When a magnetic field is applied perpendicular to the current carrying conductor, electric field is set up in a direction perpendicular to the direction of magnetic field and current. This phenomenon is called Hall effect and developed field is called Hall field. It is used to measure the amount and direction of electric current flowing through a material, by detecting changes in the magnetic field.

Consider a slab of material subjected to a external magnetic field B acting z direction and electric field Ex acting along x direction so that current density will flow along x direction. Due to magnetic field, electrons experience Lorentz force acting downward along y axis so that lower surface collects electrons while upper surface collects positive ions. This produces an electric field Ey called Hall field. Ultimately force due to Hall field becomes equal to the Lorentz force due to magnetic fielc and steady state is attained. The Lorentz force experience by electron of charge '-e' moving with velocity 'v' in electromagnetic field is given by

At steady state,

Fy = 0

(-e) [Ey - Vx B] = 0

=> Ey = Vx B ....1

Let n be the electronic concentration. Then current density along x direction is

Jx = n (-e)Vx .....2

Now, Hall coefficient is defined by the relation

Using equation 1 and equation 2

Thus hall coefficient gives the sign and concentration of carrier.

Hall mobility

Mobility is defined as magnitude of drift velocity per unit electric field. Hall mobility is a measure of how easily electric charge carriers (such as electrons or holes) can move through a material when subjected to an electric and magnetic field. It is calculated by dividing the electric current density by the product of the magnetic field strength and the electric field strength. Essentially, it tells us how quickly and easily the charge carriers can move in response to an electric field, and is an important property in the design of electronic devices. Hall mobility can be expressed as

This is the expression of Hall mobility.

The Hall effect and Hall mobility have several advantages in electronic and materials research.

The Hall effect can be used to measure the type and concentration of charge carriers in a material, as well as their mobility, which is important in determining the electrical and magnetic properties of the material. It is a non-destructive method of measurement, and can be used on a wide range of materials, including semiconductors, metals, and insulators.

Hall mobility is a useful parameter to determine the suitability of a material for electronic applications. Materials with high Hall mobility will allow electric charges to move quickly and efficiently through them, resulting in more efficient and faster electronic devices. This is particularly important for the design of high-performance electronic devices, such as transistors, solar cells, and sensors.

Overall, the Hall effect and Hall mobility provide valuable information about the electrical and magnetic properties of materials, and are important tools in the development of new electronic devices and materials.

This note is a part of the Physics Repository.

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