Question

# If the relative permeability of iron is 2000. It’s absolute permeability in S.I units isA. $8\pi \times {10^{ - 4}}$B. $8\pi \times {10^{ - 3}}$C. $\dfrac{{800}}{\pi }$D. $\dfrac{{8\pi \times {{10}^9}}}{\pi }$

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Hint: The absolute permeability of a material is equal to the product of the permeability in free space and the relative permeability of the medium.

Complete step by step solution:
The relation between absolute permeability and relative permeability is as follows:
Absolute permeability is equal to $4\pi \times {10^{ - 7}}$ times the relative permeability of the material in its respective SI unit.
Therefore, from the above relation we get:
$\mu = {\mu _0}{\mu _r}$

Where,
$\mu$ is the absolute permeability of the material in SI units
${\mu _0}$ is equal to $4\pi \times {10^{ - 7}}$
${\mu _r}$ is the relative permeability of the given material.
Therefore, from the above relation on putting the values in the given formula for absolute permeability we get,
$\begin{array}{l} \mu = {\mu _0}{\mu _r}\\ \Rightarrow \left( {4\pi \times {{10}^{ - 7}}} \right) \times 2000 \end{array}$

Now after multiplying the values we get,
$\Rightarrow 8\pi \times {10^{ - 4}}$

The above answer is in terms of the absolute permeability of the given material in terms of its SI units.

Additional information: The term absolute permeability $\mu$ of a material is the product of the permeability of free space ${\mu _0}$ and the relative permeability of the material ${\mu _r}$.
The relative permeability of a medium is defined as the force between two poles when it is placed at a fixed distance in vacuum to the force between them at the same distance in that medium.
The relative permeability in its essence is a purely numerical number and therefore has no units. As mentioned before, for air and nonmagnetic materials its values are always unity or equal to 1

Note: Students often do not know the relation between the absolute and relative permeabilities of a medium, so it is extremely hard to solve sums like this for them. Students always need to know the equations with certain quantities with other such quantities.