Flux direction through core

[FusionJim]

Suppose there is a rectangular core. At one part of the core it is split in two identical parallel sections , each section has a coil around it. Both coils are identical and current runs in the same direction through both.
The magnetic flux within the core is created by the coils.
My question is this - is there any flux in the area/airgap in the middle between the two coils? And if so, then in what direction is the flux in the airgap between the two split core legs between the two coils?



My own logic goes like this - if there was a single coil somewhere else on the core and this part simply had the core split in two equal parts later joined together again, then most of the flux would flow through the two equal legs (since they have the highest permeability) and some flux would also exist in the airgap between the legs. All fluxes would be in the same direction.

In my scenario that is shown in the picture, because the coils (the source of flux) is located on the two split legs therefore all the flux goes through those legs and loops back around the core , but the flux within the airgap , although small, loops back within the airgap region, so the flux within the airgap is in opposite direction to that within the legs that have the coils around them.


Am I correct in my assessment?

 

[renormalize]

Suppose there is a rectangular core. At one part of the core it is split in two identical parallel sections , each section has a coil around it.

Your diagram confuses me. Can your post a better one that explicitly shows and labels the "split" you describe?

 

[berkeman]

Are you familiar with the difference between magnetizing inductance (flux) and leakage inductance (flux)?

 

[DaveE]

https://en.wikipedia.org/wiki/Magnetic_circuit

 

[FusionJim]

@renormalize The split I was talking about exists in the area of the core where the coils are located. In that area the core is not one solid core but instead has two parallel legs with a gap between them. As can be seen in the "above view".


@berkeman Yes I believe I am aware of those terms.
For simplicity assume the coils are fed with DC.

My basic idea with regards to this sketch was simple - the core has much higher magnetic permeability than air so most of the flux is guided by the core and loops around the core. But some of the flux "leaks" through the air.

My question then was, is it true that in such a geometry as shown, the flux leaking through the air crosses the airgap between the two coils in the opposite direction than the flux within the coils, therefore flux made by the coils has two routes, one route takes it all around the core, but the other much shorter route is where the leakage flux passes straight through the air looping back to the other end of the coil.
I hope I have explained this clearly.

 

[DaveE]

A good approximation to this sort of problem is to solve for the flux distribution with no core, then solve for the flux in the core. In the latter case you can ignore any magnetic path outside of the core because of the higher permeability confines most all of the flux. Then the flux distribution is the superposition of those two solutions. Because the magnitudes are usually very different we would often talk about them separately.

 

[berkeman]

@berkeman Yes I believe I am aware of those terms.
For simplicity assume the coils are fed with DC.

I don't think that simplifies anything. Any voltages induced in the coils via the leakage flux path would have to come from AC signals.

For a well designed transformer, the leakage inductance will be a small fraction of the magnetizing inductance, so any extra coil-to-coil interaction can be ignored. You could probably concoct some strange core geometry to get a couple percent of extra flux coupling via a leakage path, but to what end?