Drift Velocity (vd):
When a potential difference (V) is applied across the conductor of length (l), then an electric field \(\overrightarrow{(E)}\) develops in the conductor \(\left(E=\frac{V}{l}\right)\) Due to this field each free electron of the conductor experiences an electric force \(\vec{F}=-e \vec{E}\) towards the positive end of the conductor and hence it starts accelerated motion \(\left(\vec{a}=\frac{\vec{F}}{m}\right)\) towards the positive end. During its accelerated motion it collides with the other electrons and positive ions of the conductor. Therefore its velocity always remains changing. This motion of electron is known as ‘Drift motion’ and the average velocity between two successive collisions is known as ‘Drift velocity.’ It is denoted by vd.
“i.e., the maximum velocity achieved by the electrons due to imposed electric field with which they collide with other ions, is known as drift velocity.” Time taken in two successive collisions is called ‘Relaxation time’. For most of the conductors, the relaxation time is the order of 10-14s. Just before colliding with a ion, the velocity is maximum and after collision for a moment the velocity becomes zero. Again electron gets accelerated by applied electric field and repeats the previous situation of colliding with ions of the conductor. Thus “the potential difference of battery does not provide accelerated motion to electrons but it can provide a small constant velocity along the length of the conductor, which is imposed upon the random motion of the electrons. This constant velocity of the electron is called drift velocity of electrons.” The order of this drift velocity about 10-4 m/s.
Reason of small value of drift velocity : In following figure 5.4, the random motion of electron is shown by thick lines and in presence of external electric field by dotted lines. It is obvious from the figure that the electron moves with small drift velocity and due to this reason point X is shifted to X’. Thus due to electric field, the net displacement becomes XX’. Which has very small value. This is why the drift velocity is very small.
Relaxation time (τ): The average time taken by electron in two successive collisions is known as ‘Relaxation time’ and it is denoted by τ. It is obtained by
