📘 Chapter 34: Mobility and its Relation with Electric Current (Class XII)
🔷 1. Introduction
In the previous chapter, we learned that free electrons acquire a small average velocity called drift velocity when an electric field is applied. However, not all materials allow electrons to drift equally easily. Some materials permit electrons to move more freely than others.
The property that measures how easily charge carriers move inside a material under the influence of an electric field is called Mobility.
🔷 2. What is Mobility?
Ethan: Professor, what do we mean by mobility?
Professor: Mobility tells us how quickly a charge carrier moves through a material when an electric field of unit strength is applied.
Academic Definition
Mobility is defined as the drift velocity acquired per unit electric field applied to a conductor.
🔷 3. Mathematical Expression
Ethan: Professor, how is mobility represented mathematically?
Professor: Mobility is represented by the Greek letter μ (Mu).
μ = vd / E
Where,
- μ = Mobility
- vd = Drift Velocity
- E = Electric Field
🔷 4. SI Unit of Mobility
Ethan: Professor, what is the SI unit of mobility?
Professor: Since mobility is drift velocity divided by electric field, its SI unit becomes:
m² V⁻¹ s⁻¹
🖼️ Charge Carrier Motion
The movement of electrons through a conducting material depends upon how freely they can respond to the applied electric field. Materials having high mobility allow charge carriers to move more easily, resulting in better electrical conduction.
🔷 5. Relation Between Mobility and Drift Velocity
Ethan: Professor, what is the relationship between mobility and drift velocity?
Professor: Drift velocity is directly proportional to mobility. If mobility increases, electrons drift faster under the same electric field.
vd = μE
This equation shows that for a constant electric field, larger mobility produces a larger drift velocity.
🔷 6. Relation Between Mobility and Relaxation Time
Ethan: Professor, how is mobility related to relaxation time?
Professor: Combining the drift velocity equation with the definition of mobility gives:
μ = eτ / m
Where,
- e = Charge of electron
- τ = Relaxation time
- m = Mass of electron
Hence, mobility increases if the relaxation time increases and decreases if the electron mass increases.
🔷 7. Relation Between Mobility and Electric Current
Ethan: Professor, how is mobility connected with electric current?
Professor: Electric current depends upon the drift velocity of charge carriers. Since mobility determines the drift velocity, it also directly affects electric current.
We know,
I = nAe vd
Substituting vd = μE gives,
I = nAeμE
This equation shows that if mobility increases while all other quantities remain constant, the electric current also increases.
🔷 8. Factors Affecting Mobility
| Factor | Effect |
|---|---|
| Temperature | Higher temperature usually decreases mobility in metals. |
| Impurities | More impurities reduce mobility. |
| Relaxation Time | Longer relaxation time increases mobility. |
| Electron Mass | Greater mass reduces mobility. |
📦 9. Important Results (Must Remember)
- Mobility measures how easily charge carriers move.
- Symbol of mobility is μ.
- SI unit is m² V⁻¹ s⁻¹.
- μ = vd/E
- vd = μE
- μ = eτ/m
- Electric current increases with mobility.
- Higher mobility means better electrical conduction.
🧠 10. Conceptual Questions
🔹 Q1
Ethan: What is mobility?
Professor: Mobility is the drift velocity produced per unit electric field.
🔹 Q2
Ethan: What is the SI unit of mobility?
Professor: m² V⁻¹ s⁻¹.
🔹 Q3
Ethan: How does mobility affect current?
Professor: Greater mobility increases drift velocity and therefore increases electric current.
🔹 Q4
Ethan: Does mobility depend upon temperature?
Professor: Yes. In metals, mobility generally decreases as temperature increases.
🔹 Q5
Ethan: Why are good conductors highly conductive?
Professor: Because their charge carriers have comparatively higher mobility.
🔷 11. Applications of Mobility
- Semiconductor device design.
- Electronic circuit analysis.
- Solar cells.
- Integrated circuits.
- Transistors and microprocessors.
- Electrical conductivity measurement.
🔷 12. Summary
Mobility is a measure of how easily charge carriers move through a material under the influence of an electric field. It is defined as the ratio of drift velocity to electric field and plays a crucial role in determining the electric current through a conductor. Materials with higher mobility allow electrons to move more freely and therefore conduct electricity more efficiently.
✨ End of Chapter 34: Mobility and its Relation with Electric Current ✨
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