Magnetic fields 08

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SACE Physics Section 2 Topic 3

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Magnetic fields 08

  1. 1. Magnetic Fields Section 2 Topic 3
  2. 2. Magnetic Fields <ul><li>Magnetic fields are produced by moving electric charges ; </li></ul><ul><ul><li>hence by electric currents. </li></ul></ul><ul><li>In a bar magnet ; </li></ul><ul><ul><li>iron atoms have electrons that spin. </li></ul></ul><ul><li>Each spinning electron ; </li></ul><ul><ul><li>tiny ‘magnet’. </li></ul></ul>
  3. 3. Magnetic Fields <ul><li>As all the electrons spin in the same direction ; </li></ul><ul><ul><li>there is no cancellation , </li></ul></ul><ul><ul><li>magnetic field is stable. </li></ul></ul><ul><li>Field lines can represent magnetic fields ; </li></ul><ul><ul><li>As they did in electric fields. </li></ul></ul>
  4. 4. Magnetic Fields <ul><li>The drawing of field lines follows the same rules as with electric fields. </li></ul><ul><li>A compass moved in a magnetic field ; </li></ul><ul><ul><li>follows the field lines. </li></ul></ul><ul><li>Field lines follow the direction ; </li></ul><ul><ul><li>North to South. </li></ul></ul><ul><li>Bar Magnet B Field </li></ul>
  5. 5. Magnetic Fields
  6. 6. Oersted’s Law <ul><li>Permanent magnets are not the only source of magnetic fields. </li></ul><ul><li>Hans Christian Oersted discovered ; </li></ul><ul><ul><li>a magnetic field , </li></ul></ul><ul><ul><li>around a wire carrying an electric current. </li></ul></ul><ul><li>He showed this by placing compasses around a wire ; </li></ul><ul><ul><li>carrying an electric current. </li></ul></ul>
  7. 7. Oersted’s Law <ul><li>The field is concentric circles centred on the wire ; </li></ul><ul><ul><li>strongest near the wire . </li></ul></ul><ul><li>This magnetic field is in addition to ; </li></ul><ul><ul><li>electric field produced by the charges. </li></ul></ul>
  8. 8. Oersted’s Law
  9. 9. Oersted’s Law <ul><li>To determine the direction of the magnetic field around a wire ; </li></ul><ul><ul><li>use Oersted’s right hand rule . </li></ul></ul>
  10. 10. Oersted’s Law <ul><li>G rab the wire with your right hand, </li></ul><ul><li>Thumb in the direction of the conventional current , I; </li></ul><ul><ul><li>(i.e. +ive to -ive), </li></ul></ul><ul><li>F ield is in the direction of ; </li></ul><ul><ul><li>curl of your fingers. </li></ul></ul><ul><li>Oersted's Law </li></ul>
  11. 11. Oersted’s Law
  12. 12. Oersted’s Law <ul><li>If the wire is shown as vertical ; </li></ul><ul><ul><li>the field is hard to draw, </li></ul></ul><ul><ul><li>it will be into and out of the page. </li></ul></ul><ul><li>Crosses (x) are used to show the field ; </li></ul><ul><ul><li>directed into the page. </li></ul></ul>
  13. 13. Oersted’s Law <ul><li>Dots (  ) are used to show the field ; </li></ul><ul><ul><li>directed out of the page. </li></ul></ul><ul><li>T hink of an arrow ; </li></ul><ul><ul><li>when it is flying towards you, </li></ul></ul><ul><ul><li>see a point (out of the page). </li></ul></ul>
  14. 14. Oersted’s Law <ul><li>When it is flying away from you ; </li></ul><ul><ul><li>you will see the feathers , </li></ul></ul><ul><ul><li>cross (into the page). </li></ul></ul>
  15. 15. Oersted’s Law
  16. 16. Oersted’s Law <ul><li>This concept can also be used to illustrate current. </li></ul><ul><li>Current flow through a straight wire </li></ul>
  17. 17. Oersted’s Law <ul><li>To increase the strength of the field increasing the current ; </li></ul><ul><ul><li>the wire can be bent into a loop. </li></ul></ul><ul><li>Current flow through a circular coil </li></ul>
