--- title: "Current Density, Drift Velocity and the Microscopic Ohm's Law" description: "Current is charge crossing an area per second, and inside a metal it comes from a slow drift superposed on fast random motion. Writing current density as conductivity times field turns Ohm's law into " canonical: https://lightmysky.com/learn/science/current-density-drift-velocity-and-the-microscopic-ohms-law-mt_QU-HkQrkFV source: https://lightmysky.com/learn/science/current-density-drift-velocity-and-the-microscopic-ohms-law-mt_QU-HkQrkFV.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Current Density, Drift Velocity and the Microscopic Ohm's Law Current is charge crossing an area per second, and inside a metal it comes from a slow drift superposed on fast random motion. Writing current density as conductivity times field turns Ohm's law into a statement about the material. Subject: Science · Area: Electricity & Magnetism · Ages 19 to 20 Page: https://lightmysky.com/learn/science/current-density-drift-velocity-and-the-microscopic-ohms-law-mt_QU-HkQrkFV ## Ready when they can - Relates current, current density and drift velocity for a wire of known cross-section - Estimates a drift speed and contrasts it with the speed of the signal - Explains resistivity in terms of collisions and says why it rises with temperature in a metal ## Lesson: Current, drift and the material law Current counts how much charge crosses a surface each second. One ampere means one coulomb passes per second. Current density is current per unit area, so for a uniform wire J equals I divided by A, and it points the way positive charge would flow. **Example.** Take a 12-gauge copper wire, 2.053 mm across, carrying 20.0 A. The electron drift speed works out to about 0.000454 metres per second, slower than a snail. Yet the signal races at about 100000000 metres per second, because each electron pushed in at one end shoves another out at once. Inside the metal, electrons rush randomly at huge speeds while the field adds only a slow shared drift. Each collision with the lattice wipes out the extra velocity, so drift settles where speeding up and colliding balance, giving J equals n q vd. Written locally this is J equals conductivity times field, and resistivity is its reciprocal. Heat shakes the lattice harder, collisions grow more frequent, and the resistivity of a metal rises. **Tip.** Keep three mix-ups away. Drift is not the signal. Density is not total current: the same current in a thinner wire means a larger J and a faster drift. A minus sign on drift only says electrons move against the chosen positive direction. **Recap.** Current counts charge per second, density spreads it over area, collisions set the drift, and heat raises a metal's resistivity. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Recovering the Field from the Potential Gradient](https://lightmysky.com/learn/science/recovering-the-field-from-the-potential-gradient-mt_EqCLB9bqG1) - [Dielectrics and the Polarisation of Matter](https://lightmysky.com/learn/science/dielectrics-and-the-polarisation-of-matter-mt_OYRr_k3IW6) ## Opens up - [Kirchhoff's Rules for Multi-Loop Circuits](https://lightmysky.com/learn/science/kirchhoffs-rules-for-multi-loop-circuits-mt_AS3KiGstGD)