A short bar magnet placed with its axis inclined at 30° to the external magnetic field of 800 G acting horizontally experiences a torque of 0.016 Nm. Calculate:
(i) the magnetic moment of the magnet,
(ii) the work done by an external force in moving it from most stable to most unstable position,
(iii) What is the work done by the force due to the external magnetic field in the process mentioned in (ii)?

(i) Given,
Magnetic field, B = 800 G 
$\mathrm{\theta } = {30}^{\mathrm{o}}$ 
Torqua acting, $\mathrm{\tau }$ = 0.016 Nm

Since, Torque acting on magnet, $\mathrm{\tau } = MB sin \mathrm{\theta }$

$\therefore$               $\mathrm{M} = \frac{\mathrm{\tau }}{\mathrm{B} \sin \mathrm{\theta }}$
$\Rightarrow$              $\mathrm{M} = \frac{0.016}{800 \times {10}^{-4} \times \sin 30°}$ 

                  $\mathrm{M} = 0.40 {\mathrm{Am}}^2$        [$\because$ 1G = 10^-4T]
which, is the required magnetic moment. 

(ii) Work done be an external force to move the magnet from stable to unstable position,$\mathrm{W} = -\mathrm{MB}\left[\cos {\mathrm{\theta }}_2- \cos {\mathrm{\theta }}_1\right]$ 

              $\boxed{\mathrm{W} = -\mathrm{MB} (\cos 180 ° - \cos 0°)}$ 

                 $= -\mathrm{MB} (-1-1) = 2 \mathrm{MB}$ 

              $$\begin{gathered} \mathrm{W} = 2 \times 0.40 \times 800 \times {10}^{-4} \\ = 0.064 \mathrm{J}. \end{gathered}$$ 

(iii) The displacement and the torque due to the magnetic field are in opposite direction.
So work done by the force due to the external magnetic field is W_B = – 0.064 J.

1. Properties of diamagnetic materials: 
(i) They are feebly repelled by magnets.
(ii) Susceptibilty is negative and very small. 

2. Properties of paramagnetic materials:
(i) They are feebly attracted by magnets
(ii) Susceptibility is positive and small. 

(i) Intensity of magnetisation is a small negative value for diamagnetic substance and, large positive value for a ferromagnetic substance. 

(ii) In a non-uniform magnetic field, a diamagnetic substance tends to move from stronger to weaker part while the ferromagnetic substance tends to move from weaker to stronger part of the field. 

(iii) For a diamagnetic substance, susceptibility is small negative value while, for a ferromagnetic substance, susceptibility is large positive value.

The actual length of a magnet is called the geometric length of the magnet.

The distance between the poles of a magnet is called the magnetic length of the magnet.

The geometric length of the magnet is nearly 8/7 times the magnetic length of the magnet.