Electrons in a 2D conductor under electric field E (x-direction) and magnetic field B (z-direction, into screen). The Lorentz force F = q(E + v×B) curves trajectories. Accumulated charge builds a transverse Hall voltage. R_H = 1/(ne) is a direct measure of carrier density.
Hall coefficient R_H = 1/(ne): negative for electrons (n-type), positive for holes (p-type). The Hall effect (1879) first proved electrons carry current. Integer Quantum Hall Effect (1980, von Klitzing): R_H = h/(ne²) — quantized to 1 in 10⁹.