A paramagnetic sample shows a net magnetisation of $$8 \mathrm{Am}^{-1}$$ when placed in an external magnetic field of $$0.6 \mathrm{~T}$$ at a temperature of $$4 \mathrm{~K}$$. When the same sample is placed in an external magnetic field of $$0.2 \mathrm{~T}$$ at a temperature of $$16 \mathrm{~K}$$, the magnetisation will be

In a permanent magnet at room temperature

A magnetic needle has a magnetic moment of $$5 \times 10^{-2} \mathrm{~Am}^2$$ and moment of inertia $$8 \times 10^{-6} \mathrm{~kgm}^2$$. It has a period of oscillation of $$2 \mathrm{~s}$$ in a magnetic field $$\mathbf{B}$$. The magnitude of magnetic field is approximately?

A circular current loop of magnetic moment $$M$$ is in a arbitrary orientation in an external uniform magnetic field $$\mathbf{B}$$. The work done to rotate the loop by $$30^{\circ}$$ about an axis perpendicular to its plane is