A metal is imagined as the structure of 3-dimensional array of ions in between which, there are free moving valence electrons confined to the body of the material. Such freely moving electrons cause electrical conduction under an applied field and hence referred to as conduction electrons. The free electrons are treated as equivalent to gas molecules and they are assumed to obey the laws of kinetic theory of gases. In the absence of the field, the energy associated with each electron at a temperature T is given by 3/2 kT, where k is a Boltzmann constant. It is related to the kinetic energy. 3/2 kT = ½ mvth^2 Where vth is the thermal velocity same as root mean square velocity. The electric potential due to the ionic cores is taken to be essentially constant throughout the body of the metal and the effect of repulsion between the electrons is considered insignificant. The electric current in a metal due to an applied field is a consequence of the drift velocity in a direction opposite to the direction of the field.
To find the relationship between current and drift velocity, consider a conductor of length l and area of cross-section A. If V is the potential difference across the ends of the conductor, then the strength of the electric field is
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