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Question: If the relative permeability of iron is 2000. It’s absolute permeability in S.I units is A. \[8\pi...

If the relative permeability of iron is 2000. It’s absolute permeability in S.I units is
A. 8π×10−48\pi \times {10^{ - 4}}
B. 8π×10−38\pi \times {10^{ - 3}}
C. 800π\dfrac{{800}}{\pi }
D. 8π×109π\dfrac{{8\pi \times {{10}^9}}}{\pi }

Explanation

Solution

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 4π×10−74\pi \times {10^{ - 7}} times the relative permeability of the material in its respective SI unit.
Therefore, from the above relation we get:
μ=μ0μr\mu = {\mu _0}{\mu _r}

Where,
μ\mu is the absolute permeability of the material in SI units
μ0{\mu _0} is equal to 4π×10−74\pi \times {10^{ - 7}}
μr{\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,

\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.