Consider a metallic conductor XY of length l and cross-sectional area A. A potential difference V is applied across the conductor XY. Due to this potential difference an electric field vector E is produced in the conductor. The magnitude of electric field strength E = V/l and its direction is from Y to X. This electric field exerts a force on free electrons; due to which electrons are accelerated.
The electric force on electron vector F = - e vector E
If m is the mass of electron, then its acceleration
This acceleration remains constant only for a very short duration, since there are random forces which deflect the electron in random manner. These deflections may arise due to
(i) ions of metallic crystal vibrate simple harmonically around their mean positions. Different ions vibrate in different directions and may be displaced by different amounts.
(ii) direct collisions of electrons with atoms of metallic crystal lattice. In any way after a short duration t called relaxation time, the motion of electrons become random. Thus, we can imagine that the electrons are accelerated only for a short duration. As average velocity of random motion is zero, if we consider the average motion of an electron, then its initial velocity is zero, so the velocity of electron after time τ(i.e. , drift velocity vector vd) is given by the relation vector v = vector u + vector at (here vector u = 0
At given temperature, the relaxation time t remains constant, so drift velocity remains constant.
