Electrons in a metal are always moving — but randomly. At room temperature they zip around at roughly 106 m/s, colliding with the lattice ions every few trillionths of a second. Without an electric field this motion cancels out: for every electron heading left another heads right, so the net velocity is zero.
Apply a battery and the field gives every electron a tiny, steady push in one direction. Between collisions the electron accelerates only briefly before smashing into an ion and losing its directed motion. What survives is a very small average velocity along the field — the drift velocity.
Note
The random thermal speed is about 105 m/s, but the drift velocity is only about 10−4 m/s — about a billion times slower. An electron drifts slower than a snail, yet a lamp lights instantly, because the electric field (not the electrons) propagates at nearly the speed of light and starts every electron drifting almost at once.
The precise definition
Drift velocity (vd) is the average velocity acquired by the charge carriers in a conductor under an applied electric field:
vd=meEτ
where:
e = electron charge (1.6×10−19 C)
E = electric field inside the conductor (V/m)
τ = average relaxation time — the mean time between collisions (s)
m = electron mass (9.1×10−31 kg)
vd=meEτ
Linking to current
Drift velocity connects the microscopic motion of electrons to the current an ammeter reads:
I=neAvd
where n is the free-electron number density and A the cross-sectional area. A larger vd means more current, but vd stays tiny because τ is tiny (about 10−14 s in copper).
Tip
For a copper wire carrying 1 A with area 1 mm² and n≈8.5×1028 m−3:
vd=neAI≈(8.5×1028)(1.6×10−19)(10−6)1≈7×10−5m/s
That is about 0.07 mm per second — slower than a garden snail.
Common misconception
Electrons do not race through wires near light speed. The field propagates almost instantly, so all electrons begin drifting together, but each one only crawls. It is like a hose already full of water: open the tap and water leaves the far end at once, though the individual molecules have barely moved. Drift velocity is that slow, directed crawl superimposed on the electrons' frantic random jitter.
Drift velocity of electrons and its link to current via I = neAv_d is a defining topic of the NCERT Class 12 Physics chapter on current electricity, tested through both conceptual and numerical questions in CBSE boards, JEE Main and NEET. Anyone searching "drift velocity formula and derivation class 12 physics" will find this relaxation-time explanation is the standard NCERT-aligned answer.
Why this formula?
Drift Velocity: Why the Formula Holds
Let's build this from first principles — understanding why electrons drift the way they do, not just memorizing the formula.
1. The Core Idea: What is Drift Velocity?
In a conductor, free electrons are constantly moving randomly (thermal motion, speeds ~105 m/s). Without an electric field, their net displacement is zero — they're like a swarm of bees buzzing in all directions.
When we apply an electric field E, it gently nudges each electron in the opposite direction (since electrons are negatively charged). This small, steady net velocity superimposed on the random motion is drift velocity (vd).
Key insight: Drift velocity is not the speed of individual electrons — it's the average velocity of the entire electron cloud.
2. The Derivation: Step by Step
Step 1: Force on a single electron
An electron of charge −e in an electric field E experiences:
F=−eE
The magnitude of acceleration (opposite to E) is:
a=mF=meE
where m is the electron's mass.
Step 2: What happens between collisions?
Electrons don't accelerate forever — they keep colliding with atoms/ions in the metal lattice. Let the average time between collisions be τ (relaxation time). Just after a collision an electron's velocity is essentially random (zero average in the field direction); it then accelerates for time τ before the next collision.
Step 3: Drift velocity
Averaging the field-driven velocity over the relaxation time τ gives the net drift:
vd=meEτ
Here τ is the average time since the last collision, so this expression already averages over electrons at every stage between collisions — it is the standard result used in the NCERT treatment.
3. Connecting to Current: The Big Picture
Drift velocity directly gives us current densityJ:
J=nevd
where n = number of free electrons per unit volume.
Substituting vd=meEτ:
J=mne2τE
Comparing with Ohm's law J=σE, we get:
σ=mne2τ
Why this matters: conductivity depends on:
n — more free electrons → better conductor
τ — fewer collisions → higher conductivity
m — lighter electrons → faster drift
4. Key Takeaways for Exams
Concept
Formula
Why
Drift velocity
vd=meEτ
Acceleration × average time between collisions
Current density
J=nevd
Charge × number density × drift speed
Conductivity
σ=mne2τ
From combining above two
Remember: Drift velocity is tiny — typically 10−4 m/s for copper wires — yet current flows almost instantly because the electric field propagates at near light speed, pushing all electrons simultaneously.
Drift velocity is the actual average speed of the electrons under a given field (m/s); mobility is drift velocity produced per unit field, a fixed material property (m2V−1s−1).
✓Final answer
Drift velocity vd depends on the field applied; mobility μ=vd/E is a field-independent material constant.
Step 1. Drift velocity vd is the actual average net velocity the free electrons acquire when a specific electric field E is applied to a conductor; its SI unit is m/s, and its VALUE depends on how strong the applied field E happens to be.
Step 2. Mobility μ is defined as the magnitude of drift velocity produced per unit applied electric field, μ=vd/E; its SI unit is m2V−1s−1.
Step 3. Crucially, mobility is a fixed property of the MATERIAL (and its temperature) alone -- it does not change if the applied field E is changed, whereas the drift velocity itself changes in direct proportion to E.
Step 4. So two samples of the same material always have the same mobility regardless of what field is applied to each, while their drift velocities would differ if different fields were applied.
✓Final answer
Drift velocity (vd, m/s) is the actual electron speed under a specific field and depends on that field; mobility (μ=vd/E, m2V−1s−1) is a fixed material property, independent of the field strength.
Compare the defining formulas and note which quantity depends on the applied field and which is a fixed material constant.
Treating mobility and drift velocity as the same quantity with different names.
Forgetting that mobility, unlike drift velocity, does not change if the applied field changes.