1. Magnetic Fields

2. Video from the International Space Station on Magnetism Permanent Magnets http://www.youtube.com/watch?v=NvJcrGlzGAg&feature=relmfu http://www.youtube.com/watch?v=WXvar-4M6VA Ferrofluid video

3. Permanent Magnets Poles of a magnet are the ends where objects are most strongly attracted Poles of a magnet are the ends where objects are most strongly attracted Two poles, called north and south Two poles, called north and south Like poles repel each other and unlike poles attract each other Like poles repel each other and unlike poles attract each other Similar to electric charges Similar to electric charges Magnetic poles cannot be isolated Magnetic poles cannot be isolated If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole If a permanent magnetic is cut in half repeatedly, you will still have a north and a south pole This differs from electric charges This differs from electric charges There is some theoretical basis for monopoles, but none have been detected There is some theoretical basis for monopoles, but none have been detected

4. More About Magnetism An unmagnetized piece of iron can be magnetized by stroking it with a magnet An unmagnetized piece of iron can be magnetized by stroking it with a magnet Somewhat like stroking an object to charge an object Somewhat like stroking an object to charge an object Magnetism can be induced Magnetism can be induced If a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized If a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized

5. Types of Magnetic Materials Soft magnetic materials, such as iron, are easily magnetized Soft magnetic materials, such as iron, are easily magnetized They also tend to lose their magnetism easily They also tend to lose their magnetism easily Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize They tend to retain their magnetism They tend to retain their magnetism

6. Magnetic Fields A vector quantity, symbolized by B A vector quantity, symbolized by B Direction is given by the direction a north pole of a compass needle. The needle points in that direction in Earth’s magnetic field. Direction is given by the direction a north pole of a compass needle. The needle points in that direction in Earth’s magnetic field. Magnetic field lines can be used to show how the field lines, as traced out by a compass, would look. Magnetic field lines can be used to show how the field lines, as traced out by a compass, would look. They are imaginary lines, like E field lines – they don’t really exist. They are imaginary lines, like E field lines – they don’t really exist. The number of magnetic field lines passing through a surface is the magnetic flux The number of magnetic field lines passing through a surface is the magnetic flux

7. B field lines A compass can be used to show the direction of the magnetic field lines (a) The direction is defined as the direction in which the north pole of a compass points when it is placed in the magnetic field. A sketch of the magnetic field lines (b)

8. Magnetic field lines are closed loops The closed loops leave the north pole of a magnet and enter the south pole of the same magnet. Magnetic field lines are most concentrated at the poles.

9. Magnetic Field Lines, Bar Magnet Iron filings are used to show the pattern of the electric field lines Iron filings are used to show the pattern of the electric field lines The direction of the field lines are aligned with the direction a north pole would point on a compass placed around the magnet. The direction of the field lines are aligned with the direction a north pole would point on a compass placed around the magnet.

10. Magnetic Field Lines, Unlike Poles Iron filings are used to show the pattern of the electric field lines Iron filings are used to show the pattern of the electric field lines The direction of the field is the direction a north pole would point The direction of the field is the direction a north pole would point Compare to the electric field produced by an electric dipole Compare to the electric field produced by an electric dipole

11. Magnetic Field Lines, Like Poles Iron filings are used to show the pattern of the electric field lines Iron filings are used to show the pattern of the electric field lines The direction of the field is the direction a north pole would point The direction of the field is the direction a north pole would point Compare to the electric field produced by like charges Compare to the electric field produced by like charges

12. PhET magnetism simulation magnet-and-compass_en.jar magnet-and-compass_en.jar magnet-and-compass_en.jar

13. Earth’s Magnetic Field The Earth’s geographic north pole corresponds to its magnetic south pole The Earth’s geographic north pole corresponds to its magnetic south pole The Earth’s geographic south pole corresponds to its magnetic north pole The Earth’s geographic south pole corresponds to its magnetic north pole Strictly speaking, a north pole should be a “north-seeking” pole and a south pole a “south-seeking” pole, because the N end of a magnet is attracted to Earth’s S magnetic pole. Strictly speaking, a north pole should be a “north-seeking” pole and a south pole a “south-seeking” pole, because the N end of a magnet is attracted to Earth’s S magnetic pole.

