1. Why Electrons Move Slowly in a Conductor
Even in a conductor, electrons are always moving randomly. Their motion is fast but completely disordered, so there is no net current. When a potential difference is applied, an electric field is set up inside the conductor. This field pushes electrons in one direction, giving them a small net velocity.
This small average motion in a definite direction is called drift, and the velocity associated with it is called drift velocity.
1.1. Definition of Drift Velocity
Drift velocity is the average velocity with which free electrons move through a conductor under the influence of an electric field.
It is small because electrons collide repeatedly with atoms while moving.
2. Expression for Drift Velocity
The drift velocity depends on current, number of electrons per unit volume and the area of the conductor.
2.1. Formula
\( v_d = \dfrac{I}{n A e} \)
Where:
- I = current
- n = number of free electrons per unit volume
- A = area of cross-section
- e = electronic charge
2.1.1. Meaning of the Formula
If the same current flows through a thin wire, the drift velocity is higher because fewer electrons have to carry the current. In a thick wire, more electrons participate, so each moves more slowly.
3. Relation Between Electric Field and Drift Velocity
When an electric field is applied, electrons gain acceleration but constantly collide with atoms, losing energy. Due to continuous collisions, electrons do not keep accelerating. Instead, they settle into a constant average velocity—this is the drift velocity.
3.1. Proportional Relation
\( v_d \propto E \)
This means the stronger the electric field, the higher the drift velocity.
4. Understanding Mobility
Mobility tells us how easily electrons can move through a material when an electric field is applied. It gives the drift velocity produced per unit electric field.
4.1. Definition of Mobility
Mobility is defined as the drift velocity per unit electric field.
\( \mu = \dfrac{v_d}{E} \)
4.1.1. Interpretation
A material with higher mobility allows electrons to move more easily. Semiconductors often have higher mobility than many metals.
5. Relation Between Mobility and Current
Mobility plays an important role in determining the conductivity of a material. If electrons move easily (high mobility), the material conducts better.
The drift velocity can also be written using mobility:
\( v_d = \mu E \)
5.1. Linking Back to Current
Higher mobility → higher drift velocity → higher current for the same electric field.
6. Small Example to Visualise Drift
Imagine a crowd of people inside a large hall moving randomly. When the exit door opens and a gentle push is applied, everyone slowly drifts toward the exit. Their random motion continues, but there is now a net movement in one direction. This slow net movement is similar to drift velocity.