Question

A thin iron rod is cut into $10$ equal parts parallel to its length. The intensity of magnetisation of each piece will be
A. (1/10)th of initial value
B. 10 times initial value
C. does not change
D. becomes half

Answer 1

Hint: Intensity of magnetisation($\overset{\to }{\mathop{I}}\,$) is the induced dipole moment per unit volume, developed in a magnetic material when placed in a magnetic field. It’s a vector quantity and has the direction same as that of induced dipole moment in the material.

Formula used:
$\overset{\to }{\mathop{I}}\,=\dfrac{\overset{\to }{\mathop{{{M}_{net}}}}\,}{V}$
where $\overset{\to }{\mathop{I}}\,=$Intensity of magnetisation, $\overset{\to }{\mathop{{{M}_{net}}}}\,=$ Net induced dipole moment in the material and $V=$ Volume.

Complete step by step answer:
Magnetic dipole moment gives the measure of magnetic strength and direction of field produced by it. Net induced magnetic dipole moment($\overset{\to }{\mathop{{{M}_{net}}}}\,$) is the resultant or overall magnetic dipole moment after the elimination of moments in different directions. Volume of an object is the space acquired by it.Unit of $\overset{\to }{\mathop{I}}\,$ is ampere per metre.

Intensity of magnetisation has the dimensional formula as follows:
$\left[ I \right]=\left[ {{M}^{0}}{{L}^{-1}}{{T}^{0}}A \right]$
As we can see that $\overrightarrow{I}$ depends inversely on length of the material. So, if we decrease the length of the material, it will increase the intensity of magnetisation by the same factor as the length is decreased. So, if we decrease the length of the iron rod by 10 then the change in the intensity of magnetisation will be the multiple of 10 which means the intensity of magnetisation of the resulting iron rod becomes 10 times that of the original one.

Note:Whenever there is a question about the amount of change in a specific quantity due to the change in some other quantity related, check whether the quantity in question depends on the later by analysing the dimensional formula of the former. Also, if the former depends on the later then check the factor of dependence, i.e., check for linear, quadratic, cubic, inverse, inversely quadratic, etc.