A steel wire of length $$l$$ and magnetic moment $$M$$ is bent into a semicircular arc of radius $$R$$. The new magnetic moment is

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at $$30^{\circ}$$ with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3 G . Then the magnitude of the earth's magnetic field at the location is

A compass needle oscillates 20 times per minute at a place where the dip is $$45^{\circ}$$ and the magnetic field is $$B_1$$. The same needle oscillates 30 times per minute at a place where the dip is $$30^{\circ}$$ and magnetic field is $$B_2$$. Then, $$B_1: B_2$$ is

A paramagnetic sample showing a net magnetisation of $$0.8 \mathrm{~A} \mathrm{~m}^{-1}$$, when placed in an external magnetic field of strength $$0.8 \mathrm{~T}$$, at a temperature $$5 \mathrm{~K}$$. If the temperature is raised to $$20 \mathrm{~K}$$, then the magnetisation becomes