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

Last updated date: 23rd Jul 2024
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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.

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.
$\left[ I \right]=\left[ {{M}^{0}}{{L}^{-1}}{{T}^{0}}A \right]$
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.