Let us consider a conductor under the influence of an external electric field. If represents the number of electrons per unit volume, then the charge crossing an area that is normal to the direction of the drift velocity is given by:

........................................(3.2)

This flow of charge constitutes a current across , which is given by,

................(3.3)

The conduction current density can therefore be expressed as

.................................(3.4)

where is called the conductivity. In vector form, we can write,

..........................................................(3.5)

The above equation is the alternate way of expressing Ohm's law and this relationship is valid at a point.