Figure shows two semicircular loops of radii $$R_1$$ and $$R_2$$ carrying current $I$. The magnetic field at the common centre '$$\mathrm{O}$$' is

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $$\mathrm{n}$$ turns. If the same current passes in both the cases, the ratio of magnetic fields produced at the centre for one turn to that of $$n$$ turns is

A horizontal wire of mass '$$m$$', length '$$l$$' and resistance '$$R$$' is sliding on the vertical rails on which uniform magnetic field '$$B$$' is directed perpendicular. The terminal speed of the wire as it falls under the force of gravity is ( $$\mathrm{g}=$$ acceleration due to gravity)

A straight wire carrying a current (I) is turned into a circular loop. If the magnitude of the magnetic moment associated with it is '$$M$$', then the length of the wire will be