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Motional EMF arises when a conductor moves through a magnetic field: $\varepsilon = Bvl$ for a rod of length $l$ moving at velocity $v$ perpendicular to field $B$. The physical origin is the Lorentz force on free charges ($F = qvB$), which pushes them along the conductor.

The rod-on-rails setup is the prototypical problem: a rod slides on conducting rails connected by resistance $R$ in perpendicular field $B$. Key results: EMF $= Bvl$, current $= Bvl/R$, retarding force $= B^2l^2v/R$, power dissipated $= B^2l^2v^2/R$. If released with velocity $v_0$: exponential decay $v = v_0e^{-t/\tau}$ with $\tau = mR/(B^2l^2)$. If constant force applied: terminal velocity $v_t = FR/(B^2l^2)$.

A rod rotating about one end: $\varepsilon = B\omega l^2/2$ (area swept per unit time = $l^2\omega/2$). A disc rotating: same formula with $R$ replacing $l$. Multiple spokes on a wheel: same EMF as one spoke (parallel identical sources).

Key insight: motional EMF and Faraday's law are two perspectives on the same physics. The rod changes the circuit area, changing flux. Both give $\varepsilon = Bvl$.