The Force on a Current-Carrying Wire

A wire sitting between two magnet poles does nothing until current flows. Once it does, the wire jumps. Current is just charge in motion, and a moving charge in a magnetic field feels a force, F = qvB, pointed perpendicular to both its velocity and the field. Every electron drifting down the wire feels this same sideways shove. Multiply one electron's force by the huge number of electrons moving together, and you get a force big enough to kick the whole wire out of the gap. That's the content of F = BIL: B is the field strength, I is the current, and L is the length of wire sitting in the field, with the wire held perpendicular to B for this simple form.

Direction comes from the right-hand rule: point your fingers along the current, curl them toward B, and your thumb gives the force (or use F = IL x B if you want the full vector version). This matters most inside a motor. A motor is a loop of wire sitting in a magnetic field. Current runs one way down one side of the loop and back the other way on the opposite side, so the two sides feel forces in opposite directions. That pair of opposite forces is a torque, and it spins the loop.

The spin only keeps going because a commutator flips the current's direction every half turn, right as the loop crosses vertical. Without that flip, the loop would coast past vertical and then feel a torque trying to spin it back the way it came, so it would oscillate or stall instead of turning continuously. This is the same magnetic force idea from the force on moving charges, now scaled up to currents, and it sets up why a current loop also acts like a tiny magnet with its own magnetic moment.