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A copper wire carries current density j (current per unit area). Let n be the number of free electrons per unit volume, e the electronic charge, and <v> the average thermal speed of the electrons. While an electron drifts a displacement L along the wire, what total path distance does it actually cover due to its thermal motion?

1. L * n e <v> / j
2. j / (n e <v>)
3. j <v> / (n e)
4. n e / j

Correct answer: L * n e <v> / j

Solution

Drift speed v_d = j/(ne) gives drift time t = L n e / j. In that time the actual distance covered at thermal speed <v> is <v> * t = L n e <v> / j.

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