There is current flowing in a wire as well(aside from the electromagnet) displayed in this diagram:
(Ignoring the Lorentz force acting on the wire and possibly the electromagnet)The magnetic field created by the electromagnet(that is composed of multiple turns and a ferromagnetic core like soft iron to increase the magnetic field) is \$B\$ acting on the wire that has current flowing within it. Likewise, the wire will induce it's own magnetic field \$B_W\$ as shown here:
Usually, the \$B_W\$ is insignificant due to the distance and the amount of current flowing within it,
However, if(neglecting resistance and fusing on the wire) the current was quite high enough to generate a magnetic field where this condition \$B_W\$ > \$B\$ is true, what would happen to \$B\$?