The chapter's most reliable one-mark question, and the place where direction errors are most expensive. Electrons drift one way, current points the other, and NEET knows exactly how often that gets mixed up.
NCERT §3.5, §3.5.1 · fully in syllabus · high frequency
Part 1 · The idea, told simply
Here is a puzzle. Switch on a light and it comes on instantly. Yet the electrons inside the wire are crawling along at about one millimetre per second — slower than a snail. How can both be true?
Story track
Imagine a long pipe already completely full of marbles, end to end, with no gaps. Push one marble in at your end. A marble pops out at the far end immediately — not because your marble travelled the length of the pipe, but because the whole line shuffled forward at once.
A wire is exactly like that pipe. It is already stuffed with free electrons everywhere. When you close the switch, an electric field is set up all along the wire almost instantly — at nearly the speed of light — and every electron everywhere starts shuffling at the same moment. The bulb's own electrons start moving straight away. Nobody had to travel from the switch to the bulb.
Why the crawl is so slow: electrons are terrible at walking in a straight line
Story track
Even with no battery connected, electrons in a metal are not sitting still. They are racing about at hundreds of metres per second because of heat — but in completely random directions. For every electron heading left there is one heading right, so the average comes to exactly zero and there is no current.
Now switch on a battery. Each electron gets a gentle push in one direction. But before it can build up any real speed it smashes into a heavy metal ion and bounces off in a totally random direction, forgetting everything about the push. Then it gets pushed again, and crashes again. Millions of millions of times a second.
The result is a drunken stagger: enormous random speed, plus a tiny consistent lean in one direction. That tiny lean is the drift velocity, and it is what carries the current.
Animation 1 · Random motion, then the lean
Switch the field on and off. The wild zigzag barely changes — but a slow net drift appears.
The direction rule — read this twice, it is the most examined trap in the topic
An electron carries a negative charge. The force on it is F = (−e)E, which points opposite to the field. So:
Electric field E → points from + terminal towards −
Force on an electron ← opposite to E
Drift velocity v_d ← opposite to E
Electrons move ← towards INCREASING potential (towards the + terminal)
Conventional current I → along E
Current density j → along E (j = σE, always parallel to E)
Four of those six arrows point one way and two point the other. Any question that asks "in which direction do the electrons move" or "is j parallel or antiparallel to v_d" is testing exactly this. For electrons, j and v_d are antiparallel — because j = nqv_d and q is negative.
Animation 2 · The direction compass
Flip the battery. Every arrow updates together. Drill this until it is automatic.
Current density: current spread over area
Current tells you how much charge passes per second. Current density tells you how crowded that flow is — how much current is squeezed through each square metre.
j = I/A unit: A m⁻² j = nev_d j = σE
Squeeze the same current through a thinner wire and j goes up, and so does v_d — the electrons must hurry to get the same number through a smaller doorway. This is the source of most numericals in this topic.
Animation 3 · Same current, thinner wire, faster drift
Narrow the wire at fixed current. The dots have to move quicker to keep the count per second the same.
Mobility: how responsive a carrier is
Story track
Two runners are pushed with the same force. One is nimble and speeds up easily; the other is sluggish. Mobility is that nimbleness — how much drift speed you get per unit of field.
μ = |v_d| / E unit: m² V⁻¹ s⁻¹
NCERT adds one detail worth remembering: mobility is always taken as positive, for electrons and for positive ions alike, because it is defined using the magnitude of the drift velocity. And the SI unit is 10⁴ times the practical unit cm²/Vs.
Part 2 · The physics underneath
Maths track · deriving the drift velocity
Follow NCERT §3.5. With no field, the average of all the electron velocities is zero:
(1/N) Σ vᵢ = 0
Switch on the field E. Each electron is accelerated by a = −eE/m. Take the i-th electron, which last collided a time tᵢ ago. Its velocity now is its post-collision velocity plus whatever the field has added since:
Vᵢ = vᵢ + (−eE/m) tᵢ
Average over all N electrons. The average of the vᵢ is zero (collisions randomise direction completely). The average of tᵢ is the relaxation time τ, the mean time between successive collisions. So
v_d = 0 − (eE/m)τ = −(eE/m)τ
The minus sign is the direction rule in algebra: v_d is opposite to E. NCERT calls this result surprising, and it is — the electrons are constantly being accelerated, yet the average velocity does not grow with time. Each collision wipes the slate clean, so the drift settles at a constant value.
