Drude-Lorentz Theory of Electrical Conduction

The basic assumptions of Lorentz-Drude theory are:

1. There are a large number of free electrons in a metal. These electrons are free to move about the whole volume of the metal like the molecules of a perfect gas in a container.

2. The free electrons make collisions from time to time with fixed positive ions in the lattice and also among themselves. We may neglect the collisions between electrons in comparison with the collisions between electrons and ions cores.

3. In the absence of electric field, the random motion of free electrons is equally probable in all directions so that current density vector is zero.

4. When an external electric field is applied, the electrons drift slowly with some average velocity, known as average drift velocity, in the direction opposite to that of electric field. The drift velocity of free electrons is superimposed over their random velocity. The continuous solid lines show a possible random path followed by an electron in the absence of an applied field. The dashed lines show the electron path in the presence of the electric field E. Note the steady drift in the direction of -E. The drift velocity is much smaller in magnitude than average random velocity of free electrons.

5. The average distance transverse by a free electron between two successive collisions with the positive ions is called mean free path and is denoted by λ.

If an electron of mass m and charge e is placed in an electric in an electric field E, it experiences an acceleration a given by
            a = eE/m.

Let τ be the average time – interval between two successive collisions of an electron with positive ions.
Increase in drift velocity in time-interval between two successive collisions of an electron with positive ions.
This drift velocity is reduced to zero at the next collision and again builds up to the value eEτ/m before suffering another collision and so on.

. : the average drift velocity through the conductor} = Vd = eEτ/2m

Let n be the number of conduction electrons per unit volume.

Current density = J = nevd = ne2 Eτ / 2m

But J = σ = J/E = ne2τ / 2m.

This is the expression for the electrical conductivity of a metal.