When magnetic field is applied perpendicular to a current carrying conductor, then voltage is developed across the conductor in the direction perpendicular to both current and magnetic field. This effect is called Hall effect.

Let us consider a rectangular cross sectional specimen carrying current ‘I_{x}‘ in x-axis. Then electrons get drifted in opposite direction to the flow to current. Their velocity is ‘v_{x}‘. Let uniform magnetic field ‘B_{z}‘ be applied on the specimen along z-axis. Let ‘θ’ be the angle between the direction of magnetic field and the plane of the conductor. Then each of the drifting electrons experience Lorentz force along negative y-axis which is given by

F* _{l}* = ev

_{x}B

_{z}sinθ

= ev

_{x}B

_{z}sin90

^{o}

= ev

_{x}B

_{z}

The Lorentz force causes the electrons to bend downwards which will result to the collection of large number of electrons at the lower surface and deficiency of electrons at the upper surface. Therefore, downward electric field is generated, which is called Hall Field (E_{H}).

The Hall field opposes the further downward movement of electrons. So, at steady state condition,

Electrostatic force = Lorentz force

or, e × E_{h} = ev_{x}B_{z}

or, E_{H} = v_{x}B_{z} …. (i)

The current density J_{x} is given by,

J_{x} = – nev_{x} …. (ii), where the negative sign represents the nature of charge of electrons.

Dividing equation (i) by (ii), we get,

^{EH}⁄_{Jx} = ^{vxBz}⁄_{– nevx}

∴ E_{H} = ^{JxBz}⁄_{– ne}

This gives the magnitude of Hall electric field.

Again,

^{EH}⁄_{JxBz} = ^{– 1}⁄_{ne}

∴ ^{EH⁄JxBz = RH, where RH is Hall coefficient or Hall constant.}

### Hall Constant

Hall constant is defined as the Hall field per unit current density per unit transverse magnetic field.

The applications of Hall Constant are:

- Hall constant can be used to find out the concentration of charge.
- It can be used to identify the nature of charge carrier.