# Magnetic fields in transformers and back emf?

i am having some trouble with understanding the magnetic fields inside transformers and how they relate to back emf.

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 by Lenz's law because then the magnetic field in the core would induce a back emf in the primary could which would oppose the primary coil p.d, reducing the current in the primary coil and thus reducing the magnetic field around it so there is a smaller field in the core etc so it will oscillate between decreasing and increasing magnetic field.

However my explanation above does not seem to fit when I consider the secondary coil as being part of a complete circuit and passing current. 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', but I am not sure I agree with the first part of that. I would think that 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 that means that both the primary and secondary coils have the same magnetic fields as both are opposing the core magnetic field.

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 would be really grateful if someone could clarify which fields align and which oppose each other...

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?

A conductive (iron) transformer core has both diamagnetic (excludes magnetic field) and ferromagnetic (enforces magnetic field) properties. For a microsecond or ten after the primary current is established, the B field in the core is low, because eddy currents in the iron oppose the applied H field. After 1000 microseconds, those eddy currents have died out, and the iron magnetization reinforces the magnetic induction provided by the primary winding.
$$B \simeq \mu * H$$

Many thin laminations, rather than a solid iron block, makes a core that magnetizes more quickly (and helps energy efficiency), because it minimizes that changeover time. Lenz's law applies both to the eddy currents, and to the secondary currents, but does not relate directly to "the" magnetic field. The B field comes from the sum of those currents and the iron magnetic polarization, and isn't a simple superposition of parts, because magnetization of iron is not linear. That constant "mu" in the equation is ... not exactly a constant.

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.

There is some truth in that statement, because secondary current has the effect of reducing the magnetization of the iron, and at low magnetization, the system IS linear. Still, 'the magnetic field' ought to mean the B field, inside the core, and not some theoretical H field due to part of the nearby currents. That B field is composed of induction by two (or more) transformer windings, and by eddy currents, and by the ferromagnetic polarization.

While you can add the H field sources, it is not valid (because of polarization) to confuse that sum with the B field in the core. The polarization is not linear, and that fact will cause nonideal behavior of the transformer, which should NOT be ignored.

Usually, the network sets the voltage accross the first coil. This also sets the magnetic flux inside the transformer coil. A voltage is then induced accross the secondary coil. Depending on the load, a current flows in the secondary circuit that opposes the flux (the secondary current tends to reduce its cause, i.e. the flux variation). Consequently, a current flows in the first coil to hold the magnetic flux.