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Question: The absolute permeability of a medium is \(8.792 \times {10^{ - 6}}\;{{{\rm{Henry}}} {\left/ {\vp...

The absolute permeability of a medium is 8.792×10−6  Henry/Henrymm8.792 \times {10^{ - 6}}\;{{{\rm{Henry}}} {\left/ {\vphantom {{{\rm{Henry}}} {\rm{m}}}} \right. } {\rm{m}}}. Its relative permeability is:
A) 0.7 B) 7 C) 70 D) 6×10−8\begin{array}{l} A)\,0.7\\\ B)\,7\\\ C)\,70\\\ D)\,6 \times {10^{ - 8}} \end{array}

Explanation

Solution

In this question the concept of absolute permeability and relative permeability Is tested. The absolute permeability has been given in the question and we have to calculate the relative permeability using the relation between both of them.

Complete step by step answer:
The relation between the absolute permeability, the relative permeability also involves the absolute permeability of free space. The relation is as follows: -
μr=μμ∘{\mu _r} = \dfrac{\mu }{{{\mu _ \circ }}}
Where μr{\mu _r}is the relative permeability, μ\mu is the absolute permeability of the medium , μ∘{\mu _ \circ } is the absolute permeability of free space which has the value.
Now we have all the required values and relations to solve this question.
Putting the values in the above established relation, we get
μr=8.792×10−61.2566×10−6{\mu _r} = \dfrac{{8.792 \times {{10}^{ - 6}}}}{{1.2566 \times {{10}^{ - 6}}}}
After dividing and getting the value, we get
μr=7{\mu _r} = 7
Therefore, the relative permeability of the medium is 7.
The relative change in the resultant magnetic field inside a material in comparison to the magnetizing field in which the material is located is called magnetic permeability.
It is the ratio of the magnetic flux density and the magnetic field strength. In the empty or free space, the magnetic flux is equal to the magnetizing field because there is no matter present. The SI unit system established the value of absolute permeability of free space to be equal to 4π×10−74\pi \times {10^{ - 7}} Weber per ampere-metre. And the magnetic permeability is symbolised by μ\mu .

So, the correct answer is “Option B”.

Note:**
The relation between the absolute permeability, the relative permeability and the absolute permeability of free space should be remembered correctly. During the calculation of the relative permeability appropriate unit conversion has to be considered.