  18. 18. Oersted’s Law <ul><li>To further increase the strength of the field at the centre of the loop ; </li></ul><ul><ul><li>several loops are used instead of the single wire , </li></ul></ul><ul><ul><li>to form a flat coil. </li></ul></ul><ul><li>Each loop of current carrying wire contributes ; </li></ul><ul><ul><li>to a stronger magnetic field. </li></ul></ul>
  19. 19. Oersted’s Law Current flow through a solenoid
  20. 20. Magnetic Force Around a Current- Carrying Conductor <ul><li>When a current carrying wire is placed in a magnetic field ; </li></ul><ul><ul><li>the two magnetic fields interact. </li></ul></ul>
  21. 21. Magnetic Force Around a Current- Carrying Conductor <ul><li>The two fields are ; </li></ul><ul><ul><li>the permanent field around the magnet , </li></ul></ul><ul><ul><li>the field created around the wire. </li></ul></ul>
  22. 22. Magnetic Force Around a Current- Carrying Conductor
  23. 23. Magnetic Force Around a Current- Carrying Conductor <ul><li>When the supply is switched on ; </li></ul><ul><ul><li>wire is pushed out until it no longer touches the mercury, </li></ul></ul><ul><ul><li>breaks the current, </li></ul></ul><ul><ul><li>falls back. </li></ul></ul><ul><li>It then makes contact again ; </li></ul><ul><ul><li>again is forced out. </li></ul></ul>
  24. 24. Magnetic Force Around a Current- Carrying Conductor <ul><li>This process repeats and the wire ; </li></ul><ul><ul><li>continues to bounce in and out. </li></ul></ul><ul><li>This is due to the two interacting magnetic fields producing ; </li></ul><ul><ul><li>a resultant force , </li></ul></ul><ul><ul><li>at right angles. </li></ul></ul>
  25. 25. Magnetic Force Around a Current- Carrying Conductor <ul><li>This shows that the current ; </li></ul><ul><ul><li>the applied magnetic field , </li></ul></ul><ul><ul><li>and the force on the wire , </li></ul></ul><ul><ul><li>mutually perpendicular. </li></ul></ul><ul><li>Fleming’s right hand rule shows this. </li></ul><ul><li>This is also called ; </li></ul><ul><ul><li>right hand palm rule . </li></ul></ul>
  26. 26. Magnetic Force Around a Current- Carrying Conductor
  27. 27. Magnetic Force Around a Current- Carrying Conductor <ul><li>The experiment shown above can also be used to show ; </li></ul><ul><ul><li>the force will increase , </li></ul></ul><ul><ul><li>when any of the following factors increase: </li></ul></ul>
  28. 28. Magnetic Force Around a Current- Carrying Conductor <ul><li>The current, I , in the wire . </li></ul><ul><li>The length,  l , of the wire . </li></ul><ul><li>The strength of the external magnetic field ( B ). </li></ul>
  29. 29. Magnetic Force Around a Current- Carrying Conductor <ul><li>Vector B , the direction of which is the same as the magnetic field lines ; </li></ul><ul><ul><li>describe s the strength of the magnetic field. </li></ul></ul>
  30. 30. Magnetic Force Around a Current- Carrying Conductor <ul><li>Several names are given to B including ; </li></ul><ul><ul><li>magnetic induction, </li></ul></ul><ul><ul><li>magnetic field intensity , </li></ul></ul><ul><ul><li>magnetic flux density. </li></ul></ul>
  31. 31. Magnetic Force Around a Current- Carrying Conductor <ul><li>The S.I. units for magnetic induction B are the tesla (T) ; </li></ul><ul><ul><li>or weber per square metre (Wbm -2 ). </li></ul></ul><ul><li>The magnetic induction of the Earth’s field ; </li></ul><ul><ul><li>is approx. 10 -4 T. </li></ul></ul>
  32. 32. Magnetic Force Around a Current- Carrying Conductor <ul><li>Electromagnets have values ; </li></ul><ul><ul><li>in the order of 2 T ; </li></ul></ul><ul><li>Superconducting magnets have values ; </li></ul><ul><ul><li>around 10 T. </li></ul></ul><ul><li>The relationship between the above quantities is: </li></ul>
