Derive the expression for conductivity in terms of mobility

The electron mobility is defined by the equation:

.

where:

E is the magnitude of the electric field applied to a material,
vd is the magnitude of the electron drift velocity (in other words, the electron drift speed) caused by the electric field, and
µ is the electron mobility.

There is a simple relation between mobility and electrical conductivity. Let n be the number density (concentration) of electrons, and let μe be their mobility. In the electric field E, each of these electrons will move with the velocity vector , for a total current density of  (where e is the elementary charge). Therefore, the electrical conductivity σ satisfies:

.

This formula is valid when the conductivity is due entirely to electrons

DERIVATION

answered Jan 5 by (4,450 points)