Question

Relative permeability of iron is 5500, then its magnetic susceptibility will be.
$\begin{align}
  & \text{A}\text{. }5500\times {{10}^{7}} \\
 & \text{B}\text{. }5500\times {{10}^{-7}} \\
 & \text{C}\text{. }5501 \\
 & \text{D}\text{. }5499 \\
\end{align}$

Answer 1

Hint: Magnetism susceptibility measures the ability of the substance to take up magnetisation when placed in a magnetic field. In the question we are given with relative permeability and we have to find magnetic susceptibility we will use the formula having relation between the two.

Formula used:
${{\chi }_{m}}=\left( {{\mu }_{r}}-1 \right)$

Complete answer:
We are given with relative permeability and we have to find magnetic susceptibility
Using the formula
$\begin{align}
  & {{\chi }_{m}}=\left( {{\mu }_{r}}-1 \right) \\
 & {{\chi }_{m}}=\text{magnetic susceptibility} \\
 & {{\mu }_{r}}=\text{relative permeability} \\
 & {{\chi }_{m}}=\left( 5500-1 \right) \\
 & {{\chi }_{m}}=4499 \\
\end{align}$
Hence the magnetic susceptibility is 4499.

So, the correct answer is “Option D”.

Additional Information:
Magnetic permeability: permeability is the measure of the extent to which a metal can be penetrated by a magnetic field. It can be also defined as the ratio of magnetic induction to the magnetic intensity H.
$\mu =\dfrac{B}{H}$
Relative permeability: Permeability of various substances can be compared with one another in terms of relative permeability. It is defined as ratio of magnetic permeability of medium to permeability of free space.
${{\mu }_{r}}=\dfrac{\mu }{{{\mu }_{{}^\circ }}}$
Magnetic susceptibility: Magnetism susceptibility measures the ability of the substance to take up magnetisation when placed in a magnetic field. It can be also defined as the ratio of intensity of magnetisation to the magnetic field intensity H.
${{\chi }_{m}}=\dfrac{M}{H}$
If a linear magnetic material, subjected to action of a magnetic field intensity H develops magnetisation M and magnetic induction B then
$B={{\mu }_{{}^\circ }}\left( H+M \right)$
The relative permeability of ferromagnetic material has large positive value.
The relative permeability is positive but less than 1 for a diamagnetic material.

Note:
The susceptibility of a diamagnetic substance is independent of the magnetising field and the temperature. The magnetic susceptibility of paramagnetic material is inversely proportional to temperature. The magnetic susceptibility of ferromagnetic material has large positive value.
The relative permeability for a paramagnetic material is slightly greater than 1.