Electromagnetic Induction & AC

motional EMF

Slide a plain metal rod across a magnetic field and a voltage appears between its two ends — no magnet moving, no coil, just a moving conductor. That voltage is a motional EMF. It answers a striking question: how can mere motion through a field turn a piece of wire into a battery?

Precisely, each charge inside the moving rod feels the magnetic part of the Lorentz force, F = q v B, which shoves positive charges toward one end and leaves the other negative, building up a voltage. For a rod of length L moving at speed v straight across a field B, the EMF is EMF = B L v. This is nothing but Faraday's law in another costume: as the rod slides along a pair of rails it sweeps out new area, so the flux through the circuit changes at the rate B L v.

Motional EMF is the beating heart of a generator — a wire moving through a magnetic field. The honest point is that it is the same physics as flux-change induction seen from a different angle: whether you say the flux changed or that the charges felt a v-cross-B force, you get the identical EMF. It only works when the rod cuts across the field lines; sliding straight along them produces nothing.

A rod 0.5 m long slides at 4 m/s straight across a 0.3 T field. The motional EMF is B L v = 0.3 * 0.5 * 4 = 0.6 V between its ends.

A 0.5 m rod at 4 m/s across a 0.3 T field makes 0.6 V.

The rod only makes an EMF while it moves across the field. Once a current flows it also feels a retarding force (Lenz's law), so you must keep pushing to keep generating — the electricity is paid for by your work.

Also called
EMF運動電動勢