What is Drift of Electron and How Resistivitity Originated?

In conductive materials such as metals, some electrons can freely move throughout the material. These electrons are also known as free electrons or conduction electrons. When there is no electric field, these electrons move randomly because of the thermal energy. As a result, there is no net flow in any particular direction. 

When electric field is applied across the conductor, a force is exerted on free electrons. Due to this force, electrons accelerate in direction that is opposite to the field. But, these electrons collide with ions or impurities in material, which, in turn, disrupt their motion. Even after the collisions, applied electric field causes net movement of electron in specific movement. This movement consists of the drift of electrons.

After the collisions, electrons slowly move with a net velocity, which is known as the drift velocity. This velocity is lower than random thermal velocities of electrons. NEET exam and JEE exam students must be well aware of the mathematical expression of drift velocity, which is as mentioned below:

$$v_d = \mu E$$

Here:

• $v_d$ is the drift velocity
• μ indicates the electron mobility
• E is the strength of the electric field

 

Resistivity originates because there are many obstacles that electrons encounter when they are moving through a conductor. Whenever an electric field is applied to a conductor, free electrons start drifting in response to the field.

In crystalline materials such as metals, atoms are arranged in a regular lattice structure. All these atoms vibrate around their equilibrium positions, and the amplitude of the vibrations also increases with temperature. As the temperature increases, the probability of electrons colliding with vibrating atoms also increases. This is the origin of resistivity.

The electric current (I) in a conductor is directly proportional to the drift velocity. Electric current is related to drift velocity through the following formula:

Here:

$I=nAe{v}_d$

• I is the current
• n is the number of charge carriers per unit volume
• A is the cross-sectional area of conductor
• e is the charge of one electron ( $1.6\times {10}^{-19}C$ )
• $v_d$ is the drift velocity(m/s)

IIT JAM entrance exam and IISER exam will ask questions related to this relation, which makes it an important section. Let us now understand how drift velocity and resistivity are related:

E=ρJ or V=IR

Here:

• E is the electric field
• J is the current density (I/A)
• ρ is the resistivity

By combining the following formula,

$v_d=\mu E\text{and}E=\frac{\rho I}{Ane{v}_d}$

We get that drift velocity can also be written as:

$v_d=\frac{I\rho }{neA}$

As a conclusion, it can be said that:

• Current is directly proportional to drift velocity, which means a higher current will lead to a higher drift velocity.
• Resistivity is also directly proportional to drift velocity. A higher resistivity will lead to higher drift velocity, but the electric current must be fixed.
• Drift velocity is very small () even for larger currents since there are numerous electrons, but they are slow.