Emf induction

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ghoran
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293393
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Emf induction
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2015-01-21 10:54:40
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  1. the magnetic flux is defined as
    the product of the field magnitude by the area crossed by the field lines
  2. ø =
    • B perpendicular(component of B perpendicular to the coil)A 
    • BAcosθ where θ is the angle between B and the normal to the loop
  3. if θ is 0 then ø =
    BA
  4. if the coil has N turns in series then there is
    • a flux ø through a coil of N turns and we call Nø the flux linkage 
    • Nø = NB (perpendicular)A
  5. SI units of flux linkage are
    webbers Wb
  6. if the coil has N turns in series then there is a flux through a coil of N turns , and we call this 
    flux linkage , N thigh 
  7. flux linkage = 
    Nthigh = NBperpendicularA = NBAcos(angle) 
  8. provided that the magnetic flux varies in a circuit there will be 
    a current in the circuit no matter what method is used 
  9. generating a current in a magnetic field is called 
    electromagnetic induction 
  10. Faradays law 
    the emf in a loop of wire is proportional to the rate of change of magnetic flux through the coil 
  11. we often call the emf induced by a changing magnetic flux an 
    induced emf and the current it produces is called an induced current or induction current 
  12. Lenz's law 
    the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop 
  13. the induced current tends to maintain 
    the original flux through the circuit
  14. we can write faradays law of induction mathematically 
    E = - N delta thigh / delta t 
  15. the minus sign indicates the
    direction of the emf and is in agreement with lenz's law 
  16. motional emf - 
    right hand rule 
  17. to investigate the induction of emf on a moving conductor lets consider a conducting bar of length l sliding along a stationary u shaped conductor that is perpendicular to a uniform magnetic field 
    • the bar moves with constant speed v in the z direction 
    • as the bar moves the area enclosed by the loop consisting of the bar and the u shaped conductor increases 
    • consequently the magnetic flux through the loop increases
  18. the emf developed around the loop is obtained from faradays law
    • E = -deltathigh/delta t
    • E = -dela BA/delta t 
    • E = -B delta A/delta t
    • E = - Bl delta x / delta t 
    • delta x / delta t = v 
    • E = -Blv
  19. if the magnetic field is uniform and the loop rotates with a constant angular speed , w , the magnetic flux through the single loop of area A may be expressed as
    thigh = BperpendicularA = BAcos(angle) = BAcos(wt)
  20. the flux is a function of time , from faradays law E = - delta thigh/delta t
    E = -BA delta cos(wt)/delta t
  21. delta cos(wt)/delta t = w sin(wt) so E =
    BAwsin(wt)
  22. so generalise the result to N loops
    E = NBAwsin(wt)
  23. output of an alternator is
    sinusoidal emf
  24. when an alternator is connected to a closed circuit
    it produces a sinusoidally ac current
  25. frequency of ac current =
    number of cycles per second
  26. time period of ac current =
    time for one full cycle
  27. T =
    1/f
  28. peak value of ac current
    the maximum current that is the same value in either direction
  29. peak to peak value
    difference of the peak value in the opposite direction
  30. the root mean square value of an ac current
    the value of dc that would give the same heating effect as the ac in the same resistor
  31. Irms =
    I0/root 2
  32. the mean power supplied to the resistor P=
    • IV 
    • so P mean = Irms x Vrms
  33. one of the most important applications of mutual induction and self induction takes place in a
    transfomer
  34. a transformer is a device for
    increasing or decreasing ac voltage
  35. transformer consists of
    an iron core on which two coils are wound : a primary coil with Np turns and a secondary coil with Ns turns
  36. primary coil connected to an
    ac generator
  37. ac in the primary coil establishes a
    changing magnetic field in the iron core
  38. iron is easily
    magnetised
  39. iron enhances the
    magnetic field relative to that in an air coil and guides the field lines to the secondary coil
  40. in a well designed transformer nearly all the
    magnetic flux that passes through each turn in the primary coil goes through each turn in the secondary coil .
