Suppose we bend our wire into a squarish, U-shaped loop so there are effectively two parallel wires running through the magnetic field. One of them takes the electric current away from us through the wire and the other one brings the current back again. Because the current flows in opposite directions in the wires, Fleming Left-Hand Rule tells us the two wires will move in opposite directions. In other words, when we switch on the electricity, one of the wires will move upward and the other will move downward.
Another interesting design is the brushless DC (BLDC) motor. The stator and rotor effectively swap over, with multiple iron coils static at the center and the permanent magnet rotating around them, and the commutator and brushes are replaced by an electronic circuit. You can read more in our main article on hub motors. Stepper motors, which turn around through precisely controlled angles, are a variation of brushless DC motors.
Magnetically soft materials, however, tend to be more expensive. The motor manufacturer must find that proper blend of just enough magnetically soft material to do the work required without putting too big a dent in the customer wallet.
In simple DC and universal motors, the rotor spins inside the stator. The rotor is a coil connected to the electric power supply and the stator is a permanent magnet or electromagnet. Large AC motors (used in things like factory machines) work in a slightly different way: they pass alternating current through opposing pairs of magnets to create a rotating magnetic field, which "induces" (creates) a magnetic field in the motor rotor, causing it to spin around. You can read more about this in our article on AC induction motors. If you take one of these induction motors and "unwrap" it, so the stator is effectively laid out into a long continuous track, the rotor can roll along it in a straight line. This ingenious design is known as a linear motor, and you will find it in such things as factory machines and floating "maglev" (magnetic levitation) railroads.