A conducting wire is in the shape of a regular hexagon which is inscribed inside an imaginary circle of radius $R$. If a current $I$ flows the wire, the magnitude of magnetic field at the centre of the circle is

A coil having 100 turns is wound tightly in the form of a spiral with inner and outer radii 1 cm and 2 cm , respectively. When a current 1 A passes through the coil, the magnetic field at the centre of the coil is

Two tangent galvanometers $A$ and $B$ have coils of radii 8 cm and 16 cm respectively and having resistance of 8 $\Omega$ each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30^{\circ}$ and $60^{\circ}$, respectively. If $A$ has 2 turns, then $B$ must have

A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega$. The ratio of the magnitude of its magnetic moment to that of its angular momentum is