The Hall effect

Push a current through a flat conductor and switch on a magnetic field pointing through its face, and something surprising happens: a small voltage appears across the strip's width, perpendicular to the current, even though nothing is pushing charge that way electrically. The magnetic force on the moving carriers deflects them sideways, piling up charge on one edge until the electric field from that pileup grows strong enough to cancel the magnetic push. From then on, the carriers drift straight again, but the transverse voltage stays put as long as the current and field do.

That equilibrium voltage, the Hall voltage V_H = IB/(net), is more than a curiosity. Because its sign flips with the sign of the charge carrier, it is the standard way to tell whether a material's current is actually carried by electrons or by holes — something Ohm's law alone can never reveal. And because it depends on the carrier density n, measuring it is how physicists determine how many charge carriers per cubic metre a new semiconductor actually has.

It is worth noticing what the Hall voltage does not depend on: the material's resistivity plays no role in the equilibrium value, only in how quickly that equilibrium is reached. Two conductors with wildly different resistances but the same carrier density, current, field and thickness settle to the same Hall voltage.