Electric Current And Drift Velocity

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A copper wire carries a steady current while free electrons drift slowly through it, so how does the drift speed compare with the electron random thermal speed?

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Free electrons in a metal move randomly at very high thermal speeds of the order of $10^5$ m/s, but when a field is applied they acquire only a tiny net drift velocity, typically around $10^{-4}$ m/s, as discussed in NCERT Class 12, Chapter 3 (Current Electricity). The drift velocity is given by $v_d = \frac{eE	au}{m}$, where $	au$ is the mean relaxation time between collisions; because $	au$ is extremely short, the ordered drift added on top of chaotic thermal motion is minuscule. Hence the drift speed is many orders of magnitude smaller than the thermal speed. The option that drift equals thermal speed is wrong because thermal motion is random and cancels out, contributing no net current. The option that drift exceeds thermal speed is wrong because the applied field only nudges electrons gently between frequent collisions. The option equating drift to light speed confuses the slow charge motion with the fast propagation of the electric signal, which travels near light speed. A magnitude check confirms the ratio: $10^{-4}/10^5 = 10^{-9}$, so drift is about a billion times smaller, consistent with everyday wires still carrying useful current.

Electric Current And Drift Velocity

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