The Hall effect and the physical basis of the Hall sensor. If an electric current I is passed along the sample, and a magnetic field B is created perpendicular to the plane of the plate, then an electric field is created on the side planes of the plate in the direction CD, which is called the Hall field. In practice, as a rule, the Hall field is characterized by a potential difference, which is measured between the symmetric points C and D on the side surface of the sample. This potential difference is called the Hall potential difference Uhal or Hall E.M.F. prick, Hall of εhal.
In the classical theory of conductivity, the Hall effect is explained by the fact that in a magnetic field, moving electric charges are affected by the Lorentz force, the magnitude and direction of which are determined by the vector equation:
F = e [VB] ( 1 ),
where B is a vector of induction of magnetic-field,
V is a rate of movement of charges,
е is a charge of transmitters of current taking into account a sign.
In our case, V is perpendicular to B and the electric field of the Hall is determined by:
Ehal = V B ( 2 ),
is associated E.M.F. Hall of εhal, or hall potential difference as follows:
εhal = Uhal = Ehal d= VBd ( 3 ).
Strength of current which flows through unit of area of cross-sectional of standard is equal to the closeness of current:
J = enV ( 4 ),
where п is an amount of transmitters of current in unit of volume of standard (concentration of transmitters of current). From here strength of current:
I = jbd=enVbd ( 5 ).
That enables to write down:
V = I / enbd ( 6 ),
εhal = IB/ enb ( 7 ).
Thus, E.M.F. Hall (or Uhal) proportional to strength of current, induction of magnetic-field, and inversely proportional to the thickness of standard and concentration of transmitters of current in him.
Often recorded:
εhal = R⋅ IB/b ( 8).
Where the coefficient R = 1 / ne is the Hall constant, which, for example, for semiconductors has a value from 10 - 10∧5 cm3/Cl.