Question

Derive an expression for emf (\( e \)) generated in a conductor of length (\( l \)) moving in uniform magnetic field (\( B \)) with uniform velocity (\( v \)) along x-axis.

Hint:

Motional emf is \( B l v \sin \theta \); maximum when perpendicular (\( \sin 90^\circ = 1 \)).

Answer 1

A conductor of length \( l \) moving with velocity \( v \) perpendicular to a uniform magnetic field \( B \) induces an emf due to motional electromotive force.
Assume conductor along y-axis, magnetic field along z-axis, velocity along x-axis.
The induced emf is: \[ e = B l v, \] derived from Lorentz force on charges: \( F = q (\vec{v} \times \vec{B}) \).
For perpendicular motion, the effective force separates charges, creating a potential difference \( e = B l v \).
Answer: \( e = B l v \).