Magnetic susceptibility
Materials, particularly ferromagnets such as iron, will have their dipoles line up along the direction of an applied magnetic field. The magnetic dipoles of the material's atoms will therefore create a magnetic field of their own which will strengthen the net magnetic field. The magnetic field inside a solenoid will be strengthened if iron is used for the core rather than a vacuum.
where m is the magnetic susceptiblity which can be larger than m0. We will demonstrate the increased magnetic field of a solenoid by replacing the core with iron, and show that is picks up nails more readily.