14. Earth’s Magnetic Field The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior The Earth’s magnetic field resembles that achieved by burying a huge bar magnet deep in the Earth’s interior

15. Dip Angle of Earth’s Magnetic Field If a compass is free to rotate vertically as well as horizontally, it points to the earth’s surface If a compass is free to rotate vertically as well as horizontally, it points to the earth’s surface The angle between the horizontal and the direction of the magnetic field is called the dip angle The angle between the horizontal and the direction of the magnetic field is called the dip angle The farther north the device is moved, the farther from horizontal the compass needle would be The farther north the device is moved, the farther from horizontal the compass needle would be The compass needle would be horizontal at the equator and the dip angle would be 0° The compass needle would be horizontal at the equator and the dip angle would be 0° The compass needle would point straight down at the south magnetic pole and the dip angle would be 90° (up near what we call the North Pole) The compass needle would point straight down at the south magnetic pole and the dip angle would be 90° (up near what we call the North Pole)

16. More About the Earth’s Magnetic Poles The dip angle of 90° is found at a point just north of Hudson Bay in Canada The dip angle of 90° is found at a point just north of Hudson Bay in Canada This is considered to be the location of the south magnetic pole This is considered to be the location of the south magnetic pole The magnetic and geographic poles are not in the same exact location The magnetic and geographic poles are not in the same exact location The difference between true north, at the geographic north pole, and magnetic north is called the magnetic declination The difference between true north, at the geographic north pole, and magnetic north is called the magnetic declination The amount of declination varies by location on the earth’s surface The amount of declination varies by location on the earth’s surface

17. Earth’s Magnetic Declination

18. Source of the Earth’s Magnetic Field There cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetization There cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetization The most likely source of the Earth’s magnetic field is believed to be electric currents in the liquid part of the core The most likely source of the Earth’s magnetic field is believed to be electric currents in the liquid part of the core

19. Reversals of the Earth’s Magnetic Field The direction of the Earth’s magnetic field reverses every few million years The direction of the Earth’s magnetic field reverses every few million years Evidence of these reversals are found in basalts resulting from volcanic activity Evidence of these reversals are found in basalts resulting from volcanic activity The origin of the reversals is not understood The origin of the reversals is not understood

20. Most powerful magnet in the world http://www.youtube.com/watch?v=QGytW_C6hR8 http://www.youtube.com/watch?v=QGytW_C6hR8 http://www.youtube.com/watch?v=QGytW_C6hR8 7’ video on you tube about most powerful electromagnet. 7’ video on you tube about most powerful electromagnet.

21. Forces on individual charges or current carrying wires (many charges) that are moving in a magnetic field Forces on individual charges or current carrying wires (many charges) that are moving in a magnetic field

22. Magnetic and Electric Fields An electric field surrounds any An electric field surrounds any stationary electric charge stationary electric charge A magnetic field surrounds any A magnetic field surrounds any moving electric charge moving electric charge A magnetic field surrounds any magnetic material A magnetic field surrounds any magnetic material

23. Magnetic Forces on charged particles moving in a magnetic field One can define a magnetic field B in terms of the magnetic force exerted on a test charge (like definition of E field) One can define a magnetic field B in terms of the magnetic force exerted on a test charge (like definition of E field) F = force in N F = force in N v = velocity v = velocity q = charge q = charge θ angle between v and B θ angle between v and B If angle θ is 90 degrees, sin θ = 1 (max!) If angle θ is 90 degrees, sin θ = 1 (max!) If angle θ is 0 degrees, sin θ = 0 (min!) If angle θ is 0 degrees, sin θ = 0 (min!)

