DRIFT VELOCITY | MOBILITY | ELECTRIC FIELD | ELECTRIC FORCE
A clear, example-driven guide with tricks, short-cuts and downloadable notes.
Table of Contents
Introduction — a simple mental picture
When a conductor (like a copper wire) is placed in an electric field, its free electrons don't instantly fly away at lightning speed; instead they acquire a small average velocity superimposed on their random thermal motion. That average, directed motion is the drift velocity. Drift velocity explains the actual current you measure even though individual electrons move randomly at thermal speeds.
Drift Velocity — what it is & how to compute
Drift velocity \(v_d\) is the average velocity of charge carriers in the direction of the electric field. It is related to current density \(J\), carrier density \(n\), and charge \(q\) through:
\(J = nq v_d\)
For example, for electrons in a wire with \(n = 8.5 \times 10^{28}\, \text{m}^{-3}\) and a current density of \(10^6\ \text{A/m}^2\), the drift speed is tiny — on the order of 10^-4 to 10^-3 m/s. That means electrons drift millimeters per second while signals (the field) propagate near light speed.
Mobility — the 'ease' of motion
Mobility \(\mu\) quantifies how easily carriers move under an electric field:
\(v_d = \mu E\)
Higher mobility means a larger drift velocity for the same electric field. Mobility depends on scattering (impurities, phonons), temperature, and material structure. For semiconductors, doping level strongly affects mobility; more scattering centers = lower mobility.
Electric Field & Relation to Drift
The electric field \(E\) in the conductor is what pushes charges. In Ohmic materials, the local field causes a proportional response (current density proportional to field), which links back to mobility and conductivity:
\(J = nq\mu E = \sigma E\)
Think of the field as a gentle slope: steeper slope (bigger E) → faster overall movement (larger \(v_d\)).
Electric Force — microscopic push
Each charge q in an electric field E experiences a force \(F = qE\). For an electron, \(F = -eE\), the negative sign indicates direction opposite to the field. The balance of this force and momentum-relaxing collisions sets the steady drift velocity.
Short Tricks & Familiar Examples
- Memory trick: Drift velocity is tiny — electrons crawl, the field runs. Current is field-driven, signal is field-propagated.
- Analogy: Imagine fog (random motion) with a gentle wind (field). The fog drifts slowly with the wind; that slow net motion is drift velocity.
- Quick check: If the current doubles but carrier density stays same, drift speed doubles too.
Wrap-up — key takeaways
- Drift velocity is an average slow speed superimposed on random thermal motion.
- Mobility links field to drift speed; conductivity links mobility to current.
- Electric force drives the motion; collisions limit the actual drift.
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