Derive Relation Between Current and Drift Velocity

In this lecture, we are going to learn about the Relation Between Current and Drift Velocity. We will cover the definitions of Current density, Drift velocity, and Mobility also. So let’s start with the definitions of each term.

What is Current Density?

Current density refers to the measure of electric current per unit area of a material or conductor through which the current is flowing. It represents the concentration or distribution of electric current within a given region.

Mathematically, current density (J) is calculated by dividing the magnitude of the electric current (I) by the cross-sectional area (A) perpendicular to the current flow.

It is typically expressed in units of amperes per square meter (A/m²) or amperes per square millimeter (A/mm²).

Analyzing current density is important in various applications such as electrical engineering, materials science, and circuit design, as it helps understand the behavior of electric currents and optimize the performance and efficiency of electrical systems.

Also Read: Band Theory of Solids

Drift Velocity

Drift velocity refers to the average velocity at which charged particles, such as electrons, move in a conductor in response to an applied electric field. It is a result of the interaction between the electric field and the particles in the material.

When an electric field is applied across a conductor, it exerts a force on the charged particles, causing them to accelerate in the opposite direction of the field. However, due to collisions with other particles and imperfections in the material, the charged particles experience frequent collisions that impede their motion. As a result, they do not achieve a constant, uniform velocity but rather exhibit a random motion with an overall average velocity in the direction opposite to the electric field. This average velocity is known as the drift velocity.

The drift velocity is typically much lower than the speed at which the charged particles would move in the absence of collisions and electric fields. It is influenced by factors such as the strength of the electric field, the density of charge carriers in the material, and the characteristics of the material itself, including its conductivity and mobility of charge carriers.

Understanding the concept of drift velocity is essential in the study of electrical conductivity, current flow in conductors, and the behavior of electrons in electronic devices and circuits.

Also Read: Hall Effect in Semiconductor

Mobility of Charge Carriers

Mobility refers to the ability of charged particles, such as electrons or ions, to move through a medium in response to an applied electric field. It is a fundamental property of particles in materials and is typically represented by the symbol “μ.”

The mobility of charged particles is influenced by several factors, including the nature of the particles themselves, the characteristics of the material in which they are moving, and the presence of external electric or magnetic fields. In general, mobility represents the ease with which charged particles can move in a given environment.

High mobility values indicate that the charged particles can move relatively easily through the material, while low mobility values suggest that their movement is more restricted. Mobility is an important parameter in the study of electrical conductivity, as it determines the ability of charge carriers to contribute to current flow in a material.


Relation Between Current and Drift Velocity and Mobility

The Current density J can also be defined as follows:

If n is the number of charge carriers per unit volume (also called carrier density) in a conductor of length l with cross-sectional area A, then the current flow through the conductor is given by,

\mathbf{I = \frac{Total\; Charge}{Time}}

\mathbf{I = \frac{neAl}{t} = n e A v_d} ….. Eq.(1)

Where v_d=\frac{l}{t} is called the drift velocity. It is the average velocity gained by the charge carriers in the presence of an electric field.

But, we know \mathbf{J = \frac{I}{A}}

using the Eq.(1), J can be written as

\mathbf{J = \frac{neAv_d}{A} = n e v_d}

\boxed{\mathbf{J = nev_d}} ….. Eq.(2)

Here Eq.(2), \mathbf{J = nev_d} is the relation between the current density and Drift Velocity.

But J is also equal to \sigma E. Therefore Eq.(2) becomes,

\mathbf{\sigma E = nev_d}

or, \mathbf{\sigma = ne\frac{v_d}{E}}

Hence, \boxed{\mathbf{\sigma = ne\mu}}

Where \frac{v_d}{E}=\mu is called the mobility of charge carriers. it is defined as the drift velocity per unit electric field.

SI unit of Mobility of charge carriers is \mathbf{m^2V^{-1}s^{-1}}

In the case of metals, this µ is the mobility of electrons. Hence, \sigma = ne\mu. This expression gives the relation between conductivity and mobility.

Thus, the electrical conductivity of materials can be controlled by controlling the number of charge carriers per unit volume or by controlling the mobility of charge carriers.

Mobility is important in metals. But in semiconductors and insulators, the number of charge carriers ‘n’ is important.

In semiconductors, since electrons and holes both are involved in conduction, the expression for conductivity becomes

\boxed{\mathbf{\sigma = n_ee\mu_e + n_he\mu_h}}


  • ne is the density of electrons
  • nh is the density of holes
  • µe is the mobility of electrons and
  • µh is the mobility of holes.

Frequently Asked Questions (FAQs)

is current density a vector quantity?

Current density is a vector quantity having both a direction and a scalar magnitude.

what is the si unit of current density?

SI unit of current density must be Ampere/meter2. In SI base units, the electric current density is measured in amperes per square meter.

what do you mean by drift velocity?

Drift velocity can be defined as The average velocity attained by charged particles, (eg. electrons) in a material due to an electric field. The SI unit of drift velocity is m/s.

what is the effect of temperature on drift velocity?

Due to the rise in temperature, relaxation time decreases, hence drift velocity decreases.

SI unit of mobility of charge carriers.

SI unit of Mobility of charge carriers is \mathbf{m^2V^{-1}s^{-1}}.

The mobility of charge carriers increases with

The mobility of charge carriers increases with an increase in the average collision time.

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Hello friends, my name is Trupal Bhavsar, I am the Writer and Founder of this blog. I am Electronics Engineer(2014 pass out), Currently working as Junior Telecom Officer(B.S.N.L.) also I do Project Development, PCB designing and Teaching of Electronics Subjects.

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