24. Magnetic Forces on a charged particle moving in a magnetic field When a charged particle moves through a magnetic field, a magnetic force acts on it. When a charged particle moves through a magnetic field, a magnetic force acts on it. Define θ as the angle between v (velocity) and B (magnetic field) Define θ as the angle between v (velocity) and B (magnetic field) This force has a maximum value when the charge moves perpendicularly to the magnetic field lines (when θ = 90 degrees, sin 90 = 1) This force has a maximum value when the charge moves perpendicularly to the magnetic field lines (when θ = 90 degrees, sin 90 = 1) This force is zero when the charge moves along the magnetic field lines (when θ = 0 degrees, because sin 0 = 0) This force is zero when the charge moves along the magnetic field lines (when θ = 0 degrees, because sin 0 = 0)

25. Units of Magnetic Field

26. A Few Typical B Values Conventional laboratory magnets Conventional laboratory magnets 2.5 Tesla 2.5 Tesla Superconducting magnets Superconducting magnets 30 Tesla 30 Tesla Earth’s magnetic field Earth’s magnetic field 5 x 10 -5 Tesla 5 x 10 -5 Tesla

27. Finding the Direction of Magnetic Force Experiments show that the direction of the magnetic force is always perpendicular to both v and B Experiments show that the direction of the magnetic force is always perpendicular to both v and B F max occurs when v is perpendicular to B F max occurs when v is perpendicular to B F = 0 when v is parallel to B F = 0 when v is parallel to B

28. Right Hand Rule A Hold your right hand open Hold your right hand open Place your fingers in the direction of B Place your fingers in the direction of B Place your thumb in the direction of v (or I) Place your thumb in the direction of v (or I) The direction of the force on a positive charge is directed out of your palm The direction of the force on a positive charge is directed out of your palm If the charge is negative, the force is opposite that determined by the right hand rule If the charge is negative, the force is opposite that determined by the right hand rule (v or I)

29. Practice the Right Hand Rule A Force points to leftForce points into page

30. Practice the Right Hand Rule A Force points out of pageForce points up towards top of page

31. Force on a Charged Particle moving in a Magnetic Field Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the field Consider a particle moving in an external magnetic field so that its velocity is perpendicular to the field The force is always directed toward the center of the circular path The force is always directed toward the center of the circular path The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle x’s are arrows pointing into page representing B

32. Motion of a charged particle in a uniform magnetic field

33. Bending an Electron Beam in an External Magnetic Field

34. Particle Moving in an External Magnetic Field, 2 If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral The spiral path is called a helix The spiral path is called a helix

35. Magnetic Force on a Current Carrying Conductor (a wire) A force is exerted on a current-carrying wire placed in a magnetic field A force is exerted on a current-carrying wire placed in a magnetic field The current is a collection of many charged particles in motion The current is a collection of many charged particles in motion The direction of the magnetic force is given by right hand rule A The direction of the magnetic force is given by right hand rule A

36. Force on current carrying conductor in B field ( F = ILB) http://www.youtube.com/watch?v=qqkUeQ0nsF8 11:30 into the video demos this force (MIT Lecture 11)

37. Force on a Current Carrying Conductor The blue x’s indicate the magnetic field is directed into the page The blue x’s indicate the magnetic field is directed into the page The x represents the tail of the arrow The x represents the tail of the arrow Blue dots would be used to represent the field directed out of the page Blue dots would be used to represent the field directed out of the page A dot represents the head of the arrow A dot represents the head of the arrow In this case, there is no current, so there is no force In this case, there is no current, so there is no force

38. Force on a Current Carrying Conductor B is into the page B is into the page Point your fingers into the page Point your fingers into the page The current is up the page The current is up the page Point your thumb to the top of the page Point your thumb to the top of the page The force is to the left, so the wire flexes to the left The force is to the left, so the wire flexes to the left Your palm should be pointing to the left Your palm should be pointing to the left F = ILB (L= length of wire in field) F = ILB (L= length of wire in field)

