Define the term magnetic susceptibilities of a material. Derive the relation between relative permeability and magnetic susceptibility of a material.

Dear Student,

Magnetic susceptibility is a unit less parameter which symbolises the extent to which a material is susceptible to an external magnetic field. If the material doesn't respond to an external magnetic field by producing any magnetization then its susceptibility must be zero.
 
Magnetic susceptibility of paramagnetic materials is small and positive. For diamagnetic materials it is also small but negative.
 

When a substance is placed in a magnetising field, it becomes magnetised. The total magnetic flux density  within the substance is the flux density  that would have been produced by the magnetising field in vacuum plus the flux density  due to the magnetisation of the substance.
So, effective magnetising field is,

But, 
Where,  is the intensity of magnetisation induced in the sample.
Therefore,

Where,  and also, 
Therefore,
 
Where,  = relative permeability.

Hope this information will clear your doubts about the topic.

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