how does an iron core in a solenoid strengthen the magnetic field of my electromagnet?

A magnetic core is a piece of magnetic material with a high permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, inductors and magnetic assemblies. It is made of ferromagnetic metal such as iron, or ferrimagnetic compounds such as ferrites. The high permeability, relative to the surrounding air, causes the magnetic field lines to be concentrated in the core material. The magnetic field is often created by a coil of wire around the core that carries a current. The presence of the core can increase the magnetic field of a coil by a factor of several thousand over what it would be without the core.

The use of a magnetic core can enormously concentrate the strength and increase the effect of magnetic fields produced by electric currents and permanent magnets. The properties of a device will depend crucially on the following factors:

1.the geometry of the magnetic core.

2. the amount of air gap in the magnetic circuit.

3.the properties of the core material (especially permeability and hysteresis).

4.the operating temperature of the core.

5.whether the core is laminated to reduce eddy currents.

You can think of a block of iron as consisting of a bunch of magnetic dipoles, each with their own magnetic field. If you put a block of iron in an external magnetic field, those dipoles will line up with the external magnetic field, adding their own individual magnetic fields to the external magnetic field.

Incidentally, this method of iron cores is used to increase the efficiency of power transformers. However, power transformers transform alternating current. Alternating current generates magnetic fields that are constantly changing direction. Consequently, the dipoles in the iron are constantly switching direction and this heats up the iron. That is why you find small transformers (such as the power brick for your laptop) getting warm after prolonged use.