39. Force on a Current Carrying Conductor B is into the page B is into the page Point your fingers into the page Point your fingers into the page The current is down the page The current is down the page Point your thumb down towards the bottom of the page Point your thumb down towards the bottom of the page The force is to the right, so wire bends to the right The force is to the right, so wire bends to the right Your palm should be pointing to the right Your palm should be pointing to the right F = I L B F = I L B

40. Electric Motor An electric motor converts electrical energy to mechanical energy An electric motor converts electrical energy to mechanical energy The mechanical energy is in the form of rotational kinetic energy The mechanical energy is in the form of rotational kinetic energy An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field An electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field

41. Electric Motor, 2 The torque acting on the loop will tend to rotate the loop to smaller values of θ until the torque becomes 0 at θ = 0° The torque acting on the loop will tend to rotate the loop to smaller values of θ until the torque becomes 0 at θ = 0° If the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction If the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction

42. Electric Motor, 3 To provide continuous rotation in one direction, the current in the loop must periodically reverse To provide continuous rotation in one direction, the current in the loop must periodically reverse In ac motors, this reversal naturally occurs In ac motors, this reversal naturally occurs In dc motors, a split-ring commutator and brushes are used In dc motors, a split-ring commutator and brushes are used Actual motors would contain many current loops and commutators Actual motors would contain many current loops and commutators

43. Electric Motor, final Just as the loop becomes perpendicular to the magnetic field and the torque becomes 0, inertia carries the loop forward and the brushes cross the gaps in the ring, causing the current loop to reverse its direction Just as the loop becomes perpendicular to the magnetic field and the torque becomes 0, inertia carries the loop forward and the brushes cross the gaps in the ring, causing the current loop to reverse its direction This provides more torque to continue the rotation This provides more torque to continue the rotation The process repeats itself The process repeats itself MIT video lecture on motors/commutators: MIT video lecture on motors/commutators: http://www.youtube.com/watch?v=qqkUeQ0nsF8 Demo of motor loop only – start at 48:00 Demo of motor loop only – start at 48:00 Explanation of motors and commutators – start at 34:50 Explanation of motors and commutators – start at 34:50

44. Magnetic fields created by current carrying wires (electromagnets!) Magnetic fields created by current carrying wires (electromagnets!)

45. B field around a current carrying wire The current in the wire creates a magnetic field (B field) around the wire, that consists of concentric, closed circles. The current in the wire creates a magnetic field (B field) around the wire, that consists of concentric, closed circles. B field strength is proportional to 1/r, distance from wire. B field strength is proportional to 1/r, distance from wire.

46. Magnetic Fields around a Long Straight Wire – RHR B A current-carrying wire produces a magnetic field A current-carrying wire produces a magnetic field The compass needle deflects in directions tangent to the circle The compass needle deflects in directions tangent to the circle The compass needle points in the direction of the magnetic field produced by the current The compass needle points in the direction of the magnetic field produced by the current

47. Direction of the Field around a Long Straight Wire – RHR B Right Hand Rule B Right Hand Rule B Grasp the wire in your right hand Grasp the wire in your right hand Point your thumb in the direction of the current Point your thumb in the direction of the current Your fingers will curl in the direction of the field Your fingers will curl in the direction of the field

48. Force on two current carrying conductors Current in same direction attracts Current in opposite direction repels

49. What is the effect of wire 2’s current on wire 1? The magnetic field coming from wire 2 at the location of wire 1 points in the direction shown by B 2 on the right above (blue arrow). Put your thumb in the direction of I 1 and your fingertips in the direction of B 2. What way is your palm facing? In the direction of F 1 F 12

