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Obtain an expression for the e.m.f induced across a conductor which is moved in a uniform magnetic field which is perpendicular to the plane of motion. perpendicular to the plane of motion.

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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)

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