Charge carriers and drift velocity

The transport equation

I = nqvA

• n: number density of charge carriers (carriers per m³)
• q: charge on each carrier (1.60 x 10^-19 C for an electron)
• v: drift velocity, the average speed of the carriers along the wire (m/s)
• A: cross-sectional area (m²)

Drift velocity is small

In a copper wire carrying a few amps, v is only a fraction of a millimetre per second, because n is enormous (about 10²⁹ per m³). A lamp still lights almost instantly because electrons all round the circuit start drifting at practically the same moment. In a wire whose area changes, the same current means a higher drift velocity in the thinner part.

Why resistivities vary so much

• Metals: n is very large (about 10²⁸ to 10²⁹ m^-3), so a small drift velocity gives a large current: low resistivity.
• Semiconductors: n is far smaller, so resistivity is much higher (and n rises with temperature).
• Insulators: almost no free charge carriers, so resistivity is extremely high.

Worked example

A copper wire (n = 8.5 x 10²⁸ m^-3) of area 1.0 x 10^-6 m² carries 2.0 A. Find the drift velocity.

1. v = I / (nqA)
2. = 2.0 / (8.5 x 10²⁸ x 1.60 x 10^-19 x 1.0 x 10^-6)

Answer: v = 1.5 x 10^-4 m/s (0.15 mm/s)

Check yourself

1. A wire with n = 8.0 x 10²⁸ m^-3 and area 2.0 x 10^-6 m² carries 3.0 A. Find the drift velocity in mm/s, to 3 s.f.
   Show answer

   0.117 mm/s. v = 3.0 / (8.0 x 10²⁸ x 1.60 x 10^-19 x 2.0 x 10^-6) = 1.17 x 10^-4 m/s = 0.117 mm/s.

2. A conductor has n = 1.0 x 10²⁹ m^-3, A = 5.0 x 10^-7 m² and drift velocity 2.0 x 10^-4 m/s. Find the current in A.
   Show answer

   1.6 A. I = nqvA = 1.0 x 10²⁹ x 1.60 x 10^-19 x 2.0 x 10^-4 x 5.0 x 10^-7 = 1.6 A.

3. A wire of area 1.0 x 10^-7 m² carries 0.50 A with drift velocity 4.0 x 10^-4 m/s. Find n, in units of 10²⁸ m^-3, to 3 s.f.
   Show answer

   7.81 x 10²⁸ m^-3. n = I / (qvA) = 0.50 / (1.60 x 10^-19 x 4.0 x 10^-4 x 1.0 x 10^-7) = 7.81 x 10²⁸ m^-3.

4. A wire narrows to half its cross-sectional area. The current is the same throughout. What happens to the drift velocity in the narrow part?
   • It doubles
   • It halves
   • It stays the same
   • It becomes 4 times as large
   Show answer

   It doubles. I, n and q are the same, so v is inversely proportional to A.

5. Why does a semiconductor have a much higher resistivity than a metal?
   • Its electrons have a larger charge
   • Its drift velocity is always zero
   • It has far fewer charge carriers per unit volume
   • It is always hotter
   Show answer

   It has far fewer charge carriers per unit volume. With n much smaller, the same current would need a much larger drift velocity.

6. Drift velocities are less than 1 mm/s. Why does a lamp light almost as soon as it is switched on?
   • Electrons throughout the circuit start drifting almost at the same moment
   • Electrons travel from the switch at the speed of light
   • The lamp stores charge
   • The current only flows in the lamp
   Show answer

   Electrons throughout the circuit start drifting almost at the same moment. The wires are already full of free electrons; they all start moving together.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson Edexcel IAL Physics Unit 2 (WPH12) question paper, January 2024: list of data (e, m_e, h, c, eV)

Last updated 7 November 2026. Spotted a mistake? Tell us.