# Drift velocity formula

In this post, we will present the drift velocity formula or equation in terms of different variables like the mobility of an electron, electric current, current density, relaxation time, electric field, potential difference or voltage, and the length of the wire.

## Drift velocity formula in terms of mobility

When electric field E = 1 Vm-1, the drift velocity of an electron can be expressed in terms of the mobility of a free electron in the following way:

vd = μe

Drift velocity formula in terms of mobility

This means, the magnitude of drift velocity imparted by a uniform electric field of strength 1 Vm-1 = mobility of a free electron

## Drift velocity formula in terms of current

Current I = n e vd A

vd = I / (n e A)

Drift velocity formula in terms of current

where, I = current, vd = drift velocity, A = cross-sectional area of the wire, e = charge of an electron, and n = number of electrons per unit volume of the wire.

## Drift velocity formula in terms of current density

Current density J = n e vd

vd = J / (ne)

Drift velocity formula in terms of current density

where, vd = drift velocity, J = Current density, e = charge of an electron, and n = number of electrons per unit volume of the wire.

## Drift velocity formula in terms of relaxation time

vd = a τ

Drift velocity formula in terms of relaxation time

where vd = drift velocity, a = acceleration of the electron under an electric field, and τ = relaxation time

## Drift velocity formula in terms of electric field

vd = (eE/m) τ

Drift velocity formula in terms of electric field

where vd = drift velocity, e = charge of an electron, E = electric field intensity, m = mass of an electron, and τ = relaxation time

## Drift velocity formula in terms of voltage | Drift velocity formula in terms of potential difference

vd = [(eV)/(ml)] τ

Drift velocity formula in terms of voltage | Drift velocity formula in terms of potential difference

where vd = drift velocity, V = Potential difference or voltage, m = mass of an electron, l = length of the wire, and τ = relaxation time

## Drift velocity formula in terms of length of the wire

vd = [(eV)/(ml)] τ

Drift velocity formula in terms of length of the wire

where vd = drift velocity, V = Potential difference in voltage, m = mass of an electron, l = length of the wire, and τ = relaxation time