The magnitude of magnetic field at point 'O' in the following figure will be

A coil of ' $n$ ' turns and radius ' $R$ ' carries a current 'I'. It is unwound and rewound to make a new coil of radius $\frac{R}{3}$ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the kinetic energy of the particle is increased to three times, then the new radius will be

A circular arc of radius r carrying current ' I ' subtends an angle $\frac{\pi}{8}$ at its entre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is ( $\mu_0=$ permeability of free space)