50. Wires with current in same direction I 1 I 2 XXXXXXXXXX XXXXXXXXXX F 2ON 1 F 1 ON 2

51. Wires with current in opposite direction I 1 I 2 XXXXXXXXXX XXXXXXXXXX F 2ON 1 F 1 ON 2

52. Video and tutorial on force in current carrying wires MIT Electromagnetism course Lecture 11 MIT Electromagnetism course Lecture 11 Forces on 2 current carrying wires video Forces on 2 current carrying wires video http://www.youtube.com/watch?v=qqkUeQ0nsF8 http://www.youtube.com/watch?v=qqkUeQ0nsF8 http://www.youtube.com/watch?v=qqkUeQ0nsF8 Starts at 15:00, goes to 17:00 min. Starts at 15:00, goes to 17:00 min. http://dev.physicslab.org/Document.aspx?doctype=3&filename=Magnetism_CurrentCarryingWires.xml http://dev.physicslab.org/Document.aspx?doctype=3&filename=Magnetism_CurrentCarryingWires.xml http://dev.physicslab.org/Document.aspx?doctype=3&filename=Magnetism_CurrentCarryingWires.xml Tutorial on forces in parallel wires Tutorial on forces in parallel wires

53. Magnetic field around a circular loop of wire with a current Applying the right hand rule B to any part of the wire loop, the direction of the field inside the loop is always the same. Applying the right hand rule B to any part of the wire loop, the direction of the field inside the loop is always the same. SOLENOID A solenoid has great B field strength inside it for the reason given below.

54. Right Hand Rule C Curl your fingers around the wire in the direction the current is going. Curl your fingers around the wire in the direction the current is going. Your thumb will point toward the north pole of the electromagnet. Your thumb will point toward the north pole of the electromagnet. A solenoid like this makes a strong electromagnet. The strength of the field is proportional to the current in the coil.

55. If a long, straight wire is bent into a coil of several closely spaced loops, the resulting device is a solenoid, often called an electromagnet. If a long, straight wire is bent into a coil of several closely spaced loops, the resulting device is a solenoid, often called an electromagnet. B = μ o nI where μ o = 4 π x 10 -7 T m / A μ o is the permeability of free space and n is number of turns per unit length (meter) This device is important in different applications because it acts as a magnet only when a current is moving through the wire loops. This device is important in different applications because it acts as a magnet only when a current is moving through the wire loops. The magnetic field inside a solenoid increases with current and is proportional to the number of coils per unit length. The magnetic field inside a solenoid increases with current and is proportional to the number of coils per unit length. Solenoids / Electromagnets

56. Solenoids The magnetic field lines of a loosely wound solenoid of length l and number of turns N. The field lines inside the solenoid are nearly parallel, uniformly spaced, and close together. The magnetic field lines of a loosely wound solenoid of length l and number of turns N. The field lines inside the solenoid are nearly parallel, uniformly spaced, and close together. This indicates that the B field inside the solenoid is nearly uniform and strong. The B field outside the solenoid is weaker and in the opposite direction. This indicates that the B field inside the solenoid is nearly uniform and strong. The B field outside the solenoid is weaker and in the opposite direction.

57. Solenoids If the turns are closely spaced, the field lines are as shown, entering at one end of the solenoid and emerging from the other. If the turns are closely spaced, the field lines are as shown, entering at one end of the solenoid and emerging from the other. This means that one end acts as a north pole and the other as a south pole, like a permanent magnet, with a strong B field at the ends. This means that one end acts as a north pole and the other as a south pole, like a permanent magnet, with a strong B field at the ends.

58. Want to make an electromagnet? Wrap a wire around an iron nail, then hook up the ends to a battery to complete the circuit. Wrap a wire around an iron nail, then hook up the ends to a battery to complete the circuit. Now you can pick up paper clips with your electromagnet. The more current, the more paper clips you can pick up! Now you can pick up paper clips with your electromagnet. The more current, the more paper clips you can pick up!

