NEIEP Magnetism and Electromagnetism (355)

When a coil is energized around a ferrous core, the magnetic flux takes the path of least reluctance. The ferrous core has a very high magnetic permeability, so it provides a much easier route for the magnetic field than air. As a result, the flux lines concentrate and run along the length of the iron core, effectively stretching to follow that path. This concentration through the core increases the overall flux linkage and inductance, which is why ferromagnetic cores are used in transformers and inductors.

Flux lines form closed loops, so some lines still complete the loop outside the coil, but the majority travels through the core because that path offers far less opposition to the magnetic field.