Answer and explanation;
-Voltage overcomes the resistance of the electromagnet winding to force a current through that resistance. The field strength is proportional to the coil current. More voltage pushes more current.
-There is also a time component of this process, with voltage being needed to build up the magnetic field in a certain time. More voltage builds up the current faster, as well as forcing it to a higher final value.
-When the electromagnet are wound with superconducting wire (with zero resistance) then it would take no voltage to keep current passing through the winding and once it was built up, you could just short the ends together and the current would keep going.