A student computes copper's drift speed in a field using with copper's

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch The free-electron gas: what Drude gets right and what only Fermi fixes

Problem

A student computes copper's drift speed in a field Ex=2.0 V m−1E_x=2.0\,\mathrm{V\,m^{-1}} using vd=eτEx/mv_d=e\tau E_x/m with copper's τ=2.46×10−14 s\tau=2.46\times10^{-14}\,\mathrm{s}, gets vd=8.65 mm s−1v_d=8.65\,\mathrm{mm\,s^{-1}}, and argues: "so an electron starting at a switch 3.0 m3.0\,\mathrm{m} from a lamp takes 3.0 m/vd≈350 s3.0\,\mathrm{m}/v_d\approx350\,\mathrm{s}, nearly six minutes, to reach the lamp and light it." Explain what is wrong with this reasoning, and estimate instead how quickly the lamp actually lights, assuming the signal that starts the current travels down the wire at about two-thirds of the speed of light.

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