Question

The relative permeability of iron is 6000. Its magnetic susceptibility will be then
$\left( A \right)5999$
$\left( B \right)6001$
$\left( C \right)6000 \times {10^{ - 7}}$
$\left( D \right)6000 \times {10^7}$

Answer 1

Hint: In this question use the direct relation between magnetic susceptibility and relative permeability which is given as ${\chi _m} = {\mu _r} - 1$ so use this direct relation to reach the solution of the problem.

Formula used - ${\chi _m} = {\mu _r} - 1$

Complete step-by-step solution -

Relative permeability – The relative permeability is the ratio of the permeability of the specific medium to the permeability of the free space.
Relative permeability is often denoted by $\left( {{\mu _r}} \right)$ and permeability of the free space is often denoted by $\left( {{\mu _o}} \right)$ and permeability is often denoted by $\left( \mu \right)$
$ \Rightarrow {\mu _r} = \dfrac{\mu }{{{\mu _o}}}$
Relative permeability is dimensionless.
Permeability of free space is given as ${\mu _o} = 4\pi \times {10^{ - 7}}$ Wb/A-m.
Magnetic susceptibility – It is the measure of the degree of how much a magnetic material becomes magnetized when applied in a magnetic field.
There are 5 types of magnetic material which are given as:
Di magnetic materials, paramagnetic materials, ferro magnetic materials, ferri magnetic materials and anti-ferro magnetic materials.
Among above materials ferro magnetic materials are highly magnetized when applied in a magnetic field.
Its relative permeability is very high and greater than 1
Given data:
Relative permeability = 6000.
Now as we know that there is a direct relation between magnetic susceptibility and relative permeability which is given as
${\chi _m} = {\mu _r} - 1$................... (1), where ${\chi _m}$ = magnetic susceptibility.
                                                                  ${\mu _r}$ = relative permeability.
So substitute the value of relative permeability in equation (1) we have,
$ \Rightarrow {\chi _m} = {\mu _r} - 1 = 6000 - 1 = 5999$
So this is the required magnetic susceptibility.
Hence option (A) is the correct answer.

Note – Whenever we face such types of questions, always recall the relation between magnetic susceptibility and relative permeability which is stated above, then just simply substitute the given value in this relation as above and simplify, we will get the required answer.