Start with the commuter picture, then switch tabs to see the same thing as real physics. The sliders stay in step.
Commuters stream down a corridor while an invisible hand shoves them sideways. What happens to the crowd?
Crowd sizes and pushes are shown in arbitrary units to keep the idea clear.
The same experiment with real charge carriers in a thin Hall sensor slice.
For a slice of thickness t with n charge carriers per unit volume, each with charge q: VH = IB / (nqt). The sign of VH tells you whether the carriers are negative (electrons) or positive (holes).
Voltage and force sizes are shown in arbitrary units to keep the idea clear.