Changing the current changes the "what" of an electromagnet

An electromagnet is only magnetic when there's current going through
the wire.  If there's no current flowing, then the electromagnet is just a
lump and doesn't attract anything.

The strength of the electromagnet depends on the amount of current
that's flowing through the coil of wire around it.

Changing the current immediately changes ==> the magnitude of the
magnetic field, ==> the strength of the electromagnet, and what it's
able to pick up.