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					                Chapter 15: Electromagnetic Machines

       The Main Idea:
                                                                Current-turns: Current x No of Turns.
                                                                       Current-turns, therefore Current and No of Turns (per unit
                                                                length), influences the flux.

                                                                Permeance: it has to do with the effect of a material on the
                                                                magnetic field in it.

                                                                        where Λ = permeance and μ = permeability

                                                                To Note:
                                                                     The magnetic flux of an electromagnet increases with
                                                                      current, number of turns, cross-sectional area and the
                                                                      permeance of the core.
       Key Words:                                                    Eventually the steel core saturates and thus there is a
                                                                      maximum field, when the domains within the metal are lined
Magnetic Field Strength (B): The strength of a magnetic field         up as well as possible.
Area (A): Cross sectional area of ring/coil wire                     You may have seen a hysteresis loop indicating energy
                                                                      storage within an iron core. In a transformer it is important
                                                                      that this loop is not too large, otherwise the transformer will
           Flux (Φ) = B x A                                           be inefficient.
  Magnetic Field Strength   ||   Area

                              Flux strength
     Permanent Magnet

                                                         Up (first time)

                                                 Magnetising current
                                              Up again

                                Area in loop  heat produced in core.
                                For a transformer you also do not want
                                to do work reversing the domains so
                                you want this area to be as small as

    Hysteresis is like a memory, where the amount of magnetism
     depends on the core’s history.
    Hard disks etc rely on hysteresis.                                    Faraday’s Law:
Graphs to see dependence on frequency etc:                                                         d
                                                                           induced emf   N          where N is the number of turns (remember Φ = BA),
                                                                           and Φ is the flux.
                                                                           If Φ changes sinusoidally, then:

                                                                                    y  A sin t
                                                                                    y  A sin t
Magnetic flux:                                                                               The flux in a coil is proportional to the current in that coil.
                                                                                             The emf across a coil is proportional to the rate of change of flux linkage.
  NI                                                                                      The flux change in a coil is proportional to the sum over time of emf ´
Magnetic Flux Density:                                                                        time.

B          , (inside the coil)                                                      Lenz’s Law: Induced voltage produces a current whose magnetic field opposes the
        L                                                                            change.
For a toroid (circular coil) or inside a long coil,     NI  BA , B          .   Magnet down copper tube:
                                                                                        1.    Flux down tube increases.
The SI unit of magnetic flux is the weber (Wb). The SI unit of magnetic flux            2.    By Faraday induced emf proportional to rate of change
density is the tesla (T), equal to 1 weber per square metre (Wb m–2).                   3.    Direction, by Lenz’s law, is so that resulting flux is up.
                                                                                        4.    Magnetic field repels magnet, pushing up, therefore slowing it down.
                                                                                        5.    As S pole falls through, flux reduces.
                                                                                        6.    emf induced
                                                                                        7.    in direction such as to increase/maintain flux
                                                                                        8.    magnetic field attracts magnet.

                                                                                     P.S. If copper was a perfect conductor, the magnet would not fall at all.

                                                                                     Flux linkage =   N =Number of turns x Ф in each.

                                                                                     Two forces, opposite and parallel, produce a turning moment, called a couple,
                                                                                     required to turn something.

                                                                                     F  BIL
Area under graph = total flux change which is the same.
                                                                                     Two aluminium strips in series, current going in opposite directions, will repel.
                                                                                     Two aluminium strips in parallel, current in same direction, will attract.
                                                                                     Forces between poles act so as to make the flux paths shorter.
                                                                                     Flux behaves like an elastic string.

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