Maths track · from drift to current, and to Ohm's law
Take a cross-section of area A. In time Δt, every electron within a distance |v_d|Δt of the section will cross it. That slab has volume A|v_d|Δt and contains nA|v_d|Δt electrons, each carrying charge e. So the charge crossing in time Δt is
IΔt = neA|v_d|Δt ⇒ I = neAv_d
Divide by A to get the current density, then substitute the drift velocity:
j = nev_d = ne · (eEτ/m) = (ne²τ/m) E
Compare with j = σE and the conductivity falls out:
σ = ne²τ/m ρ = 1/σ = m/(ne²τ)
This is the punchline of the whole section: a very simple picture of electrons crashing about reproduces Ohm's law exactly. NCERT is careful to flag the assumptions — that n and τ are constants independent of E. When that fails, Ohm's law fails, which is Topic 11.
The three speeds, and why they are so wildly different
NCERT Example 3.1 works out all three for copper. Learning the orders of magnitude is worth a mark on its own:
Drift speed of electrons ≈ 10⁻³ m/s (about 1 mm per second)
Random thermal speed ≈ 10² m/s (about 10⁵ times larger)
Speed of the field / signal ≈ 3×10⁸ m/s (about 10¹¹ times larger)
Animation 4 · Three speeds, on a scale that fits
A linear bar chart is useless here — the numbers differ by eleven powers of ten. This one is logarithmic.
Each step across the axis is a factor of ten
Animation 5 · The sawtooth — why drift is an average, not a speed
Velocity builds after each collision and is wiped out by the next. The dashed line is the average: that is v_d.
Trap · the six that cost marks
Saying electrons move along E. They move opposite to E, towards higher potential.
Saying j is antiparallel to E. j is always along E. It is antiparallel to the electron drift.
Forgetting that A in I = neAv_d is the cross-sectional area, so halving the radius divides A by four, not two.
Confusing drift speed with thermal speed. Only the drift carries current; the thermal motion averages to zero.
Thinking current takes time to reach the bulb. The field arrives at the speed of light; local drift starts everywhere at once.
Giving mobility a negative sign for electrons. Mobility is defined with |v_d| and is always positive.
Part 3 · Formula sheet
Drift velocity
v_d = eEτ/m (magnitude; direction opposite to E)
v_d = eVτ/(ml) using E = V/l
v_d = I/(neA) the workhorse form
a = eE/m acceleration between collisions
τ = relaxation time = mean time between collisions
Current and current density
I = neAv_d
j = I/A = nev_d unit A m⁻²
j = σE (vector form: j is parallel to E)
I = j · ΔS (scalar product — current is a SCALAR)
Electrons crossing per second = I/e
e = 1.6 × 10⁻¹⁹ C m = 9.1 × 10⁻³¹ kg
n (copper) ≈ 8.5 × 10²⁸ m⁻³
τ (metals) ≈ 10⁻¹⁴ s
v_d ≈ 10⁻³ m/s · thermal ≈ 10² m/s · signal ≈ 3×10⁸ m/s
n = (N_A/atomic mass in g) × density in g/m³ × (electrons per atom)
How things respond to a change
Same I, area halved → v_d doubles (v_d ∝ 1/A)
Same I, radius doubled → v_d becomes 1/4 (A ∝ r²)
Same V, length doubled → E halves → v_d halves
Temperature raised → τ falls → v_d falls, ρ rises
V doubled at fixed wire → E, v_d, j and I all double
Dimensions
Current density j : [L⁻²A]
Drift speed v_d : [LT⁻¹]
Relaxation time τ : [T]
Mobility μ : [M⁻¹L⁰T²A]
Conductivity σ : [M⁻¹L⁻³T³A²]
Part 4 · 50 NEET-pattern questions with full solutions
Includes 4 graph-based questions, 3 assertion–reason questions, and 8 questions tagged Direction — a deliberately heavy dose, because direction reasoning is where this topic bleeds marks. Year labels are not attached: the patterns are authentic, the wording is mine.