# Drift Velocity, Carrier Mobility and Drift Current โ Definition, Formula and Examples

The slow movement of something toward an object is termed as drift. The average velocity of electrically charged particles in a material under the influence of an electric field is called the drift velocity. In this article, we will learn in detail about drift velocity, carrier mobility, and drift current.

## What is Drift Velocity?

When a voltage is applied across the ends of a conducting wire, an electric field is applied at every point of the copper wire. Due to this electric field, the free electrons in the conductor wire experience a force that accelerates them toward the positive end or higher potential end.

When the free electrons move, they successively collide with the positive atoms of the conductor material. At each collision, the free electrons loss the extra velocity gained. Consequently, the free electrons move towards the positive end with a small constant velocity. This constant velocity of free electrons is known as the drift velocity.

Therefore, we may define the drift velocity as under โ

The average velocity with which the charged particles (like electrons, holes, etc.) move in a conductor under the influence of an electric field is called the drift velocity. It is usually represented by the symbol vd, and is measured in meters per second (m/s).

## What is Carrier Mobility?

The parameter which indicates how fast a charged particle will move through a conductor or semiconductor is known as mobility or carrier mobility. For electrons, it is referred to as electron mobility, and for holes, it is known as hole mobility. Mobility is denoted by the Greek letter mu (ยต).

Mathematically, the mobility of charged particles (let electrons) is given by,

$$\mathrm{\mu= \frac{v _{d}}{E\: }\:\cdot \cdot \cdot \left ( 1 \right ) }$$

Where, vd is the drift velocity of electrons, and E is the applied electric field.

## The Formula of Drift Velocity

We can calculate the drift velocity of a charged particle in a conductor by using the following formula โ

$$\mathrm{Drift \: velocity,v _{d}= \frac{I}{nQA\: }\:\cdot \cdot \cdot \left ( 2 \right ) }$$

Where,

• I = current through the conductor in amperes.
• n = number of charged particles (let electrons).
• A = cross-sectional area of the conductor in m2.
• Q = charge of an electron measured in coulombs.

## What is Drift Current?

The electric current flowing through a conducting material created by the drifting of charged particles by the electric field is called the drift current.

When a conducting material is subjected to an electric field, the free electrons in the material are dragged by the electric field. This movement of free electrons in a certain direction constitutes a current through the conductor. This current is known as drift current. It is named so because it flows due to the drifting of charged particles.

For a given conductor, the total drift current is determined by the concentration and mobility of charge carriers.

## Relation between Current and Drift Velocity

Consider a conducting wire of l meters having an area of cross-section of A m2. If n is the electron density per unit volume in the conductor. Then, the total number of electrons in the conductor wire is,

$$\mathrm{Total \: electrons=nAl }$$

Therefore, the total electric charge in the conductor is

$$\mathrm{Total \: charge, Q=nAl\times e }$$

If vd is the drift velocity of electrons, then the total time taken to cross the conductor is

$$\mathrm{t=\frac{l}{v _{d}} }$$

By the definition of electric current, we have,

$$\mathrm{Current,I=\frac{Q}{t}=\frac{neAl}{t} }$$

$$\mathrm{\Rightarrow I=\frac{neAlv_{d}}{l}}$$

$$\mathrm{\therefore I=neAlv_{d}\: \: \cdot \cdot \cdot \left ( 3 \right )}$$

Hence, from equation (3), it is clear that the current flowing through a given conductor is directly proportional to the drift velocity of the free electrons.

## Relation between Current Density and Drift Velocity

The electric current density is defined as the current (I) flowing per unit area (A), i.e.,

$$\mathrm{Current\: density, J=\frac{I}{A}\: \: \cdot \cdot \cdot \left ( 4 \right )}$$

From equations (3) & (4), we have,

$$\mathrm{J=\frac{neAv_{d}}{A}}$$

$$\mathrm{\therefore J=nev_{d}\: \: \cdot \cdot \cdot \left ( 5 \right )}$$

## Numerical Example

A metallic wire of cross-sectional area 3 mm2 is 5 meters long and carries a current of 15 A. The electron density in the conductor is 8 ร 1027 per m3. Calculate the drift velocity of electrons. If the strength of the applied electric field is 5 V/m, find the mobility of electrons in the wire.

## Solution

Given data,

$$\mathrm{Area\: of\: cross\: section, A = 3 mm^2 = 3 \times 10^{-6} m^2}$$

$$\mathrm{ length\: of\: wire, l = 5\: m }$$

$$\mathrm{ Current, I = 15\: A}$$

$$\mathrm{Electron\: density, n = 8 \times 10^{27} m^{-3}}$$

Thus, the drift velocity will be,

$$\mathrm{v_{d}=\frac{I}{neA}=\frac{15}{(8 \times 10^{27}) \times (1.6 \times 10^{-19}) \times (3 \times 10^{-6})}}$$

$$\mathrm{\therefore v_{d} = 3.91 \times 10^{-3}\: ms^{-1}}$$

Also, it is given that the intensity of the applied electric field is equal to 5 V/m, then the mobility of charge carriers will be,

$$\mathrm{\mu =\frac{v_{d}}{E}=\frac{3.91\times 10^{-3}}{5} }$$

$$\mathrm{\therefore \mu = 7.8125 \times 10^{-4}\, m^2Vs}$$