Question

A magnetising field of $2 \times {10^3}A{m^{ - 1}}$ produces a magnetic flux density of $8\pi T$ in an iron rod. The relative permeability of the rod will be.
A. ${10^2}$
B. $1$
C. ${10^4}$
D. ${10^3}$

Answer 1

Hint: We have studied magnetic permeability in magnetism. We can solve this problem with the concept of magnetic permeability. Magnetic permeability is a property of material. When a material is placed in a magnetic field, there is relative increase or decrease in the total magnetic field inside the material with respect to the outside magnetic field this is known as magnetic permeability of material.

Complete answer:
Magnetic permeability is represented as $\mu $ and formula is: $\mu = B/H$ where $B$ is the magnetic flux density, $H$ is the magnetising field. In this formula $B/H$ is called as absolute permeability of medium while the relative permeability of material is defined as ratio $\dfrac{\mu }{{{\mu _0}}}$. Hence, the relative permeability of any material is defined as the comparison of the permeability concerning the air or vacuum.
So, The relative permeability of the rod can be calculated by the formula ${\mu _r} = \dfrac{B}{{{\mu _0}H}}$, where $B$ is the magnetic flux density, $H$ is the magnetising field and ${\mu _0} = 4\pi \times {10^{ - 7}}$.
We have been given in the question that-
Magnetising field, $H = 2 \times {10^3}A{m^{ - 1}}$
Magnetic flux density, $B = 8\pi T$
Now, putting these value in the formula, we get
${\mu _r} = \dfrac{{8\pi }}{{4\pi \times {{10}^{ - 7}} \times 2 \times {{10}^3}}} = \dfrac{{8\pi }}{{8\pi \times {{10}^{ - 4}}}} = {10^4}$
Therefore, the relative permeability of the rod is ${10^4}$.

So, the correct answer is “Option C”.

Note:
Whenever such types of questions appear then always write the things given in the question and then by using the formula of relative permeability of rod is found out as mentioned in the solution. The relative permeability of a free space is equal to one. According to permeability, materials are divided into: diamagnetic, paramagnetic, and ferromagnetic.