Explain drift velocity and obtain an expression for it.

Explanation

In a conductor the charge carriers are free electrons. These electrons move freely through the conductor and collide repeatedly with the positive ions.
Suppose a potential difference is set across the conductor by connecting a battery, an electric field `vecE` is created in the conductor. This electric field exerts a force on the electrons. Then it produces a current. The electric field accelerates the electrons, while ions scatter the electrons and change the direction of motion. In this way, we have zigzag paths of electrons. In addition to the zigzag motion due to the collisions, the electrons move slowly along the conductor in a direction opposite to that of `vecE` as shown in the Figure.

The drift velocity is the average velocity acquired by the electrons inside the conductor when it is subjected to an electric field. The average time between successive collisions is called the mean free time denoted by `tau`. The acceleration `vec a` experienced by the electron in an electric field `vecE` is given by.
` vec a = (e vec E)/m ("since" vec F = e vecE)`
The drift velocity `vec v_d` is given by
` vec v _d = vec a tau`
`vecv_d = (e tau)/m vec E`
` vec v_d = mu vec E`