The motion of carriers in the presence of electric and magnetic fields gives rise to a number of galvanometric effects. The most important of these effects is the Hall Effect.

When a semiconductor sample carrying a current I is placed in a transverse magnetic field B, then an electric field E0 is induced in the specimen, in the direction perpendicular to both B and I. This phenomenon is called the Hall Effect.

The Hall Effect may be used for determining whether a semiconductor is n-type or p-type by finding the carrier concentration and calculating the mobility $\mu$, by measuring the conductivity $\sigma$.

Expression for Hall voltage:

In equilibrium condition the electric field intensity EH due to Hall Effect exerts a force on charge carriers which just balance the magnetic force.

$qE_H=BqV_d$

q is the magnitudeof charge carrier and Vd is the drift speed

$E_H=BV_d$....(1)

If d is the width of the conductor i.e., distance between upper and lower surfaces, then the Hall voltage is 

$V_H=E_Hd$

$V_H=V_dBd$....(2)

Thus, the measured Hall voltage gives a value for the drift speed of the charge carriers if d and B are known.

If J is the current density, nq is the charge carrier density, I is the current, w is the width of specimen in direction of magnetic field then,

$J=nqV_d$.....(3)

$J=\dfrac{I}{wd}$.....(4)

$V_h=V_dBd$.....from (2)

$V_H=\dfrac{JBd}{nq}$.....from (3)

$V_H=\dfrac{I}{wd}\times\dfrac{Bd}{nq}$.....from(4)

$\therefore\ V_H=\dfrac{BI}{nqw}$

As,

$J=\dfrac{I}{A}$.....(5)

We can obtain the charge carrier density n by measuring the current in the sample. We can express the drift speed from (3) and (5) as-

$V_d=\dfrac{I}{nqA}$

Where $A=wd$ and A is the cross-sectional area of the conductor.

$V_H=\dfrac{IBd}{nqA}$

As,

$V_H=\dfrac{BI}{nqw}$

$V_H=R_H\dfrac{IB}{w}$

Therefore hall voltage  is given by -

$V_H=R_H\dfrac{IB}{w}$

where $R_H=\dfrac{1}{nq}$ is the Hall coefficient.

This relationship shows that a properly calibrated conductor can be used to measure the magnitude of an unknown magnetic field.