Topic 11.211 min read
Drift Velocity
Drift velocity is the average velocity acquired by charge carriers in an applied electric field.
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Free electrons inside a metal move rapidly in random directions. With no electric field, their random motions cancel and there is no net charge flow.
When a potential difference creates an electric field, the electrons gain a small average motion opposite to the field. This average motion is called drift velocity.
- I
- current (A)
- n
- charge carriers per unit volume (m⁻³)
- q
- magnitude of charge per carrier (C)
- A
- cross-sectional area (m²)
- v_d
- drift-speed magnitude (m·s⁻¹)
A larger carrier density, charge, wire area or drift speed produces a larger current.
Recommended for Class 11
Drift velocity is the average velocity acquired by mobile charge carriers in a conductor when an electric field is applied. It is superimposed on their much faster random thermal motion.
Random motion without an electric field
Conduction electrons continually move and collide with the vibrating ions of the metal lattice. With no applied electric field, every direction is equally likely, so the average velocity of a very large number of electrons is zero.
Random electron motion therefore does not produce a sustained current through a cross-section.
Effect of an applied electric field
An electron of charge −e experiences force opposite to the applied electric field.
- m_e
- electron mass (kg)
Between collisions an electron accelerates, but collisions repeatedly change its motion. The combined effect is a small average drift velocity opposite to E⃗.
Direction of drift and current
| Quantity | Direction in a metal |
|---|---|
| Electric field E⃗ | Direction a positive test charge would accelerate |
| Electron drift velocity v⃗d | Opposite to E⃗ |
| Conventional current I | Along E⃗ and opposite to electron drift |
For a general carrier with signed charge q, current direction follows qv⃗d. Negative q reverses the direction associated with the carrier velocity.
Derivation of the current relation
Consider a conductor of cross-sectional area A containing n mobile charge carriers per unit volume. In time Δt, carriers with drift speed vd travel the distance:
The carriers that cross the section occupy a cylinder of volume:
The number of carriers in this volume is nΔV, so the magnitude of charge crossing the section is:
Dividing by Δt gives the magnitude of current:
When to use: Use magnitudes when finding drift speed.
What changes the drift speed
| Change while I is fixed | Effect on vd=InqA |
|---|---|
| Area A increases | Drift speed decreases |
| Carrier density n increases | Drift speed decreases |
| Charge magnitude q increases | Drift speed decreases |
For the same material, n and q are fixed. A thinner wire must therefore have a greater drift speed than a thicker wire carrying the same current.
Current density
Current density is current per unit area. For uniformly distributed current its magnitude is:
- J
- current-density magnitude (A·m⁻²)
In vector form, the signed carrier charge determines the relationship between current density and drift velocity.
Why a lamp turns on quickly
Individual electrons have a small drift speed and do not travel from the switch to the lamp instantly. Closing the switch establishes an electric field around the complete circuit very rapidly, so electrons already present throughout the wire begin drifting almost together.
Worked example
A wire carries 2.0 A. Its area is 1.0×10⁻⁶ m² and it contains 8.5×10²⁸ free electrons per cubic metre. Find the drift speed using e=1.60×10⁻¹⁹ C.
Exam-ready method
- Define drift velocity as an average velocity caused by an applied field.
- Explain why random thermal motion alone gives zero net current.
- State that electron drift is opposite to E⃗ and conventional current.
- Derive ΔV=AvdΔt, ΔQ=nqAvdΔt and I=nqAvd.
- Use SI units and the magnitude of electron charge in calculations.
- Do not confuse electron drift speed with signal propagation speed.
Exam Focus
Exam Focus
Important points
- Definition of drift velocity
- Random motion and zero net current
- Direction of electron drift
- Derivation of I=nqAvd
- Current density
- Slow drift and rapid circuit response
Important formulas
- I=nqAvd
- vd=InqA
- J=IA=nqvd
Common exam traps
- Use area in m².
- Use charge magnitude for drift-speed calculations.
Long question structure
Random motion → applied field → drift direction → swept volume → transferred charge → current relation → implications
Common Mistakes
Common Mistakes
- Mistake
Confusing drift velocity with random thermal velocity.
- Mistake
Drawing electron drift in the conventional-current direction.
- Mistake
Leaving area in mm² instead of converting to m².
- Mistake
Using a signed electron charge when only drift-speed magnitude is requested.
- Mistake
Claiming electrons cross the whole circuit almost instantly.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Without a field, random carrier motion averages to zero and produces no net current.
Electrons drift opposite to the electric field and conventional current.
In time Δt, carriers sweep through volume AvdΔt.
The current magnitude is I=nqAvd.
Drift velocity is the average velocity acquired by charge carriers in an applied electric field.
I=nqAvd, vd=InqA, J=nqvd
- Definition
- Drift velocity is the average velocity acquired by charge carriers in an applied electric field.
- Formula
- I=nqAvd, vd=InqA, J=nqvd
- Example
- For the sample metal wire, vd≈1.47×10⁻⁴ m·s⁻¹.
- Critical warning
- Electron drift is opposite to conventional current in a metal.
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Exam Practice
Definition
Q1. Define drift velocity.
Derivation
Q2. Derive I=nqAvd.
Concept
Q3. Why does random electron motion not produce current?
Reasoning
Q4. Why does a lamp glow quickly although electron drift is slow?
Numerical
Q5. Find vd for I=2.0 A, n=8.5×10²⁸ m⁻³, A=1.0×10⁻⁶ m² and e=1.60×10⁻¹⁹ C.