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In support of all the students who are displaced from school due to the Corona virus. Access to physics zone and chemistry zone lessons are now available free of charge. This will be maintained at least through August 1st 2020. Learn and be well.

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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. 
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