# 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
- Drift velocity formula in terms of current
- Drift velocity formula in terms of current density
- Drift velocity formula in terms of relaxation time
- Drift velocity formula in terms of electric field
- Drift velocity formula in terms of voltage | Drift velocity formula in terms of potential difference
- Drift velocity formula in terms of 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:

Drift velocity formula in terms of mobility

v_{d}= μ_{e}

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 v _{d} A**

Drift velocity formula in terms of current

v_{d}= I / (n e A)

where, I = current, v_{d} = 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 v_{d}

Drift velocity formula in terms of current density

v_{d}= J / (ne)

where, v_{d} = 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

Drift velocity formula in terms of relaxation time

v_{d }= a τ

where v_{d} = drift velocity, a = acceleration of the electron under an electric field, and τ = relaxation time

## Drift velocity formula in terms of electric field

Drift velocity formula in terms of electric field

v_{d }= (eE/m) τ

where v_{d} = 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

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

v_{d }= [(eV)/(ml)] τ

where v_{d} = 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

Drift velocity formula in terms of length of the wire

v_{d }= [(eV)/(ml)] τ

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