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:
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. …