HALL EFFECT
A sideways voltage V_H = IB/nqt — and its SIGN names the carrier. Electrons and holes bend the same way but flip the voltage.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Run a current through a flat strip and lay a magnetic field across it, into the page. A voltage appears — not along the current but ACROSS it, between the two edges. Edwin Hall found it in 1879 as a graduate student, and it still runs half the sensors in your car.
Sideways push
The moving carriers feel a sideways magnetic force qv×B and drift to one edge. Charge piles up there until its own electric field pushes back just as hard. At balance qE = qvB — the same condition the velocity selector uses, only now the strip reaches it on its own.
The voltage
The pile-up is a measurable voltage: V_H = IB/nqt. It grows as the strip gets thinner and its carriers scarcer — which is why copper gives microvolts and a semiconductor gives hundreds of millivolts. Hall probes are never made of metal.
The sign
Here is the beautiful part. Electrons and holes drift oppositely but bend to the SAME edge — so they leave opposite charge there, and the sign of V_H flips between them. Measuring that sign is how physics discovered that in some materials the current is carried by positive holes.
Audit
Audited: V_H = IB/nqt, the sign exactly opposite for electron and hole at the same current, the density recovered by inversion, and the balance drift speed equal to E/B to the bit — the velocity selector run in reverse. The positive-carrier verdict is a fact Coulomb’s law cannot explain, and quantum band theory was built to.