  33. 33. Magnetic Force Around a Current- Carrying Conductor <ul><li>  F = B I  l </li></ul><ul><ul><li>F is the force on the wire , </li></ul></ul><ul><ul><ul><li>i n newtons, </li></ul></ul></ul><ul><ul><li>I is the current flowing in the wire , </li></ul></ul><ul><ul><ul><li>in amperes, </li></ul></ul></ul>
  34. 34. Magnetic Force Around a Current- Carrying Conductor <ul><ul><li>B is the magnetic induction of the magnetic field , </li></ul></ul><ul><ul><ul><li>in tesla, </li></ul></ul></ul><ul><ul><li> l is the length of wire in the magnetic field , </li></ul></ul><ul><ul><ul><li>in metres. </li></ul></ul></ul>
  35. 35. Magnetic Force Around a Current- Carrying Conductor <ul><li>This formula only applies when ; </li></ul><ul><ul><li>wire and the magnetic field is perpendicular. </li></ul></ul><ul><li>If the angle is reduced ; </li></ul><ul><ul><li>force will be reduced. </li></ul></ul><ul><li>The formula is more correctly shown by: </li></ul>
  36. 36. Magnetic Force Around a Current- Carrying Conductor <ul><li>F = B I  l sin  </li></ul><ul><li> is the angle ; </li></ul><ul><ul><li>between the wire , </li></ul></ul><ul><ul><li>and the magnetic field. </li></ul></ul><ul><li>Note sin  is at a maximum when ; </li></ul><ul><ul><li> = 90 o , </li></ul></ul><ul><ul><li>ie when B and I are perpendicular. </li></ul></ul>
  37. 37. Magnetic Force Around a Current- Carrying Conductor <ul><li>The quantity I  l is known as ; </li></ul><ul><ul><li>the current element. </li></ul></ul><ul><li>Rearranging the formula above ; </li></ul><ul><ul><li>to make B the subject of the equation: </li></ul></ul>
  38. 38. Magnetic Force Around a Current- Carrying Conductor <ul><li>  This leads to the definition of B </li></ul>
  39. 39. Magnetic Force Around a Current- Carrying Conductor <ul><li>The magnitude B of a magnetic field is defined as the force per current element placed at right angles to the field. </li></ul><ul><li>The direction of magnetic induction is perpendicular to both the force and the current element. </li></ul>
  40. 40. Magnetic Force Around a Current- Carrying Conductor <ul><li>The direction is given by the right hand rule described above. </li></ul><ul><li>Force is measured in ; </li></ul><ul><ul><li>newtons (N); </li></ul></ul><ul><li>Electric current, </li></ul><ul><ul><li>in amperes (A) , </li></ul></ul>
  41. 41. Magnetic Force Around a Current- Carrying Conductor <ul><li>Length of wire, </li></ul><ul><ul><li>in metres (m) , </li></ul></ul><ul><li>Magnetic induction, </li></ul><ul><ul><li>in tesla (T). </li></ul></ul><ul><li>1 T = 1 N A -1 m -1 . </li></ul>
  42. 42. Magnetic Force Around a Current- Carrying Conductor Try Example 1
  43. 43. Solution
  44. 44. Solution <ul><li>B = 4.5 T up </li></ul><ul><li>I = 0.3 A east </li></ul><ul><li> l = 2.0 m </li></ul><ul><li> = 90 o </li></ul><ul><li>F = BI  lsin  </li></ul><ul><li>F = 4.5 x 0.3 x 2 x sin 90 o </li></ul><ul><li>F = 2.7 N </li></ul>
  45. 45. Solution <ul><li>Use the right hand rule to determine the direction. </li></ul>
  46. 46. Solution <ul><li>Palm faces out of the page. </li></ul><ul><li>Direction is south </li></ul><ul><li>F = 2.7 N south </li></ul>
  47. 47. Magnetic Force Around a Current- Carrying Conductor Try Example 2
  48. 48. Solution
  49. 49. Solution <ul><li>I = 0.1 A </li></ul><ul><li> l = 0.1 m </li></ul><ul><li>g = 9.8 ms -1 </li></ul><ul><li>m = 2 g = 0.002 kg </li></ul>
  50. 50. Solution <ul><li>For the wire to be supported against gravity, </li></ul><ul><ul><li>| F B | = | F g | </li></ul></ul><ul><li>BI  l sin  = m g </li></ul>
  51. 51. Solution <ul><li>Use the right hand rule to determine the direction. </li></ul><ul><li>B = 2.0 T to the right </li></ul>
