Drift VelocityJEE Main

Concept

Electrons in a wire drift astonishingly slowly — often less than a millimetre per second — yet a lamp lights instantly because the electric field travels near light-speed and pushes all electrons at once. Drift velocity is this slow average motion superimposed on rapid random thermal motion.

Key formula

Derivation

In time $dt$ every electron advances $v_d\,dt$, so all electrons within a length $v_d\,dt$ cross a section. Their number is $n A (v_d dt)$ and total charge $nAe\,v_d\,dt$.

Dividing by $dt$ gives $I = nAev_d$. The current density $J = I/A = nev_d$ is the microscopic form of Ohm's law, $\vec J = \sigma \vec E$.

Scenarios to explore

• Drift Velocity — How slowly electrons really move: v_d = I/nAe.

Real-world applications

• Explaining why thin wires heat up (higher $J$ for the same $I$).
• Hall effect measurements of carrier density and sign.
• Designing conductor thickness for safe current ratings.

JEE exam tips

• Typical copper drift speed for a few amps is ~0.1 mm/s — memorise the order of magnitude.
• $v_d = \dfrac{eE\tau}{m}$ links drift to the relaxation time $\tau$ and field $E$.

Common mistakes

• Confusing drift velocity (mm/s) with the signal speed (near $c$).
• Using diameter instead of area, or forgetting the mm²→m² conversion.
• Thinking higher current means faster individual electrons rather than more of them drifting.

Exam traps to avoid

• Drift velocity is independent of the wire's length for a fixed current.
• Current density $J$, not current $I$, is what stays meaningful when area changes.