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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
Current counts charge per second, density spreads it over area, collisions set the drift, and heat raises a metal's resistivity.
More to read
9.1 Electrical Current
Electric current counts charge crossing a surface each second, measured in amperes. In a metal wire the carriers are electrons drifting from the negative end toward the positive end of the applied voltage. Current density refines the picture as current per unit area, a vector pointing with the flow of positive charge. For a uniform wire it is simply total current divided by cross section.
9.2 Model of Conduction in Metals
Inside a metal, electrons race randomly at huge thermal speeds while the field adds only a slow steady drift, often slower than a snail. Current comes from that tiny average drift shared by enormous numbers of electrons. Each collision with the lattice resets an electron's extra velocity, and the balance between acceleration and collisions sets the drift speed. This microscopic view gives current density as charge density times drift velocity.
9.3 Resistivity and Resistance
Resistivity captures how strongly a material fights current, with resistance scaling as resistivity times length over area. Collisions cause the fight, so heating a metal, which shakes the lattice harder, raises its resistivity. Microscopic Ohm's law writes the same physics locally: current density equals conductivity times field. It is Ohm's law per point of material rather than per whole component.
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.