How does an electric motor make a shaft turn?

A fan's spinning shaft begins with forces on a coil of wire. In a simplified brushed direct-current motor, the coil sits between magnetic poles. Current runs in opposite directions along its opposite sides, so the magnetic field pushes those sides in opposite directions and transfers electrical energy into rotation.

Those pushes do not cancel their turning effects. They act on different sides of the shaft: one side is pushed one way and the other the opposite way, like two hands turning a steering wheel. Together they create torque, the turning effect of a force. Several wire turns add their contributions.

As the coil rotates, its orientation changes and so does its torque. If its current simply kept the same direction, the turning effect would eventually reverse. A commutator, the current reverser, switches the coil’s connections each half-turn. Momentum carries the rotor through positions where this ideal single coil has zero torque, while the reversed current supports continued turning.

For a flat coil, torque magnitude is N × B × I × A × sin θ. N counts turns, B is field strength, I is current, A is coil area, and θ is the angle between the field and the coil’s perpendicular direction. At the pictured maximum-torque orientation, 20 turns, 0.5 tesla, 1 ampere and 0.02 square meter give 0.2 newton meter.

The pictured torque is an instantaneous turning effect, not a speed prediction. Load, resistance and losses affect a real motor's motion, while rotation induces an opposing voltage called back emf that changes current. Fixing the coil's orientation and current lets this illustration isolate how a pair of forces turns a shaft.