The electron mobility is defined by the equation:

{\displaystyle \,v_{d}=\mu E}.
where:

E is the magnitude of the electric field applied to a material,

v_{d} 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 μ_{e} be their mobility. In the electric field E, each of these electrons will move with the velocity vector {\displaystyle \mu _{e}\mathbf {E} }, for a total current density of {\displaystyle ne\mu _{e}\mathbf {E} } (where e is the elementary charge). Therefore, the electrical conductivity σ satisfies:

{\displaystyle \sigma =ne\mu _{e}}.
This formula is valid when the conductivity is due entirely to electrons
DERIVATION