The higher the magnetic permeability, the stronger the magnetic field.

Some materials are more susceptible to magnetic fields than others.   We say they are more "permeable" to the magnetic field. .

Magnetic field in air

magnetic field with soft iron inbetween

This is diagram illustrates the magnetic field in the air between two poles of a horseshoe magnet This diagram is for the same magnet with a piece of soft iron placed between the poles.  The soft iron is more permeable to the magnetic field than the air is. Notice how the field seems to focus the magnetic field.  This is a result of the iron actually becoming a magnet while placed in the existing field.  As a result, when a compass is moved to map the field it is influenced by the iron.  Thus showing a more "focused" or stronger field.

Air Core solenoid

Solenoid with more permeable core

The solenoid above would be considered an "air core" solenoid since the coils are wrapped around a hollow core.  This solenoid has a soft iron core which is more permeable and as a result, creates a much stronger magnetic field.  As a result, it is a much stronger electromagnet. 



1999 Science Joy Wagon