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The cross-sectional area of a copper wire is equal to the area of a square of side 2 mm. If this copper wire carries an electric current of 8 A, find the drift velocity of the free electrons. The number density of electrons in copper is 8×10²⁸ m⁻³.

Asked in GUJCET 2008 · Drift velocity, mobility and current density

• (1) 1.56×10⁻⁴ m s⁻¹
• (2) 1.56×10⁻² m s⁻¹
• (3) 3.12×10⁻³ m s⁻¹
• (4) 3.12×10⁻² m s⁻¹

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 1.56×10⁻² m s⁻¹. It is 100 times the correct value and would need an area of only 0.04 mm²; remember 1 mm²=10⁻⁶ m², so the area here is 4×10⁻⁶ m².
• (3) No single slip gives 3.12×10⁻³ m s⁻¹. Even taking the 2 mm side as if it were the area gives 3.12×10⁻⁴ m s⁻¹, ten times smaller than this; the area is (2 mm)²=4×10⁻⁶ m².
• (4) No single slip gives 3.12×10⁻² m s⁻¹, which is 200 times the correct value. Drift speeds in copper wires carrying a few amperes are of the order of 10⁻⁴ m s⁻¹.

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