Drift Velocity Derivation: Overview, Questions, Preparation

Electrons are subatomic particles and have no direction; they move randomly in different directions. They slowly start or drift to move in a single direction when electrons are put through to an electric field. These electrons drift at a certain velocity, and the net velocity is called drift velocity.

The SI unit of the drift velocity is denoted as m/s. It can be written as m2 / (V.s)

The electrons that possess above zero temperature move freely like metals at a random velocity. The electrons move to the potential when applied on it through the conductor; in this process, they lose kinetic energy because they collide with atoms on the way and bounce back. The electrons will bounce back again and again, and these collisions occur as well. Acceleration occurs in the same direction, and the net velocity of the electrons will also move in the same direction.

The formula used to calculate the drift velocity is:

Here, I is referred to the flowing current in the conductor, the unit of I is ampere

n is referred to the electrons present

A is the area of the conductor, and the unit of A is m2

v is the drift velocity

Q is referred to as the charge of an electron and is measured in Coulombs. 

The derivation of the drift velocity is as below:

F = −μE a = F/m = −μE / m u = v +at

here, v = 0,

t = T, which is the relaxation time required by the electron to get back to the starting equilibrium value.

U = at (acts as a substitution for u and v)

The final equation of the drift velocity can be shown above.

It shows that the drift velocity increases with the increase in temperature in a metallic conductor. On the other hand, drift velocity decreases with a decrease in temperature in the metallic conductor.

The chapter 'Introduction to Motion' holds a weightage of 6 marks. It includes 3 questions in total. These 3 questions consist of one objective type question of 1 mark, one very short question of 2 marks, and one short question of 3 marks bringing a total up to 6 marks.

Example 1) State the SI unit of Drift velocity.

Answer – The SI unit of Drift velocity is m/s which can be written as m2 / (V.s)

Example 2) Illustrate the formula of Drift Velocity.

Answer – The formula of Drift velocity is I = nAvQ

Example 3) state the number of electrons present in copper.

Answer – The number of electrons present in copper is 8.5 x 1028 per m3

1) What is the meaning of drift velocity?

2) What is the net velocity of the electrons?

3) What is the mobility of an electron?

4) What is the meaning of current density?

5) What is the formula of current density?