8.0 Hall effect

  Magnetics

According to Hall, if a current-carrying conductor is placed in a transverse magnetic field, an emf is set up across the conductor perpendicular to both current and magnetic field. This was first observed by Hall, and therefore is called Hall effect

Suppose we have a steady current $i$ flowing in a uniform conducting strip along $x-$axis. If the strip is placed in a uniform magnetic field $B,$ acting along the $y-$axis, the field $\vec B$ will exert a deflecting force on electrons along $z-$axis and on positive ions along negative $z-$axis. Because of this force, the electrons displace towards front face, $ABCD$ and positive ions on back face $PQRS.$ The displacement of charge carriers gives rise to a transverse field, known as Hall electric field which acts along positive $z-$axis, and opposes the sideways drift of the carriers. When equilibrium is reached in which the magnetic deflecting force on the charge carriers is just balanced by the electric force caused by Hall electric field. Thus$${V_H} = \frac{{iR}}{{nel}}$$