When a current is made to flow in the presence of a magnetic field, the charge carriers that constitute the current experience a force. The force is given by the Lorentz force Law
or more accurately, the second term in the Lorentz force law.
In the diagram above B and I are perpendicular. Charges will build up on both sides of the conductor, producing an electric field, until for each charge carrier that makes up the current, the magnetic force pushing it to one side of the conductor is balance by an equal electric force. There will be no net force on the charge carriers, so
in (1) .
If the width is d as in the diagram then
the Hall voltage between the sides of the conductor is given by
ignoring the signs. Use the equation for electric current
in the form
to get