Question

The intensity of magnetisation of a bar magnet is $5.0\times {{10}^{4}}A{{m}^{-1}}$. The magnetic length and the area of the cross section of the magnet are $12cm$ and $1c{{m}^{2}}$ respectively. The magnitude of magnetic moment of this bar magnet will be given in SI unit as,
$\begin{align}
  & A.0.6 \\
 & B.1.3 \\
 & C.1.24 \\
 & D.2.4 \\
\end{align}$

Answer 1

Hint: The intensity of the magnetisation is defined as the magnetic moment acting per unit volume. The intensity of magnetisation of a bar magnet is found by taking the product of magnetic moment and the volume of the magnet. Therefore by rearranging the equation, we will get the magnetic moment equation. Substitute all the values in it. These all may help you to find out the answer.
Formula used:
Intensity of magnetisation is given as,
$I=\dfrac{M}{V}$
Where $M$ be the magnetic moment and $V$ be the volume of the magnet.

Complete answer:
First of all let us mention what all are given in the question.
The intensity of magnetisation of a bar magnet is given by the equation,
$I=5\times {{10}^{4}}A{{m}^{-1}}$
The area of cross section of the bar magnet will be,
$A=1c{{m}^{2}}$
And the magnetic length has been given as,
$l=12cm$
Therefore we can calculate the volume of the magnetic given. It is calculated by taking the product of the area of the cross section and the length of the magnet.
That is,
$V=A\times l=1\times 12=12c{{m}^{3}}$
The intensity of magnetisation is described using the formula which is given as,
$I=\dfrac{M}{V}$
Where $M$ be the magnetic moment and $V$ be the volume of the magnet.
By rearranging this equation, we can find out the magnetic moment of the magnet.
$M=VI$
Substituting the terms in the equation will give,
$M=12\times {{10}^{-6}}\times 5\times {{10}^{4}}=60\times {{10}^{-2}}=0.6A{{m}^{2}}$.

So, the correct answer is “Option A”.

Note:
Magnetic moment is the measure of the interaction of an object placed in a magnetic field. It is a vector quantity. Intensity of magnetisation is defined as the measure of how much the object has been magnetised.