  41. magnetic field is changing , the flux through each coil is changing consequently
    emf is induced in both coils
  42. in the secondary coil E =
    -Ns delta thigh/delta t
  43. the induced emf arises from
    mutila induction
  44. in the primary coil E =
    - Np delta thigh/delta t
  45. in the primary coil the induced emf arises from
    self induction
  46. the term delta thigh/delta t is the same in both equations since the same flux penetrates each turn of both coils so Es/Ep =
    Ns/Np
  47. in a high quality transformer the resistance of the coils are
    negligible
  48. therefor the magnitudes of the emf's are
    nearly equal to the terminal voltages across the coils
  49. Vs/Vp =
    Ns/Np
  50. if Ns is greater than Np the
    secondary voltage is greater than the primary voltage so we have a step up transformer
  51. a transformer can change the voltage of secondary coil but the conservation of energy requires that
    the energy delivered to secondary coil must be the same as the energy delivered to primary coil provided no energy is dissipated on heating coils or is otherwise lost
  52. in a well designed transformer less than ... of the input energy is lost in the form of heat
    1%
  53. power is
    energy per unit time
  54. assumimg 100% efficiency energy transfer
    Ps = Pp
  55. hence
    • IpVp = IsVs 
    • Vp/Vs = Ip/Is = Ns/Np
  56. in fact energy is dissipated so the efficiency of the transformer can be calculated in this form
    • IsVs
    • ----- x 100 
    • IpVp
  57. when a bar magnet is moved relative to a coil of wire connected in a circuit an
    electric current is made to flow in the coil and the pd is called induced emf
  58. direction of current depends on direction of
    motion of magnet
  59. flemmings right hand rule
  60. induced emf can be increased by 
    • moving wire/magnet faster 
    • using a stronger magnet 
    • more turns in coil
    • increasing area of coil 
    • increasing angle between magnetic field and the normal of the loop 
  61. alternate methods of inducing emf 
    • dynamo (spins a magnet in a coil creating a current) 
    • an electric motor in reverse (motor normally turns on an axle but turning axle (rotating magnet) would have reverse effect) 
  62. in a dynamo energy is transferred from 
    dynamo to lamp the current through the dynamo coil causes a reaction force on the coil due to the magnet . work must be done to keep the magnet spinning . 
  63. energy from the coil to the lamp is equal to 
    the work done on the coil to keep it spinning assuming no wastage 
  64. the rate of transfer of energy from source of emf to the other components of the circuit is equal to
    the product of induced emf and current 
  65. this is because 
    • emf is energy transferred from the source per unit charge that passes through the source 
    • E = V/Q 
    • current is the charge flow per second Q = It 
    • E = V/It 
    • V/It = EQ/It 
    • VI = EQ x 1/Qt 
    • VI = E/t 
  66. when a north magnet is pushed towards the coil the induced emf causes 
    • current to flow which creates a magnetic field , the end of the coil nearest to the magnet becomes a north pole which repels the magnet . the quicker you push the magnet into the coil the larger the induced emf , the larger the force opposing the motion 
    • can't be south because that would attract bar magnet and this would increase kinetic energy and electrical energy of magnet which is impossible 
  67. the induced emf is equal to the 
    rate of change of magnetic flux linkage 
  68. when a coil cuts the field lines an 
    emf is induced 
  69. the greater the rate of cutting lines the 
    greater the emf 
  70. when the plane of the coil is parallel to the field lines the flu linkage is 
    0 the coil doesn't experience magnetic force so no emf induced 
  71. rate of change of flux linkage at this point is 
    max 
  72. when the plane of the coil is perpendicular to the field the flux linkage is 
    maximum but the rate of change of flux linkage is zero 
  73. when the plane of the coil is again parallel to the field the rate of change of flux linkage is 
    again maximum but the sides of the coil are moving through the field in the opposite direction thus an alternating emf is induced 
  74. emf is the rate of change of 
    flux linkage 
  75. fixed coil in changing magnetic field 
    • the B field of the solenoid passes through the small coil 
    • if the current in the solenoid changes an emf is induced in the small coil 
    • this is because the magnetic field through the coil changes so the flux linkage through it changes , causing an induced emf 
    • Nthigh = BAN 
    • Ndeltathigh = delta BAN 
    • emf = N deltathigh/delta t = ANdeltaB/delta t 
