# Obtain an expression for motional emf from Lorentz force

1.7k views

closed

Obtain an expression for motional emf from Lorentz force

+1 vote
by (49.5k points)
selected

Motional emf from Lorentz force:

Consider a straight conducting rod AB of length l in a uniform magnetic field $\vec B$ which is directed perpendicularly into the plane of the paper. The length of the rod is normal to the magnetic field. Let the rod move with a constant velocity $\vec v$ towards right side. When the rod moves, the free electrons present in it also move with same velocity  $\vec v$ in $\vec B$ . As a result, the Lorentz force acts on free electrons in the direction from B to A and is given by the relation The action of this Lorentz force is to accumulate the free electrons at the end A. This accumulation of free electrons produces a potential difference across the rod which in turn establishes an electric field E directed along BA. Due to the electric field E, the coulomb force starts acting on the free electrons along AB and is given by

$\vec F_E$= -e $\vec E$  ........... (2)

The magnitude of the electric field $\vec E$ keeps on increasing as long as accumulation of electrons at the end A continues. The force $\vec F_E$ also increases until equilibrium is reached. At equilibrium, the magnetic Lorentz force $\vec F_B$ and the coulomb force   $\vec F_E$ balance each other and no further accumulation of free electrons at the end A takes place, i.e., vB sin 90° = E

vB = E ……. (3)

The potential difference between two ends of the rod is Figure: Motional emf from Lorentz force

V = El

V = vBl

Thus the Lorentz force on the free electrons is responsible to maintain this. potential difference and hence produces an emf

ε = Blv ….. (4)

As this emf is produced due to the movement of the rod, it is often called as motional emf