# Understanding the flux linkage in transformers

I am having difficulty understanding the concept of flux linkage in transformers, particularly how the secondary winding receives its flux when all the flux is said to be confined to the iron core. I understand that the primary winding produces an alternating flux when excited by an AC source, but I am unsure how this flux links to the secondary winding when it is wound over the core.

I have read that some flux lines will pass through the secondary winding, but I do not understand how this is possible when all the flux is said to be confined to the core. I would appreciate a physical and intuitive explanation of this concept or any relevant simulations or visualizations to help me understand.

Additionally, if there are any books or resources that are recommended for better understanding this concept, I would appreciate any suggestions.

It is good if the flux is confined to inside the core. Magnetic flux changes result in a circular electric field. Any closed loop wire encircling the flux, no matter what diameter and how located, will exhibit a voltage difference no matter where you cut the loop open. Multiple loops, multiple voltage.

The flux only needs to pass through a wire loop, it doesn't need to touch it: the flux is a magnetic field, but what the wire picks up is not the magnetic field but the circular electric field surrounding the flux change.

There is an converse device, a current clamp which encloses a conductor with a magnetic circuit and uses the strength of the circular magnetic field to deduce the electric current passing through. Again, it doesn't matter just how the magnetic loop encloses the electric conductor or whether it touches it or not.

• Can you please explain more about how Wire picks up electric field from generated by magnetic field. Does the changing flux in core creates a electric field outside the core? Commented Mar 18, 2023 at 18:50
• @Neil_UK Well, it's Maxwell's equations that are responsible, as well as some differential geometry. It's just that the explanation doesn't really fit the StackExchange format. Commented Mar 18, 2023 at 19:28
• @Neil_UK Maxwell's equations exist in an engineer's form, a physicist's form, and a theoretical physicist's form. The engineer's form is an integral form, the physicist's form uses vector differential forms, and the theoretical physicist uses tensors. The latter two, differential forms are strictly local, and the engineer's forms fall out due to mathematics: Gauss' laws and Greene's law. QED concerns the fine structure of the local fields, but the macroscopic engineer's laws with path and surface integrals fall out independently of how currents and fluxes are structured. Commented Mar 18, 2023 at 21:07
• @AdhithyaS Yes. Any net magnetic flux change through any bounded area causes a net circular electric field around the boundary, and putting a wire along that path will pick off that field. It doesn't matter where the flux change in the bounded area happens. The principal reason to keep the windings close to the core is to save copper by keeping the turns as short as possible. Commented Mar 22, 2023 at 15:30
• @AdhithyaS We are talking about the field from a line source (the ring-topology part of the core), not a point source. Consequently, the EMF decreases by simple inverse distance from the core to an electric winding, at the same rate the circumference of the wire loop increases. But while this reasoning relies on a certain geometry, the math actually does not care what shape a wire loop has. It can be as wonky as it wants to, every closed path encircling the same flux once will acrue the same voltage when integrating the electric field. Commented Apr 7, 2023 at 15:31

particularly how the secondary winding receives its flux when all the flux is said to be confined to the iron core.

If an alternating voltage on the the primary produces an alternating flux wholly contained in the core then, by reciprocity, the flux wholly contained in the core can induce a voltage in the secondary. The alternating flux does not have to come in contact with the secondary wires for this to happen.

I have read that some flux lines will pass through the secondary winding

Yes, but, that is not what induces voltage. This would be called a leakage flux i.e. a small fraction of the flux is passing through the air and bypassing the core. This happens in all real transformers and, it means that flux coupling is never 100%. It's more like 99% for a big power transformer ranging to a few percent for coils used for wireless charging (still a transformer).

Additionally, if there are any books or resources that are recommended for better understanding this concept, I would appreciate any suggestions.

Requests for materiel is generally regarded as off-topic. Please treat this site as a resource.

Think of flux like a current, as it "flows" in the core. Current forms in a close path. So does flux as shown in this image from Wikipedia

how the secondary winding receives its flux when all the flux is said to be confined to the iron core.

The winding receives the flux in the same way that the primary delivers it by wrapping the wire of the inductor around the core so that any flux in the core will pass through the area created by "winding" the inductor around the core.

The flux is not in the wire itself but within the area of the loops.