Assume that a metallic solid consists of atoms arranged in a regular fashion. Each atom usually contributes free electrons, also called conduction electrons. These electrons are free to move in the metal in a random manner, almost the same way as atoms or molecules of a gas move about freely in the a container. It is for this reason that sometimes conduction electrons are referred to as electron gas. The average speed of conduction electrons is about 106 ms–1.
No current flows through a conductor in the absence of an electric field, because the average velocity of free electrons is zero. On an average, the number of electrons moving in +x direction is same as number of electrons moving in –x direction. There is no net flow of charge in any direction.
The conduction electrons frequently collide with the atoms in the solid. The free electrons drift slowly in a direction opposite to the direction of the applied electric field. The average drift velocity is of the order of 10–4 ms–1. This is very small compared to the average speed of free electrons between two successive collisions (106 ms–1).
On applying an electric field, the conduction electrons get accelerated. The excess energy gained by the electrons is lost during collisions with the atoms. The atoms gain energy and vibrate more vigorously. The conductor gets heated up.
Let e and m be the charge and mass respectively of an electron. If E is the electric field, the force on the electron is eE. Hence, acceleration experienced by the electron is given by
a = eE/m
If τ is the average time between collisions, velocity of drifting electrons in terms of electric field is
vd = (eE/m)τ
I = – neAvd
I = –neA(eE/m)τ
I = – (Ane2E/m)/τ