A cylindrical long wire of radius $R$ carries current $I_0$ uniformly distributed in its cross-sectional surface. The pressure developed due to magnetic force in wire at distance $\frac{R}{2}$ from its axis is given by $\frac{3{\mu }_0{I}_0^2}{n{\pi }^2{R}^2}.$ Find value of $n.$

Two circular rings each of radius $\text{'}a\text{'}$ are joined together such that their planes are perpendicular to each other as shown in figure. (circle with solid line representation in vertical plane and the other circle with dotted line representation is horizontal plane respectively) A very small loop of mass $m$ and radius $r$ carrying a current $I_0$ is placed in the plane of the paper at common centre of each ring. The loop can freely rotate about any of its diametric axis. Find the time period (in s) of loop for small oscillations $\left(ma=\frac{2\pi {\mu }_0{I}_0}{{\pi }^2}\right)·$ Resistances of each half ring is shown in figure.