Electric current & drift speed

Until now charge sat still. Now it flows — and "current" is just how much flows past a point each second.

Source: Serway & Jewett, Physics for Scientists and Engineers, 7th ed., §27.1.

Before you start

What you need first

Topic 1 — conductors have free electrons that can move.
Charge in coulombs; the elementary charge $e = 1.60\times10^{-19}$ C.

What you'll be able to do

Use $I = Q/t$ and the ampere.
Find the charge delivered, $Q = It$, and count electrons.
Relate current to drift speed: $I = nqv_d A$.
State the direction of conventional current.

The idea

What is electric current?

Current $I$ is how much charge flows past a point each second — like counting how much water flows past you in a river each second.

Water-pipe picture: current is the amount of water flowing per second. It is measured in amperes (A): one ampere is one coulomb of charge every second.

Current — the formula

$$ I = \frac{Q}{t} \qquad\Longleftrightarrow\qquad Q = It $$

where:
Symbol	Meaning	SI unit
I	current	A = C/s
Q	charge that flows past the point	C
t	time it takes	s

📐 Worked example 1

Current and charge delivered

(a) $Q = 60$ C flows past a point in $t = 30$ s — find the current. (b) A current $I = 0.50$ A flows for $t = 120$ s — find the charge delivered.

1Current from $I = Q/t$:

$$ I = \frac{60}{30} = 2.0\ \text{A} $$

2Charge from $Q = It$:

$$ Q = (0.50)(120) = 60\ \text{C} $$

The microscopic picture

What the charges actually do: drift speed

Inside a wire, countless free charges jiggle randomly but drift slowly along when a field is applied. The current depends on how many carriers there are, their charge, how fast they drift, and the wire's thickness:

$$ I = nqv_d A $$

Positive charge carriers drifting along a wire in the current direction

Charge carriers drift slowly along the wire; the arrow is the conventional current direction.

where:
Symbol	Meaning	SI unit
n	number of charge carriers per unit volume	1/m³
q	charge on each carrier ($e$ for electrons)	C
v_d	drift speed — the slow net crawl along the wire	m/s
A	cross-section area of the wire	m²

Direction: conventional current points the way a $+$ charge would move — from $+$ to $-$ through the circuit. In a metal the actual carriers are electrons drifting the opposite way. The drift is astonishingly slow (well under a millimetre per second), even though the light comes on instantly.

📐 Worked example 2

How slowly do electrons drift?

A copper wire of cross-section $A = 1.0\times10^{-6}$ m² carries $I = 2.0$ A. Copper has $n = 8.5\times10^{28}$ electrons/m³ ($q = e = 1.60\times10^{-19}$ C). Find the drift speed.

1Rearrange $I = nqv_dA$ for $v_d$:

$$ v_d = \frac{I}{nqA} = \frac{2.0}{(8.5\times10^{28})(1.60\times10^{-19})(1.0\times10^{-6})} $$

2Work it out:

$$ v_d \approx 1.5\times10^{-4}\ \text{m/s} \;(\approx 0.15\ \text{mm/s}) $$

The electrons crawl, yet the current — the whole crowd shifting at once — starts the instant you flip the switch.

✏️ Try it yourself

A wire carries a steady current of $I = 3.0$ A.

(a) How much charge flows past in one minute?
(b) How many electrons is that? ($e = 1.60\times10^{-19}$ C)

(a) $Q = It = (3.0)(60) = 180\ \text{C}.$ (b) $N = \dfrac{Q}{e} = \dfrac{180}{1.60\times10^{-19}} \approx 1.1\times10^{21}$ electrons.

Common mistakes

Mistake	Fix
Thinking electrons race through the wire at light speed.	The drift is very slow; it's the field (the "push") that travels almost instantly.
Using minutes or hours for $t$.	Convert time to seconds first ($I$ is C per second).
Confusing conventional current with electron flow.	Conventional current is $+$ to $-$; electrons move the opposite way.
Forgetting current is charge per second.	$I = Q/t$: an ampere is a coulomb every second.

Recap — the whole topic on one screen

Idea	What you own now
Current	$I = Q/t$; ampere = C/s. Charge: $Q = It$.
Drift	$I = nqv_d A$; carriers crawl slowly along.
Direction	Conventional current $+\to-$; electrons go the other way.

Next topic

Resistance, resistivity & Ohm's law

What pushes the current is voltage; what holds it back is resistance. Next we meet Ohm's law $V = IR$ — the most useful equation in circuits — and what sets a wire's resistance.

→ Topic 17 · Resistance, resistivity, Ohm's law & temperature

Symbol	Meaning	SI unit
n	number of charge carriers per unit volume	1/m³
q	charge on each carrier (\(e\) for electrons)	C
v_d	drift speed — the slow net crawl along the wire	m/s
A	cross-section area of the wire	m²

Mistake	Fix
Thinking electrons race through the wire at light speed.	The drift is very slow; it's the field (the "push") that travels almost instantly.
Using minutes or hours for \(t\).	Convert time to seconds first (\(I\) is C per second).
Confusing conventional current with electron flow.	Conventional current is \(+\) to \(-\); electrons move the opposite way.
Forgetting current is charge per second.	\(I = Q/t\): an ampere is a coulomb every second.

Idea	What you own now
Current	\(I = Q/t\); ampere = C/s. Charge: \(Q = It\).
Drift	\(I = nqv_d A\); carriers crawl slowly along.
Direction	Conventional current \(+\to-\); electrons go the other way.