The Hall Effect
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 Lawor 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 thenthe Hall voltage between the sides of the conductor is given byignoring the signs. Use the equation for electric currentin the formto get