Question

The magnetic susceptibility of a material of a rod is 499. Permeability of vacuum ​is $4\pi \times {10^{ - 7}}H{m^{ - 1}}$ Absolute permeability of the material of the rod is:
A $\pi \times {10^4}$
B $2\pi \times {10^4}$
C $3\pi \times {10^{ - 4}}$
D $4\pi \times {10^{ - 4}}$

Answer 1

Hint
As the magnetic susceptibility is given and permeability is also given then we find the value of absolute permeability by using the formula $\mu = {\mu _o}\left( {1 + {\chi _m}} \right)$

Complete step-by-step answer:
Magnetic susceptibility is the measure of how much a material can be magnetised in the presence of a magnetic field.
Here, it is given that the susceptibility of a material of a rod ${\chi _m} = 499$
Permeability of the vacuum ${\mu _o} = 4\pi \times {10^{ - 7}}H{m^{ - 1}}$
We have to find the value of absolute permeability of the material of the rod
As, we know the relation between the magnetic susceptibility and permeability is
⇒ $\mu = {\mu _o}\left( {1 + {\chi _m}} \right)$
Where, μ is the absolute permeability of the material.
${\mu _o}$ is the permeability of the vacuum
${\chi _m}$ is the magnetic susceptibility of the material.
Now, put the given values in the above equation, we get
⇒$\mu = 4\pi \times {10^{ - 7}}\left( {1 + 499} \right)$
⇒ $\mu = 2\pi \times {10^{ - 4}}H{m^{ - 1}}$
Hence, the value of absolute permeability is $\mu = 2\pi \times {10^{ - 4}}H{m^{ - 1}}$
Therefore, (B) option is correct.

Additional information
Magnetic susceptibility is the measure of how much the material is magnetized in the presence of a magnetic field. It is the ratio of the magnetization to the applied magnetic field.

Note
Magnetic permeability helps us measure a material's resistance to the magnetic field or measure of the degree to which the magnetic field can penetrate through a material. It is the ratio of the magnetic induction to the magnetic intensity.