  76. because B is proportional to I in the solenoid the magnitude of the emf is 
    proportional to the rate of change of current in the solenoid 

    • F = BIL 
    • Emf = ANdletaB/deltat 
  77. consider a rectangular coil of N turns , length l and a width w moving into a uniform magnetic field of flux density B at constant speed v . suppose the coil enters the field at time t=0 
    time taken to enter field completely =
    coil width / speed = w/v 
  78. during this time the flux linkage Nthigh increases from 0 to 
    • BAN
    • which is BlwN 
  79. therefor the rate of change of flux per second 
    N deltathigh/delta t = BNlwv/w = BNlv 
  80. when the coil is completely in the field 
    the flux linkage doesn't change so induced emf = 0 
  81. a battery powered or hybrid electric vehicle contains an alternator that can be used as 
    an electric motor 
  82. when the alternator is used as an electric motor its driven by the
    batteries 
  83. when the brakes are applied the alternator is 
    used to generate electricity which is used to recharge the battery 
  84. som kinetic energy is transferred to 
    electrical energy in the battery 
  85. the induced current through the alternator coil creates 
    a magnetic field that acts against the magnetic field of the alternator , so the alternator experiences a braking force which helps slow the vehicle down 
  86. the fuel consumption of a hybrid car is ls less than that of a petrol vehicle this is because 
    some of the kinetic energy is converted to chemical energy in its battery when the vehicle brakes . the battery supplies this energy to the motor when it takes over from the the petrol engines at low speeds 
  87. generators 
    produce current 
  88. types of generators 
    • dynamo 
    • alternator 
  89. motor 
    current is put in and spins coil producing kinetic energy 
  90. regenerative braking uses a 
    motor first then a generator 
  91. thigh is 
    magnetic flux 
  92. B is
    magnetic flux density 
  93. flux linkage is
    N thigh
  94. if got a magnetic flux density vs t graph to find emf
    • E = delta thigh/delta t x N 
    • E = delta BAN/delta t 
    • so E = gradient x AN
  95. if got a magnetic flux density vs t graph to draw emf graph
    • E = delta NAB/delta t 
    • draw a delta B delta t graph since N and A are constant
  96. a power station alternator has three sets of coils at 
    120 degrees to one another 
  97. each coil produces an alternating emf 
    120 degrees out of phase with each of the other two emf's 
  98. the coils are called the 
    stators because they are stationary so they don't need slip ring connectors and an electromagnet called the rotor spins between them
  99. the electromagnet is supplied with a current from 
    a generator
  100. so the turning rotor 
    induces an emf in each set of stator coils 
  101. the three phases are distributed via 
    transformers and power lines to factories and local sub stations 
  102. a local sub station supplies 
    mains electricity to local premises , a third on each of the three phases this is why your home can sometimes suffer a blackout when other homes nearby still have electricity . This happens when a fault in the local sub station cuts out one phase but not the others 
  103. back emf 
    an emf is induced in the spinning coil of an electric motor because the flux through the coil changes 
  104. the induced emf is referred to as back emf because 
    it acts against the pd applied to the motor in accordance with lens's law 
  105. at any instant 
    • V - emf = IR
    • where I is current through motor and R is circuit resistance 
  106. emf is proportional to 
    v so the current changes as the motor speed changes 
  107. at high speeds 
    low current because induced emf is high 
  108. at low speeds 
    high current because induced emf is low
  109. IV - emfI = 
    • I2R - electrical power wasted due to circuit resistance 
  110. IV is
    electrical power supplied by source 
  111. Emf is
    electrical power transferred to mechanical power
  112. prove T is 2pi/Bq
    • F = Bqv 
    • Bqv = mv2/r 
    • Bq = mv/r
    • Bqr/m = v 
    • v = s/t 
    • Bqr/m = 2pir/T 
    • BqrT = 2pirm
    • T = 2pim/Bq
  113. alpha particle electric charge
    +2 
  114. beta particle electric charge 
    -1 
  115. angle in F = Bqvsinangle
    angle between the field and direction of the particles motion 
  116. prove E = blv 
    • E = delta thigh/delta t 
    • E = delta BA/delta t 
    • E = B deltaA/delta t 
    • A = ls 
    • v = s/delta t 
    • v x delta t  = s 
    • E = Blv delta t / delta t 
  117. units of magnetic flux (thigh) 
    • Wb 
    • Tm2
    • Nsm/C 
    • NmA-1

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