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The number density of free electrons in a copper conductor is estimated as 8.5×10²⁸ m⁻³. How long does an electron take to drift from one end of a wire 6 m long to its other end? The area of cross-section of the wire is 1.0×10⁻⁶ m² and it is carrying a current of 1.5 A.

Asked in GUJCET 2022 · Drift velocity, mobility and current density

• (1) 8.1×10⁴ s
• (2) 5.4×10⁴ s
• (3) 12.7×10⁴ s
• (4) 4.5×10⁴ s

Step-by-step solution

Why the other options are wrong

• (1) 8.1×10⁴ s is neAℓ = 8.16×10⁴ without dividing by the current. The time is (neAℓ)/I, and I = 1.5 A.
• (3) No single slip gives 12.7×10⁴ s; even multiplying by I instead of dividing gives 12.2×10⁴. Sanity check: t = (8.16×10⁴)/(1.5) = 5.44×10⁴ s.
• (4) No single slip gives 4.5×10⁴ s. Sanity check: t = (neAℓ)/I = (8.16×10⁴)/(1.5) = 5.44×10⁴ s.

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