Motional emf

A rod of length l slides at speed v along two rails in a uniform field B at right angles to the plane of the circuit. The enclosed area changes at the rate lv, so the flux Blx changes at Blv and the induced emf is ε = Blv. This is called motional emf.

Lorentz-force view: every free charge q in the rod moves with it at speed v, so it feels a force qvB along the rod. Carrying a charge along the rod's length l takes work qvBl, and emf is work per unit charge, so ε = Blv again.

Here the flux changes because the conductor moves through a steady field. When the conductor is at rest and the field changes, v = 0 and the only possible force is qE, so a changing magnetic field must create an electric field.

The electric field made by a changing magnetic field behaves differently from the field of static charges. Moving charges exert forces on magnets, and moving magnets exert forces on charges: electricity and magnetism are linked.

With the rails closed through a resistance R, the current is I = Blv/R. The field then pushes on the current-carrying rod with a force BIl that opposes its motion, as Lenz's law requires; keeping v steady needs an equal pull.