Electron drift velocity in conductors: Compared with the speed of light, how large is the typical drift velocity of electrons under DC conditions in a metal?

Introduction / Context:
Students often confuse the rapid propagation of electrical signals with the actual drift motion of electrons through a conductor. The drift velocity is the average net velocity of charge carriers due to an applied electric field. This question clarifies the scale of electron drift in metals compared to the speed of light, an essential idea for understanding conduction and signal transmission.

Given Data / Assumptions:

• Ordinary metallic conductor (e.g., copper) at room temperature.
• Direct current (steady-state) conditions with practical current densities.
• Comparison is qualitative against the speed of light c ≈ 3 x 10^8 m/s.

Concept / Approach:

Drift velocity v_d is given by v_d = I / (n * q * A), where I is current, n is free-electron number density, q is electron charge, and A is cross-sectional area. For typical values (n ≈ 8.5 x 10^28 m^-3 for copper, I in amperes, and A in mm^2 to cm^2 range), v_d evaluates to millimeters or micrometers per second to a few centimeters per second—orders of magnitude lower than c. In contrast, the electromagnetic wave (signal) propagates near a significant fraction of c depending on medium permittivity, which is why light-bulbs appear to turn on virtually instantly, even though individual electrons move very slowly on average.

Step-by-Step Solution:

Verification / Alternative check:

Even at higher currents or smaller cross sections, v_d rarely exceeds a few cm/s in household wiring. Thus, it remains negligible compared with c by factors of 10^9 or more.

Why Other Options Are Wrong:

• Equal, almost equal, half, or one-tenth of c: these refer to signal or field propagation speeds in media, not carrier drift, and are many orders of magnitude too large for electron drift in metals.

Common Pitfalls:

• Conflating signal propagation (an electromagnetic phenomenon) with carrier drift (a material transport phenomenon).
• Ignoring that thermal velocities are high but random, while drift is the small net average superimposed on random motion.

Final Answer:

very small as compared to speed of light