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

$A$ long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is $B$. If it is bent into a circular loop of radius $r_1$ having $n$ turns,the magnetic field at the centre of the coil for the same current is:

Two parallel wires carry currents $i_1$ and $i_2$ $(i_1 > i_2)$. When the currents are in the same direction,the magnetic field at a point midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,the magnetic field at that point becomes $30 \, \mu T$. What is the ratio $\frac{i_1}{i_2}$?

$A$ long straight wire carries a current of $35\; A$. What is the magnitude of the field $B$ at a point $20\; cm$ from the wire?

$A$ rod with a circular cross-section area $2 \text{ cm}^2$ and length $40 \text{ cm}$ is wound uniformly with $400$ turns of an insulated wire. If a current $0.4 \text{ A}$ flows in the wire winding, the total magnetic flux produced inside the winding is $4\pi \times 10^{-6} \text{ Wb}$. The relative permeability of the rod is (Given permeability of vacuum $\mu_0 = 4\pi \times 10^{-7} \text{ N m A}^{-2}$)

The magnetic induction at the centre of a current-carrying circular coil of radius $8 \ cm$ is $6 \sqrt{6}$ times the magnetic induction at a point on its axis. Then the distance of the point from the centre of the coil in $cm$ is $(\sqrt{5} = 2.236)$.