Question

Out of the two magnetic materials, 'A' has relative permeability slightly greater than unity while 'B' has less than unity. Identify the nature of the materials 'A' and 'B'. Will their susceptibilities be positive or negative?

Answer 1

Hint: The properties of paramagnetic and ferromagnetic substances are dependent on \[{\mu _r}\]and\[{\chi _m}\]. The relative permeability is greater than unity in paramagnetic and ferromagnetic substances and less than unity in diamagnetic substances. Also, magnetic susceptibility is positive for paramagnetic and ferromagnetic substances and is negative for diamagnetic substances.

Complete step by step answer:
The ratio of permeability of the medium and the vacuum is called relative permeability. It is denoted by \[{\mu _r}\]and also it is a unit less number. On the other hand, magnetic susceptibility is the ratio of the intensity of magnetization of a material and the magnetizing field. It is denoted by\[{\chi _m}\]. Thus,
\[{\chi _m} = \dfrac{M}{H}\]
where,\[M\] is the intensity of magnetization and \[H\]is the magnetizing field.
The magnetic susceptibility and relative permeability are related to each other as follows:
\[{\chi _m} = {\mu _r} - 1\]
The properties of paramagnetic and ferromagnetic substances are dependent on \[{\mu _r}\]and\[{\chi _m}\]. For paramagnetic substances \[{\mu _r} > 1\] but small and the\[{\chi _m}\]is positive but small. For ferromagnetic substances \[{\mu _r} > > 1\] but small and\[{\chi _m}\]is positive and large. For diamagnetic substances \[{\mu _r} < 1\] but small and the\[{\chi _m}\]is negative and small.
According to the question, material 'A' has relative permeability slightly greater than unity. Thus, material ‘A’ is a paramagnetic material. Therefore, it’s susceptibility is positive and small. And, material 'B' has relative permeability less than unity. Thus, material ‘B’ is a diamagnetic material. Therefore, its susceptibility is negative and small.

Note:
Both the magnetic susceptibility and relative permeability are unit less quantities.
Note that,\[{\mu _r}\]is greater than unity both for paramagnetic and ferromagnetic substances but is small for paramagnetic substances and is comparatively large for ferromagnetic substances.