  52. 52. Moving Coil Loudspeaker <ul><li>The principle of a moving coil loudspeaker is that ; </li></ul><ul><ul><li>a coil carrying an electric current , </li></ul></ul><ul><ul><li>oscillating with amplitude , </li></ul></ul><ul><ul><li>and frequency , </li></ul></ul><ul><ul><li>proportional to the sound to be produced , </li></ul></ul><ul><ul><li>is suspended in a uniform magnetic field. </li></ul></ul>
  53. 53. Moving Coil Loudspeaker <ul><li>The magnetic force on the oscillating current ; </li></ul><ul><ul><li>drives the coil in and out , </li></ul></ul><ul><ul><li>through the field. </li></ul></ul>
  54. 54. Moving Coil Loudspeaker <ul><li>A cone is attached to the coil ; </li></ul><ul><ul><li>the movement of the cone back and forth , </li></ul></ul><ul><ul><li>sets up compressions and rarefactions , </li></ul></ul><ul><ul><li>in the adjacent air, </li></ul></ul><ul><ul><li>creating a sound wave . </li></ul></ul>
  55. 55. Moving Coil Loudspeaker <ul><li>Motion of Loudspeaker </li></ul><ul><li>Loudspeaker Animation </li></ul>
  56. 56. Components <ul><li> Frame (or housing or basket) </li></ul><ul><ul><li>Stationary Component </li></ul></ul><ul><li>Generally an open metal frame ; </li></ul><ul><ul><li>supporting the cone, </li></ul></ul><ul><ul><li>with a magnetic structure attached , </li></ul></ul><ul><ul><li>at the centre rear. </li></ul></ul>
  57. 57. Components Cross section of a Speaker
  58. 58. Components
  59. 59. Components <ul><li> Magnetic Structure - Stationary Component </li></ul><ul><li>A fixed permanent magnet provides ; </li></ul><ul><ul><li>magnetic field , </li></ul></ul><ul><ul><ul><li>in almost all modern designs. </li></ul></ul></ul>
  60. 60. Components <ul><li>The diagrams above and below show ; </li></ul><ul><ul><li>a ring magnet providing the magnetic field , </li></ul></ul><ul><ul><li>with one polarity on each flat face of the ring. </li></ul></ul>
  61. 61. Components <ul><li>Magnetic poles are induced in soft iron pole pieces ; </li></ul><ul><ul><li>as shown below . </li></ul></ul><ul><li>Resulting in north and south magnetic poles ; </li></ul><ul><ul><li>on opposite sides of a small air gap. </li></ul></ul>
  62. 62. Components <ul><li>The voice coil moves ; </li></ul><ul><ul><li>in the approximately uniform magnetic field , </li></ul></ul><ul><ul><li>in the air gap. </li></ul></ul>
  63. 63. Components
  64. 64. Components <ul><li> Cone (or diaphragm) </li></ul><ul><ul><li>Moving Component </li></ul></ul>
  65. 65. Components <ul><li>A conical surface ; </li></ul><ul><ul><li>made of light but rigid material , </li></ul></ul><ul><ul><ul><li>such as paper pulp , </li></ul></ul></ul><ul><ul><ul><li>or plastic , </li></ul></ul></ul><ul><ul><ul><li>even Kevlar </li></ul></ul></ul><ul><ul><li>that sets the air vibrating . </li></ul></ul>
  66. 66. Components <ul><li> Voice Coil </li></ul><ul><ul><li>Moving Component </li></ul></ul><ul><li>A coil of wire wound on a lightweight tube ; </li></ul><ul><ul><li>passes through the gap , </li></ul></ul><ul><ul><li>in the magnetic structure. </li></ul></ul>
  67. 67. Components <ul><li>The voice coil is attached to the cone ; </li></ul><ul><ul><li>wires from the two ends of the coil terminate in , </li></ul></ul><ul><ul><li>electrical connections on the frame. </li></ul></ul><ul><li>Aluminium wire is often used ; </li></ul><ul><ul><li>because it is much lighter than copper. </li></ul></ul>
  68. 68. Components <ul><li> Inner Suspension </li></ul><ul><ul><li>or Spider </li></ul></ul><ul><li>A flat ring of springy material. </li></ul><ul><li>The outside edge of the ring is connected to the frame ; </li></ul><ul><ul><li>inside edge is connected to the voice coil , </li></ul></ul><ul><ul><li>where it joins the cone. </li></ul></ul>
