# Drift Velocity: Definition, Formula, Mobility of Electron and Examples

A vector measurement of the rate and direction of motion is what is meant by the term “velocity”. Simply put, velocity is the rate at which something goes in one direction. The speed of a car driving north on a major highway and the speed of a rocket launching into space may both be calculated using velocity. A velocity-time graph is frequently used to depict the speed and direction of an object over a given time period.

Drift is the slow movement towards something/object. The average velocity of charged particles in a material due to an electric field is known as drift velocity. Let’s learn in detail about drift velocity.

## What is Drift Velocity?

Subatomic particles, such as electrons, move in random directions all the time. When electrons are exposed to an electric field, they move in a random but slow path, the direction of the applied electric field. The drift velocity refers to the overall velocity of these electrons.

It can be defined as:

The average velocity of charged particles (e.g., electrons) in a material as a result of an electric field.

The SI unit of drift velocity is metres per second (m/s). It is also expressed as m 2 / (V.s).

## Formula To Calculate Drift Velocity

To compute drift velocity, we can apply the following formula:

I=nAvQ

Where,

I = Current (in Ampere) flowing through the conductor

n= Number of electrons

A = Cross-section area of the conductor which is measured in m 2

v = Drift velocity of the electrons

Q = Charge (in Coulomb) of an electron

Example:

A conductor wire with 10 29 free electron/m 3 may carry a current of 20 amps. If the cross- section of the wire is 1 mm 2 , what is the electron’s drift velocity?

Given:

n = 10 29 m -3

I = 20A,

A = 1 mm 2 = 10-6 m2

e = 1.6 × 10 -19 C

To Find: Vd

Solution:

We know, I = A × n × e × vd

∴ v d = i / A × n × e

∴ v d = 20 / 10 -6 × 10 29 × 1.6 × 10 -19

∴ v d = 1.25 × 10 -3 m/s

## Mobility of an electron

The mobility of an electron is defined as its drift velocity in a unit electric field.

An electron’s mobility can be computed as follows:

u=Vd /E

## Relation between Drift Velocity and Electric Current

Mobility is always positive and relies on the type of the charge carrier; the drift velocity of an electron is typically in the 10-3 ms -1 range. As a result, at this speed, it will take approximately It takes 17 minutes for electrons to flow through a 1 metre-long conductor. Surprisingly, we can turn on electrical gadgets in our homes at lightning speeds with the flick of a switch because an electric current is established at the speed of light rather than the drift velocity.

When an electric field is generated, current begins to flow within the conductor at the speed of light rather than the speed at which electrons are wandering, resulting in an insignificant little delay between an input and an output when turning on an electric bulb.

## Relation between Drift Velocity and Current Density

The total amount of current traveling through a unit cross-sectional conductor in unit time is defined as current density. We may calculate drift velocity using the following

formula:

I = nAvQ

J = I/A = nVQ

Where,

J = Current density measured in Amperes per square meter

v = Electron’s drift velocity

We can argue that the electrons’s drift velocity and current density are directly proportional to each other. Furthermore, as the intensity of the electric field grows, so do the drift velocity and the current flowing through the conductor.