebAssign on RC Don’t miss the WebAssign on RC RC will not be on the exam (you’re welcome!)RC will not be on the exam (you’re welcome!) Problem session on Wednesday Morning – 7:30 AM – Rm 306 – for BOTH sections. Problem session on Wednesday Morning – 7:30 AM – Rm 306 – for BOTH sections. Spring Break Cancelled. Spring Break Cancelled. Today we start on a new topic MAGNETISM. Today we start on a new topic MAGNETISM. Check the two files on the website concerning vector products. Check the two files on the website concerning vector products. They may be helpful in this topic.They may be helpful in this topic.

4. Magnetism3 Magnetism was known long ago.

5. Magnetism4 Lodestone (Mineral) Lodestones attracted iron filings. Lodestones seemed to attract each other. Lodestone is a natural magnet.

6. Magnetism5 New Concept The Magnetic Field –We give it the symbol B. –A compass will line up with it. –It has Magnitude and direction so it is a VECTOR. There are some similarities with the Electric Field but also some significant differences.

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 Observations Bring a magnet to an electrically charged object and the observed attraction will be a result of charge induction or polarization. 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.)

12. Magnetism11 Magnets Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles. Magnetic Field

13. Magnetism12 Consider a Permanent Magnet NS The magnetic Field B goes from North to South.

14. Magnetism13 Introduce Another Permanent Magnet NS N S The bar magnet (a magnetic dipole) wants to align with the B-field. pivot

15. Magnetism14 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

16. Magnetism15 Field of a Permanent Magnet NS NS The bar magnet (a magnetic dipole) wants to align with the B-field.

17. Magnetism16 Convention For Magnetic Fields X  Field INTO Paper Field OUT of Paper B

18. Magnetism17 Typical Representation

19. Magnetism18 Experiments with Magnets Show Current carrying wire produces a circular magnetic field around it. Force (actually torque) on a Compass Needle (or magnet) increases with current.

20. Magnetism19 Current Carrying Wire Current into the page. B Right hand Rule- Thumb in direction of the current Fingers curl in the direction of B

21. Magnetism20 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.

22. Magnetism21 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.

23. Magnetism22 Planet Earth

24. Magnetism23 Inside it all. 8000 Miles

25. Magnetism24 On the surface it looks like this..

26. Magnetism25 Inside: Warmer than Floriduh

27. Magnetism26 Much Warmer than Floriduh

28. Magnetism27 Finally

29. Magnetism28 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.

30. Magnetism29 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.

31. Magnetism30 This planet is really screwed up! NORTH POLE SOUTH POLE

32. Magnetism31 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.

33. Magnetism32 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. ++ + + ++

34. Magnetism33 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.

35. Magnetism34 WHAT THE HECK IS THAT??? A WHAT PRODUCT? A CROSS PRODUCT – Like an angry one?? Alas, yes …. F=qv X B

36. Magnetism35 The Lorentz Force This can be summarized as: v F B q m or:  is the angle between B and V

37. Magnetism36 Nicer Picture

38. Magnetism37 Another Picture

39. Magnetism38 VECTOR CALCULATIONS

40. Magnetism39 Practice Which way is the Force??? B and v are parallel. Crossproduct is zero. So is the force.

41. Magnetism40 Units

42. Magnetism41 t e s l a s are

43. Magnetism42 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)

44. Magnetism43 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”.

45. Magnetism44 The Wire in More Detail B out of plane of the paper Assume all electrons are moving with the same velocity v d. L

46. Magnetism45 Magnetic Levitation Current = i mg Magnetic Force Where does B point????Into the paper.

47. Magnetism46 MagLev

48. Magnetism47 A conductor suspended by two flexible wires as shown in the diagram has a mass per unit length of 0.040 0 kg/m. What current must exist in the conductor in order for the tension in the supporting wires to be zero when the magnetic field is 3.60 T into the page? What is the required direction for the current? Concrete Insulator

49. Magnetism48 There was a crooked man who lived in a crooked house that was wired with crooked wires

50. Magnetism49 Crooked Wire (in a plane) in a constant B field

51. Magnetism50 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.

52. Magnetism51 Case 2 The net magnetic force on a closed current carrying loop is ZERO!

53. Magnetism52 Current Loop Loop will tend to rotate due to the torque the field applies to the loop. What is force on the ends??

54. Magnetism53 The Loop (From the top) 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,

55. Magnetism54 An Application The Galvanometer

56. Magnetism55 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)

57. Magnetism56 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.

58. Magnetism57 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.

59. Magnetism58 A 40.0-cm length of wire carries a current of 20.0 A. It is bent into a loop and placed with its normal perpendicular to a magnetic field with a magnitude of 0.520 T. What is the torque on the loop if it is bent into (a)an equilateral triangle? (b)What is the torque if the loop is (c) a square or (d) a circle? (e) Which torque is greatest?

60. Magnetism59 Motion of a charged particle in a magnetic Field

61. Magnetism60 Trajectory of Charged Particles in a Magnetic Field ++++++++++++++++++++++++++++++++++++++++ v B F ++++++++++++++++++++++++++++++++++++++++ v B F (B field points into plane of paper.)

62. Magnetism61 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

63. Magnetism62 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

64. Magnetism63

65. Magnetism64 ++++++++++++++++++++++++++++++++++++++++ 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!

66. Magnetism65 Cyclotron Frequency ++++++++++++++++++++++++++++++++++++++++ v B F r The time taken to complete one orbit is:

67. Magnetism66 More Circular Type Motion in a Magnetic Field

68. Magnetism67 Review Problem. An electron moves in a circular path perpendicular to a constant magnetic field of magnitude 1.00 mT. The angular momentum of the electron about the center of the circle is 4.00 × 10–25 J · s. Determine: (a)the radius of the circular path and (b)the speed of the electron.

69. Magnetism68 Mass Spectrometer Smaller Mass

70. Magnetism69

71. Magnetism70 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

72. Magnetism71 Problem Continued r

73. Magnetism72 crossed Let’s Look at the effect of crossed E and B Fields: x x x x x x q, m B v E

74. Magnetism73 What is the relation between the intensities of the electric and magnetic fields for the particle to move in a straight line ?. 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 x x x x x x q m B v E B E