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.
Key equation
\langlev\rangle=0\qquad(E=0)
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.
Key equation
F=-eE
Key equation
a=-eEme
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:
Key equation
Δ x=vdΔ t
The carriers that cross the section occupy a cylinder of volume:
Key equation
Δ V=AΔ x=AvdΔ t
The number of carriers in this volume is nΔV, so the magnitude of charge crossing the section is:
Key equation
Δ Q=nqAvdΔ t
Dividing by Δt gives the magnitude of current:
Key equation
I=Δ QΔ t=nqAvd
Key equation
vd=InqA
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:
Key equation
J=IA=nqvd
J
current-density magnitude (A·m⁻²)
In vector form, the signed carrier charge determines the relationship between current density and drift velocity.
Key equation
J=nqvd
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.
Key equation
vd=IneA
Key equation
vd=2.0(8.5×1028)(1.60×10-19)(1.0×10-6)
Key equation
vd≈1.47×10-4\ m\,s^{-1}
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.
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Exam preparation
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
Common mistakes
Confusing drift velocity with random thermal velocity.
Drawing electron drift in the conventional-current direction.
Leaving area in mm² instead of converting to m².
Using a signed electron charge when only drift-speed magnitude is requested.
Claiming electrons cross the whole circuit almost instantly.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Drift Velocity
Sticky Notes — Quick Revision
1.
Key Point 1
Drift velocity is the average velocity acquired by charge carriers in an applied electric field.
2.
Key Point 2
Electrons drift opposite to the electric field and conventional current.
3.
Key Point 3
The current magnitude is I=nqAvd.
4.
Key Point 4
A circuit responds quickly even though individual electron drift is slow.
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8 concept questions
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Explanation after each answer
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.