60. Atomic magnetism, spins, and magnetic domains Atomic magnetism, spins, and magnetic domains

61. Magnetic Effects of Electrons - - Orbits An individual atom should act like a magnet because of the motion of the electrons about the nucleus An individual atom should act like a magnet because of the motion of the electrons about the nucleus Each electron circles the atom once in about every 10 -16 seconds Each electron circles the atom once in about every 10 -16 seconds This would produce a current of 1.6 mA and a magnetic field of about 20 T at the center of the circular path (that’s a large number!) This would produce a current of 1.6 mA and a magnetic field of about 20 T at the center of the circular path (that’s a large number!) However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom

62. Magnetic Effects of Electrons – Orbits, cont The net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials The net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials

63. Magnetic Effects of Electrons - - Spins Electrons also have spin Electrons also have spin The classical model is to consider the electrons to spin like tops The classical model is to consider the electrons to spin like tops It is actually a relativistic and quantum effect It is actually a relativistic and quantum effect

64. Electron spin The magnetic spin of an electron follows in the direction of the magnetic field lines as shown in the diagram (use left hand!)

65. Magnetic Effects of Electrons – Spins, cont The field due to the spinning is generally stronger than the field due to the orbital motion The field due to the spinning is generally stronger than the field due to the orbital motion Electrons usually pair up with their spins opposite each other, so their fields cancel each other Electrons usually pair up with their spins opposite each other, so their fields cancel each other That is why most materials are not naturally magnetic That is why most materials are not naturally magnetic

66. Magnetic Effects of Electrons - - Domains In some materials, the spins do not naturally cancel In some materials, the spins do not naturally cancel Such materials are called ferromagnetic Such materials are called ferromagnetic Large groups/clusters of atoms in which the spins are aligned are called domains Large groups/clusters of atoms in which the spins are aligned are called domains When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others This causes the material to become magnetized This causes the material to become magnetized

67. Domains, cont Random alignment, in graphic (a), shows an not magnetized material Random alignment, in graphic (a), shows an not magnetized material When an external field is applied, the domains aligned with B grow, see graphic (b) When an external field is applied, the domains aligned with B grow, see graphic (b)

68. Domains and Permanent Magnets In hard magnetic materials, the domains remain aligned after the external field is removed In hard magnetic materials, the domains remain aligned after the external field is removed The result is a permanent magnet The result is a permanent magnet In soft magnetic materials, once the external field is removed, thermal agitation cause the materials to quickly return to an not magnetized state In soft magnetic materials, once the external field is removed, thermal agitation cause the materials to quickly return to an not magnetized state With a magnetic core in a coil (solenoid), the magnetic field is enhanced since the domains in the core material align, increasing the magnetic field (don’t forget that for the lab!) With a magnetic core in a coil (solenoid), the magnetic field is enhanced since the domains in the core material align, increasing the magnetic field (don’t forget that for the lab!)

69. QUICK QUIZ 1 A charged particle moves in a straight line through a certain region of space. The magnetic field in that region (a) has a magnitude of zero, (b) has a zero component perpendicular to the particle's velocity, or (c) has a zero component parallel to the particle's velocity.

70. QUICK QUIZ 1 ANSWER (b). The force that a magnetic field exerts on a charged particle moving through it is given by F = qvB sin θ = qvB, where B is the component of the field perpendicular to the particle’s velocity. Since the particle moves in a straight line, the magnetic force (and hence B, since qv ≠ 0) must be zero.

71. QUICK QUIZ 2 The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic (a) attracted, (b) repelled, or (c) unaffected by the magnet?

72. QUICK QUIZ 2 ANSWER (c). The magnetic force exerted by a magnetic field on a charge is proportional to the charge’s velocity relative to the field. If the charge is stationary, as in this situation, there is no magnetic force.

73. http://www.youtube.com/watch?v=6jyraFLqfqE http://www.youtube.com/watch?v=6jyraFLqfqE High speed homopolar motor (just for fun) http://www.youtube.com/watch?v=6jyraFLqfqE