Drift Velocity

Charge transport in a metal is described by relating the macroscopic current to the average velocity with which free electrons drift under an applied field, captured by (I = nAev_d), where (n) is the free-electron density, (A) the cross-section, (e) the electronic charge, and (v_d) the drift speed. Solving for the drift speed gives (v_d = I/(nAe)). Inserting (I = 3.2) A, (n = 1.0 \times 10^{29}) m(^{-3}), (A = 2 \times 10^{-6}) m(^2), and (e = 1.6 \times 10^{-19}) C gives (v_d = 3.2 / (1.0 \times 10^{29} \times 2 \times 10^{-6} \times 1.6 \times 10^{-19}) = 1.0 \times 10^{-4}) m/s. The value (1.0 \times 10^{-3}) m/s is wrong by a factor of ten, arising from a misplaced power of the area. The value (2.0 \times 10^{-4}) m/s mistakenly drops the factor of two in (A). The value (1.0 \times 10^{-5}) m/s overcounts the electron density. This follows the NCERT microscopic model of conduction. The remarkably small drift speed, despite a sizeable current, is the expected and well-known result, since the enormous electron number density compensates for the sluggish motion. It is worth emphasising that this drift speed is many orders of magnitude smaller than the random thermal speeds of the electrons, yet it is precisely this tiny field-driven net displacement, summed over a vast population of carriers, that constitutes the observable conduction current in the wire.