  69. 69. Components <ul><li>The purpose of the inner suspension ; </li></ul><ul><ul><li>to hold the cone centrally in the frame , </li></ul></ul><ul><ul><li>while allowing it to move in and out freely , </li></ul></ul><ul><ul><li>without rocking . </li></ul></ul>
  70. 70. Components <ul><li> Outer Suspension </li></ul><ul><ul><li>Moving Component </li></ul></ul><ul><li>Performs a similar function to the inner suspension ; </li></ul><ul><ul><li>but between the outer edge of the cone and the frame. </li></ul></ul>
  71. 71. Components <ul><li> Centre Cap and Dust Dome </li></ul><ul><ul><li>Moving Component </li></ul></ul>
  72. 72. Components <ul><li>Moulded paper or aluminium ; </li></ul><ul><ul><li>covers the centre of the cone at the end of the voice coil, </li></ul></ul><ul><ul><li>to prevent dust from entering the gap , </li></ul></ul><ul><ul><li>in the magnet assembly. </li></ul></ul>
  73. 73. Components <ul><li>It also adds to the moving components ; </li></ul><ul><ul><li>acts as an extension of the cone , </li></ul></ul><ul><ul><li>moving air to create sound. </li></ul></ul>
  74. 74. Action of a Loudspeaker <ul><li>The two ends of the voice coil are connected ; </li></ul><ul><ul><li>to the output terminals of an amplifier. </li></ul></ul><ul><li>Across the terminals, is a P.D. ; </li></ul><ul><ul><li>oscillates in proportion to the sound waveform. </li></ul></ul>
  75. 75. Action of a Loudspeaker <ul><li>This produces an oscillating current in the voice coil. </li></ul><ul><li>To examine this, we will look at in two stages. </li></ul><ul><li>The first being when the P.D. is constant. </li></ul>
  76. 76. Action of a Loudspeaker <ul><li>A constant P.D. gives rise to ; </li></ul><ul><ul><li>a constant I from V = IR. </li></ul></ul><ul><li>The magnetic force is determined by ; </li></ul><ul><ul><li>F = BI  l . </li></ul></ul>
  77. 77. Action of a Loudspeaker <ul><li>The direction is determined by the right hand rule. </li></ul><ul><li>Assume the current is at first, </li></ul><ul><ul><li>into the page. </li></ul></ul>
  78. 78. Action of a Loudspeaker
  79. 79. Action of a Loudspeaker <ul><li>The voice coil moves in the direction of ; </li></ul><ul><ul><li>the magnetic force. </li></ul></ul><ul><li>The inner and outer suspensions ; </li></ul><ul><ul><li>oppose the motion and , </li></ul></ul><ul><ul><li>exert a restoring force. </li></ul></ul>
  80. 80. Action of a Loudspeaker <ul><li>Eventually the forces have equal but opposite magnitude and ; </li></ul><ul><ul><li>the voice coil no longer moves. </li></ul></ul><ul><li>The rest position is approximately given by ; </li></ul><ul><ul><li>F = BI  l. </li></ul></ul>
  81. 81. Action of a Loudspeaker <ul><li> As F  I and V  I </li></ul><ul><li>F  V . </li></ul><ul><li>If the P.D. is reversed ; </li></ul><ul><ul><li>hence the current . </li></ul></ul><ul><li>The force and displacement ; </li></ul><ul><ul><li>are also reversed. </li></ul></ul>
  82. 82. Action of a Loudspeaker
  83. 83. Action of a Loudspeaker <ul><li>Effect of Changing the Current </li></ul><ul><li>Summary of How it Works </li></ul><ul><li>It appears from above that the P.D. is ; </li></ul><ul><ul><li>proportional to the cone displacement , </li></ul></ul><ul><ul><li>therefore is proportional to the sound waveform. </li></ul></ul>
  84. 84. Action of a Loudspeaker <ul><li>There are some factors that prevent this from being true. </li></ul><ul><li>The skill in producing a good speaker is to reduce these factors. </li></ul><ul><li>These factors, are outside the scope of this course. </li></ul>

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