Suppose you take a length of ordinary wire, make it into a big loop, and lay it between the poles of a powerful, permanent horseshoe magnet. Now if you connect the two ends of the wire to a battery, the wire will jump up briefly. It is amazing when you see this for the first time. It is just like magic! But there is a perfectly scientific explanation. When an electric current starts to creep along a wire, it creates a magnetic field all around it.
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.
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.
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.