Drift velocity and mobility of an electron

In this post, we will see how the drift velocity of an electron is related to its mobility.

The drift velocity of an electron can be expressed as v_d = ( Ee/m) τ, where v_d is the drift velocity, E is the electric field, e is the charge of an electron, and m is the mass of an electron. You can find the derivation of drift velocity here. We will use this equation to find out the relationship between mobility and the drift velocity of an electron.

Drift velocity and mobility of an electron (relationship)

The drift velocity of an electron v_d = ( Ee/m) τ …………….. (1)

(v_d is the drift velocity, E is the electric field, e is the charge of an electron, and m is the mass of an electron.)

This equation can be rewritten as the following:

=> v_d = (τe/m) E …………. (2)

τe/m is a constant and it is known as the mobility of electron (μ_e).

So, we can write the equation of the drift velocity using mobility:

v_d = μ_e E ……………. (3)

equation of the drift velocity using mobility

Now, when electric field E is 1 V m^-1, then equation (3) gives this equation of drift velocity in terms of mobility of an electron only:

v_d = μ_e

when E = 1 V m^-1

So, we can define mobility in this way: Mobility of an electron is the drift velocity of an electron under the effect of an electric field equalling 1 V/m.