How does adding more turns of wire affect an electromagnet’s strength?

Adding more turns of wire to the coil of an electromagnet increases its strength.

The strength of an electromagnet is determined by its magnetomotive force, which is defined as the product of the number of turns in the coil ($N$) and the current flowing through it ($i$). Because the magnetomotive force is expressed as $Ni$, increasing the total number of turns ($N$) directly increases the force that generates the magnetic field and the resulting magnetic flux.1

Essentially, by increasing the number of turns, you increase the density of the magnetic field generated by the coil, provided the current remains constant. This principle is fundamental to the design of electromagnets, which are used in applications where controllable magnetic flux is required.12