A long straight rod of diameter 4 mm carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is

A straight wire of length 20 cm carrying a current of $\frac{3 .}{\pi^2} \mathrm{~A}$ is bent in the form of a circle. The magnetic field at the centre of the circle is

A circular coil carrying a current of 2.5 A is free to rotate about an axis in its plane perpendicular to an external field. When the coil is made to oscillate, the time period of oscillation is $T$. If the current through the coil is 10 A , the time period of oscillation is

Two points $A$ and $B$ on the axis of a circular current loop are at distances of 4 cm and $3 \sqrt{3} \mathrm{~cm}$ from the centre of the loop. If the ratio of the induced magnetic fields at points $A$ and $B$ is $216: 125$, then radius of the loop is