Question

The intensity of magnetization of a bar 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 1$$c{m}^2$$respectively. The magnitude of magnetic moment of the bar is (in SI unit).
  A. 0.6
  B. 1.3
  C. 1.24
  D. 2.4

Answer 1

Hint: To solve this question we must know the definitions of the given parameters and relation between them. Also, in the options the units are not given. So, appropriate conversions should be done. We shall use the formula for intensity of magnetization to calculate magnetic moment. All the required values to be substituted such as area will also be calculated.

Formula used:
$$I={\displaystyle \frac{M}{V}}$$

Complete step by step answer:
Intensity of magnetization is the change a magnet undergoes when it is placed in a magnetic field. Therefore, this change in magnetic moment per volume is called the intensity of magnetization. Now we must also know what a magnetic moment. Its magnetic moment can be described as the orientation and magnetic strength of a magnet that produces a magnetic field. As we know from the definition of intensity of magnetization is given as magnetic moment per unit volume.
$$I={\displaystyle \frac{M}{V}}$$,
Where I = Intensity of magnetization
         M = magnetic moment
          V = volume
So, on rearranging above formula,
We get,
$$M=IV$$………. (1)
Now,
We are given Intensity of magnetization and volume V is unknown but we have been given the length L and area of cross section of the magnet A to calculate the volume
As the length and area are given in cm their conversion into meter is necessary
$$L=12cm=0.12m$$
$$A=1c{m}^2=1\times {10}^{-4}{m}^2$$
Therefore,
$$V=L\times A$$
$$V=0.12\times 1\times {10}^{-4}$$
$$V=12\times {10}^{-6}$$
Now,
After substituting the volume and the given value in equation (1)
$$M=5.0\times {10}^4\times 12\times {10}^{-6}$$
Therefore,
$$M=0.6A{m}^2$$

Additional Information:
There is no other way to calculate the magnetic moment of the magnet through given parameters.

Note:
The students must be careful while writing the powers of units. During conversion of units, there is a probability of students making errors in the powers which may lead to difference in answers. Magnetic moment is a vector quantity. It means that it has magnitude as well as direction. The direction of the field is calculated using the right hand’s rule.