Question

use the expression for lorentz force acting on the charge carriers of a a conductor to obtain the expression for the induced emf across the conductor of length l moving with velocity v through a magnetic field B acting perpendicular to its length

Answer 1

Lorentz force : total force experienced by charged particle is moving in a region where both electric and magnetic field are present, is called Lorentz force.

A charge q , in an electric field $\vec{E}$ experience electric force , $\vec{F_e}=q\vec{E}$.

force $\vec{F_e}$ acts along electric field and it is independent of the velocity of the charged particle.

now, magnetic force experienced by the charged particle q moving with velocity $\vec{v}$ in the magnetic field $\vec{B}$ is given by, $\vec{F_m}=q(\vec{v}\times\vec{B}$

magnetic force $\vec{F_m}$ acts perpendicular to the magnetic field $\vec{B}$ and depends on the velocity of charged particle.

so, Lorentz force, $\vec{F}=\vec{F_e}+\vec{F_m}$

= $q\vec{E}+q(\vec{v}\times\vec{B})$