When a conductor of length $l$ moves with velocity $v$ perpendicular to a uniform field $B$: $\varepsilon = Bvl$. Origin: the Lorentz force $F = qvB$ acts on free electrons in the conductor, pushing them to one end, creating a potential difference. The induced EMF is equivalent to a battery with the higher potential end determined by the direction of $\vec{v} \times \vec{B}$. For a rod on rails with resistance $R$: current $I = Bvl/R$, retarding force $F = B^2l^2v/R$, power dissipated $P = B^2l^2v^2/R = Fv$.