What two factors determine the strength of the magnetic field in a solenoid?

The Strength of a magnetic field  is dependent on several factors such as

What are Solenoids?

A solenoid is a piece of wire wound around and along a metal bar, it is an electro magnet used to generate a controlled field through a coil

When a direct electric current is passed through it, the shape of the magnetic field is very similar to the field of a bar magnet.

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The magnetic field within a solenoid depends upon the current and density of turns. The energy density of the magnetic field depends on the strength of the field, squared, and also upon the magnetic permeability of the material it fills.