If current flows in a bar of conductor or semiconductor that is placed in a magnetic field, where the current flow and magnetic field are at right angles, an electric field is set up across the bar, orthogonal to both current flow and magnetic field directions. This effect arises because the charge carriers in the bar experience a force F due to the magnetic field:
where v is the drift velocity of carriers of charge e, and B is the magnetic flux density. Charge carriers are thus forced towards one side of the bar, creating an excess space charge and hence an electric field Ey in the y-direction, across the bar. In equilibrium the forces due to the transverse electric field and the magnetic field are in balance:
or
where J is the current density along the bar, and RH is the Hall coefficient of the material of the bar and is related to the carrier concentration in the bar. The voltage due to this transverse electric field is known as the Hall voltage. Measurement of the Hall voltage enables the Hall coefficient to be found, and hence the type and density of the charge carriers in the bar to be determined:
in an n-type semiconductor,
in a p-type semiconductor,
where n and p are the electron and hole densities, respectively, and r is a function of the detailed charge-scattering mechanisms in the material.
https://www.allaboutcircuits.com/technical-articles/understanding-and-applying-the-hall-effect/ An introduction to the Hall effect, on the All About Circuits website
https://www.youtube.com/watch?v=AcRCgyComEw A video demonstration of the Hall effect