What is motional E.M.F? Derive expression for it.

Motional emf: When an conducting loop or rod moves in the in an uniform magnetic field, so that flux through the loop changes, due to the change in the flux through the loop, an emf is induced it the loop, which is called motional emf.

$$\begin{gathered} Lorentz force on the conducting loop is given by: \\ F = qvB \sin \theta \\ let magnetic field and velocity of the charge are perpendicular to each other. \\ \theta = 90 \\ F = qvB \\ this force must be equal to the electrioc force on the charge. \\ qvB = qE \\ E = vB \\ potential across the rod or conductor whose length is L id given by: \\ V = electric field\times length of the conductor \\ V = EL \\ V = BLv \\ Where V is the motional emf. \end{gathered}$$