Consider a conductor PQ of length l moving freely in a uniform magnetic field vector B with uniform velocity υ on a rectangular conductor ABCD.
Let any arbitrary charge q in the conductor also move in the field with same velocity.
Magnitude of lorentz force on this charge (F) = Bqυ —— (1)
Workdone in moving the charge from P to Q is given by
W = Force × displacement W = Bqυ × l —— (2)
(∵Direction of force on the charge as per Fleming's left hand rule)
Electromotive force (ε) =w/q
ε = Bqυl/q ⇒ ε = Blυ —— (3)