# Magnetic Susceptibility- Formula, Definition, Unit

Magnetic susceptibility is a measure of the degree of magnetization of material with the applied magnetic field. In other words, how much material magnetize in an applied magnetic field indicates the magnetic susceptibility of that material. Its symbol is χ.

## Unit of Magnetic Susceptibility

It is the ratio quantity of the same units, therefore it is dimensionless. It has no unit.

## Types of Magnets as per Magnetic Susceptibility

We can categorize the material into three categories.

### Paramagnetic Material

The magnetic susceptibility of paramagnetic materials is χ>0. The atom of paramagnetic material has small magnetic dipole moments that partly line up with the external field. Paramagnetic materials have small and constant positive susceptibilities at room temperature. Therefore, the alignment of dipoles of paramagnetic material is small compared to the applied magnetic field.

The susceptibility of the paramagnetic material is temperature dependent, and it is inversely proportional to the temperature. The increased temperature causes greater vibrations of atoms that hinder the alignment of dipoles. Platinum is an example of paramagnetic material. The magnetic susceptibility of platinum is 0.0001.

### Diamagnetic Material

The susceptibility of diamagnetic materials is χ<0. It means the susceptibility of the diamagnetic materials has a negative value. These materials are repelled by the magnets and they move from a stronger field to a weaker field. The susceptibility of the paramagnetic material is temperature independent. Examples of diamagnetic materials are Gold, tin, mercury, water, etc

### Ferromagnetic Material

The ferromagnetic material strongly attracts the magnet and moves from a weaker field to a stronger field. The magnetic permeability of the ferromagnetic material is not constant and it may be in the range of 1000 to 100000. The susceptibility of ferromagnetic material is very high and its value is positive. Examples of ferromagnetic materials are iron, cobalt, nickel, and their alloys.

## Solved Problem

### The Magnetic fieldand magnetic susceptibility are respectively 1.6 T and 900 A/m. Find the relative permeability and susceptibility.

Given:
Magnetic Field(B)= 1.6 T
Magnetic Intensity(H)=900 A/m
Permeability of air(μ) = 4π×10-7

Relative Permeability(μr)