At what distance on the axis,from the centre of a circular current-carrying coil of radius $r$,does the magnetic field become $1/8$th of the magnetic field at the centre?

The ratio of the magnetic field at the centre of a current-carrying coil of radius $r$ to the magnetic field at a distance $r$ from the centre of the coil on its axis is $\sqrt{x}: 1$. The value of $x$ is $............$

An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is:

An arc of a circle of radius $R$ subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $i$. The magnetic field at the centre will be

$A$ thin ring of radius $R$ meter has charge $q$ coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $f$ revolution/s. The value of magnetic induction in $Wb/m^2$ at the center of the ring is $(\mu_0 = \text{Permeability of free space})$

$A$ circular coil is in the $y-z$ plane with its centre at the origin. The coil carries a constant current. Assuming the direction of the magnetic field at $x = -25 \, cm$ to be the positive direction of the magnetic field,which of the following graphs shows the variation of the magnetic field along the $x-$ axis?