If a rod moves on parallel conducting rails, the area enclosed by the loop increases with time. In time t, the swept area is A = lvt, the linked flux is phi = B A = Blvt, and therefore the induced emf magnitude is e = dphi/dt = Bvl. If the circuit is closed, the induced current is i = e/R = Bvl/R.

• The magnetic field may be constant; it is the loop area that changes and causes flux variation.
• Generated area is the bridge between motional emf and Faraday's law in this arrangement.
• Trap: thinking flux can change only when B changes with time.

The current-carrying rod in the field experiences magnetic force opposite to its motion, so an external agent must supply force to keep the motion uniform. The magnetic force is Fm = Bil = B squared v l squared by R, mechanical input power is Fext times v, and this equals the Joule-heating rate in the resistance.

• Retarding force is the mechanical manifestation of Lenz's law in the moving-loop setup.
• Uniform motion requires external force equal in magnitude to the magnetic braking force.
• Trap: writing magnetic force correctly but forgetting that the same current produces thermal power i squared R.

If the rod is released in a vertical plane, its initial speed is small, so induced emf, current, and magnetic force are small. As speed rises, all three rise until magnetic force equals weight. At that stage acceleration stops and the rod reaches terminal velocity vT = mgR divided by B squared l squared.

• This is a feedback system: larger speed generates stronger magnetic opposition.
• Terminal speed comes from force balance, not from setting emf equal to weight or power equal to weight directly.
• Trap: assuming the rod keeps gaining speed because gravity is constant while forgetting magnetic force grows with velocity.