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Question: A magnetising field of \(2 \times {10^3}A{m^{ - 1}}\) produces a magnetic flux density of \(8\pi T\)...

A magnetising field of 2×103Am−12 \times {10^3}A{m^{ - 1}} produces a magnetic flux density of 8πT8\pi T in an iron rod. The relative permeability of the rod will be.
A. 102{10^2}
B. 11
C. 104{10^4}
D. 103{10^3}

Explanation

Solution

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 μ\mu and formula is: μ=B/H\mu = B/H where BB is the magnetic flux density, HH is the magnetising field. In this formula B/HB/H is called as absolute permeability of medium while the relative permeability of material is defined as ratio μμ0\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 μr=Bμ0H{\mu _r} = \dfrac{B}{{{\mu _0}H}}, where BB is the magnetic flux density, HH is the magnetising field and μ0=4π×10−7{\mu _0} = 4\pi \times {10^{ - 7}}.
We have been given in the question that-
Magnetising field, H=2×103Am−1H = 2 \times {10^3}A{m^{ - 1}}
Magnetic flux density, B=8πTB = 8\pi T
Now, putting these value in the formula, we get
μr=8π4π×10−7×2×103=8π8π×10−4=104{\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 104{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.