A current flows in a small copper block (shown greatly enlarged). The volume of copper contains ten Coulombs of charge carriers (free electrons) and is 10 cm long. When a current of one Amp is flowing, the drift velocity of the electrons is one cm/s.
A vertical magnetic field now penetrates the copper. Electrons are deflected, creating an electric field across the conductor. At equilibrium, the magnetic force Bev is balanced by the electric force eE. The Hall voltage voltage,VH, measured across the block of width d can be calculated since....
1 If the copper block is one cm wide, the Earth's field is taken as 2x10-5 T and the drift velocity is 1.0 cm/s, the Hall voltage is given by VH = Bvd as 2x10-9 Volts. Two nanovolts is a very small voltage, of little practical use.
2 If the copper block is replaced by a very thin (0.001 mm) copper layer and one Amp flows as before, the drift velocity is increased 1000 times. VH becomes 2 microvolts which is measurable.
3 If the copper block is replaced with a semiconductor containing one charge carrier per thousand atoms, the drift velocity is similarly increased and VH is again measurable.
A Hall-effect probe can be calibrated to measure magnetic field strength. The Hall-effect probe shown here, used to measure the field strength near a pair of Helmholtz coils, is made from a small wafer of semiconducting material (silicon).