Run a current down a strip across a magnetic field and a voltage appears ACROSS it. Resistance can't tell whether a current is positive charges going one way or negative charges going the other — can this transverse voltage?
▶ Launch the interactive simulationDrive two strips with the SAME conventional current (left→right) in the SAME field B (out of the page): one conducts by positive carriers (holes, drifting +x), the other by negative carriers (electrons, drifting −x). Each is a swarm of Drude carriers under F = q(E_H − v×B) whose transverse field E_H is itself dynamical — dE_H/dt ∝ −⟨q·v_y⟩, the sideways current charging the edges. The carriers bend to an edge, charge it up, and the growing Hall field straightens the flow; the lab reads the steady E_H and, separately, forward-models a real copper foil's V_H = IB/(net) with noise and inverts it.
the Hall law E_H = v_d·B and R_H = E_H/(J·B) = 1/(n·q): both species deflect to the SAME edge yet charge it with OPPOSITE sign, so V_H flips sign — sign(R_H) = sign(q) reads the carrier charge straight off (no resistance measurement can), and |R_H| = 1/(ne) recovers copper's free-electron density n ≈ 8.5×10²⁸ m⁻³ with R_H < 0 confirming electron conduction