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Ask a class how fast electrons move in a wire and you get guesses near the speed of light. The real answer is less than a millimetre per second. Understanding why both "slow electrons" and "instant current" are true is the key to this chapter, and it gives you the formulas JEE and NEET test every year. This post builds the model, works one problem from start to finish and lists the usual traps.
What is drift velocity?
NCERT's Current Electricity chapter builds the picture. Free electrons in a metal move randomly at high speeds, colliding with ions. With no field, their average velocity is zero. Apply a field E and each electron accelerates between collisions. Averaged over all electrons, the result is a steady drift velocity
v_d = −(eE/m)τ
where τ, the relaxation time, is the average time between collisions. The minus sign says electrons drift opposite to the field.
Counting the electrons crossing an area A in time Δt gives
I = neAv_d and current density j = I/A = nev_d
where n is the number of free electrons per cubic metre. Drift velocity, mobility and resistivity are in the JEE (Main) 2026 and NEET (UG) 2026 syllabi and the CBSE 2026-27 curriculum. Check the current year's syllabus.
How slow is drift, really?
NCERT's Example 3.1 takes a copper wire of area 1.0 × 10⁻⁷ m² carrying 1.5 A. Assuming one free electron per copper atom gives n = 8.5 × 10²⁸ m⁻³, and the drift speed comes out at 1.1 mm/s. NCERT compares this with thermal speeds of copper atoms (about 2 × 10² m/s) and with the speed at which the electric field travels along the wire (3.0 × 10⁸ m/s).
So why does a bulb light at once? Because, as NCERT's Example 3.2 explains, the field is set up throughout the circuit almost instantly, and electrons everywhere in the wire start drifting together. Current does not wait for electrons to travel from the switch.
A full worked example
Example. A copper wire of diameter 1.0 mm and length 10 m carries 2.0 A. Take n = 8.5 × 10²⁸ m⁻³, e = 1.6 × 10⁻¹⁹ C, electron mass 9.11 × 10⁻³¹ kg and resistivity ρ = 1.72 × 10⁻⁸ Ω m (from OpenStax College Physics, Table 20.1).
Area: r = 0.50 mm, so A = π(0.50 × 10⁻³)² = 7.85 × 10⁻⁷ m².
Current density: j = 2.0/7.85 × 10⁻⁷ = 2.55 × 10⁶ A/m².
Drift speed: v_d = j/(ne) = 2.55 × 10⁶/(8.5 × 10²⁸ × 1.6 × 10⁻¹⁹) = 2.55 × 10⁶/1.36 × 10¹⁰ = 1.9 × 10⁻⁴ m/s. An electron takes about 5300 s, nearly 90 minutes, to drift one metre.
Resistance: R = ρL/A = 1.72 × 10⁻⁸ × 10/7.85 × 10⁻⁷ = 0.22 Ω. The voltage across the wire is IR ≈ 0.44 V.
Field inside: E = ρj = 1.72 × 10⁻⁸ × 2.55 × 10⁶ = 0.044 V/m. Check: 0.44 V over 10 m gives the same.
Relaxation time: ρ = m/(ne²τ) gives τ = m/(ne²ρ) = 9.11 × 10⁻³¹/(8.5 × 10²⁸ × 2.56 × 10⁻³⁸ × 1.72 × 10⁻⁸) ≈ 2.4 × 10⁻¹⁴ s.
Mobility: μ = v_d/E = 1.9 × 10⁻⁴/0.044 ≈ 4.3 × 10⁻³ m²/(V s). Check with μ = eτ/m: same value.
Does a thinner wire mean faster electrons?
It depends on what is held fixed. This is the most tested idea in the chapter.
Same current, thinner wire: v_d = I/(neA), so halving A doubles v_d.
Same voltage across the same length: E = V/L is fixed, so v_d = eEτ/m does not depend on area at all. The thinner wire just carries less current.
Stretching a wire to twice its length: volume is constant, so area halves. R = ρL/A becomes four times larger. Resistivity does not change; it is a property of the material.
NCERT also notes that resistivity of metals rises with temperature, ρ_T = ρ₀[1 + α(T − T₀)], while alloys such as nichrome change very little.
Common mistakes
Diameter for radius. A = πr², with r half the diameter.
Mixing resistivity and resistance. ρ is in Ω m and depends on material and temperature; R depends on shape too.
Thinking current is used up. The same current flows in and out of every series element. Faulty current models are common: in Engelhardt and Beichner (2004), the idea that a battery is a constant source of current was the one students used most often in interviews.
Forgetting the sign. Electrons drift opposite to E; conventional current is along E.
For what happens to the energy, see our post on the heating effect of current.
Practice routine
Rework NCERT Example 3.1 without looking, then change the current to 3.0 A and predict the new drift speed first.
Solve three "what is held fixed" questions: same I, same V, stretched wire.
For one wire, compute j, v_d, E, τ and μ, and run both checks from the callout.
When the steps blur together, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can review mobility and resistivity one at a time.
Tonight, do question 2 of the routine; it takes ten minutes and covers the idea examiners test most.
