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Magnetic fields in transformers and back emf?

  1. Jan 16, 2015 #1
    i am having some trouble with understanding the magnetic fields inside transformers and how they relate to back emf. In particular, I am considering the two cases of current passing through the primary coil but not the secondary coil, and then with the secondary coil as part of a complete circuit so that current flows through the secondary could too.

    My first query is: is the magnetic field produced inside the soft iron core aligned with the magnetic field produced in the primary coil, or does it oppose it?
    I think it has to oppose the magnetic field in the primary coil, because then when you have the first case scenario (so no magnetic field is created by the secondary coil and I only have to consider the magnetic field of the primary coil and the iron core), then the magnetic field in the core would induce a back emf in the primary could which would oppose the primary coil p.d. And so there would be a smaller net p.d. In the primary coil and so little current would flow in the primary coil leading to less power being lost due to resistance in the primary coil.
    Then I am slightly confused about the second case, because my text book says that 'when the secondary current is on, the magnetic field it creates is in the opposite direction to the magnetic field of the primary current. In this situation, the back emf in the primary coil is reduced so the primary current is larger than when the secondary current is off'. I am not sure I agree with the first part of that. I would think that the magnetic field generated in the iron core would oppose the direction of the primary current to create a back emf in the primary coil by Lenz's law, and then when considering the secondary coil and the magnetic field in the iron core, the current induced in the secondary could would have to create a magnetic field that would oppose the magnetic field in the iron core by Lenz's law, so both the primary and secondary coils have the same magnetic fields and so their currents flow the same way. But then when I think about this another way it does not make sense, because then if the secondary could had the same magnetic field as the primary coil, then the magnetic field it would induce in the iron core would oppose the magnetic field of the secondary could even more, and so it would strengthen the magnetic field in the iron core which would cause a greater back emf in the primary could but greater induced emf in the secondary coil so in the secondary coil it would be violating the conservation of energy?

    I realise that much of the above probably doe not make sense, but I gave the explanation my best shot...

    Thank you in advance! :)
  2. jcsd
  3. Jan 16, 2015 #2


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    Staff: Mentor

    It is aligned with the field produced by the primary coil.

    The field is aligned with the primary coil, so it produces a very large magnetic field that induces a large amount of back EMF in the primary coil and you have relatively little current flow. (Remember that even without a core, the coil's own magnetic field still induces a counter EMF in the coil. This is how inductors work) When you complete the secondary circuit and allow current to flow, the magnetic field from the secondary coil is indeed acting against the magnetic field from the primary, which reduces the magnitude of the change in magnetic field strength/flux, causing less EMF in the primary than before, so more current flows through the primary.
  4. Jan 21, 2015 #3

    jim hardy

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    Science Advisor
    Gold Member

    Hyperphysics has a pretty good diagram over at


    What Drakkith said you can demonstrate on that picture with right hand rule.

    Remember that MMF is the force pushing flux around the core, and MMF is measured in amp-turns
    and it doesn't take a lot of amp-turns to magnetize the core else magnetizing current would be excessive and you'd have a crummy transformer.

    What is going on in the core is
    sum of mmf's is constant and a small number , just enough to magnetize the core
    so ( primary amp-turns) - (secondary amp-turns) = a small constant
    the minus sign is because primary amp-turns push clockwise and secondary counterclockwise

    Meaning when you let secondary amps flow, primary amps must follow to keep total amp-turns constant.

    I hope that memory aid helps.

    It is also helpful to keep in mind the derivative relationship between voltage and flux, that's why we study transformers with sine waves - shape doesn't change when you differentiate a sine.
    Current and flux however share a direct relationship, there's no derivative in
    Φ = μ X Number of turns X Iamps X Area / length

    Transformers are fun.
    If you can keep that "sum of mmf's is small" in the back of your mind,
    it'll help when you get to current transformers where we strive to keep it zero.

    old jim
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