Does same pole magnetic field flow past each other in a iron core

Question

In a textbook transformer design like the one in the image, if I put DC current on both coils making sure that they both have the same poles on the same side, for example, they both have north poles at top, will each coil's magnetic field flow past and into one another to reach its south pole or will they repel each other in the core causing the magnetic field to flow outwards so as to connect to their south?

The image is just to show the transformer type. Assume they both have the same resistance and voltage. Someone said magnetism is just like water, that they will flow past/into each other if the the connecting pipe is large enough. I want to confirm if that's true

Answer 1

if I put DC current on both coils....

If you are using DC current then you might as well use bar-magnets and analyse the resulting magnetic fields using iron filings. Here's what happens when the two north poles meet (let's say at the top dead centre of your transformer core): -

Image from here.

As you can see, the fields repel and field lines will move outside the constraints of the core to return to their respective south poles.

If the poles are opposite (i.e. North and South) then you'd see this: -

Image from here.

It's not totally clear but, the external fields (outside the core) are significantly less in this 2nd case and, there is a strong continuation of the field lines through each magnet (as opposed to none on the pervious example).

Answer 2

If you want a water analogy, then one is available, up to a point.

Terminology around magnetic fields is a bit confusing. Whereas electricity has voltage and current, and water has a corresponding pressure and flow, both aspects in magnetism tend to be called 'magnetic field'. Magnetic H field is the loose equivalent of pressure, and is measured in Amps/m. Magnetic B field is the equivalent of flow, and is measured in Tesla. Caveat, I haven't checked that all the flow/flux/charge dimensions I've presented are consistent as in per second, or per area.

It's still not clear from your diagram and text whether the H field from each coil adds up round the loop, which would result in twice the H and B fields of a single coil, or cancels each other, which results in a net zero round the loop for both.

The water analogy for this part is quite reasonable. Consider the coils as pumps, the iron core as a pipe, pressure as H field, and flow as B field. If the pumps oppose, there's zero flow, and if the add, the flow rate is higher round the loop than for a single pump.

In neither case does water, or magnetic field, 'flow past'. They are both the same 'stuff', the pressures add, and a single total flow results from that.

We can even consider that the air round the core is made of a material that only allows 1/1000th the flow of water that the 'open pipe' iron does, perhaps porous cement or something. This also handles both cases of pumps adding or opposing each other. When the pumps add round the loop, the pressure at each end is similar, and there's little flow in the cement outer, or little field external to the core. When the pumps oppose each other round the loop, the 'top' of the loop will be at a significant pressure difference to the 'bottom', and there will be a leakage flow through the porous outer, and a significant leakage field outside the core. This is why we like toroidal transformers wound uniformly, to reduce leakage fields from just this effect.

Although the water analogy seems to work quite well up to this point, don't push it further to try to make other predictions. Magnetic fields are not like water at all.