Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)

What is the ratio of the magnetic field at point $O$ in the given figures?

The magnetic field at the center of a current-carrying circular loop is $B_{1}$. The magnetic field at a distance of $\sqrt{3}R$ from the center on its axis is $B_{2}$,where $R$ is the radius of the loop. The value of $B_{1} / B_{2}$ is:

An infinitely long wire carrying current $I$ is along the $Y$-axis such that its one end is at point $A(0, b)$ while the wire extends up to $+\infty$. Find the magnitude of the magnetic field strength at point $(a, 0)$.

$A$ coil having $2000$ turns is wound tightly in the form of a spiral with inner and outer radii $1 \,cm$ and $3 \,cm$, respectively. When a current $\frac{1}{\pi} \,mA$ passes through the coil, the magnetic field at the centre is calculated to be $K \ln 3 \times 10^{-6} \,T$. The value of $K$ is

Magnetic field $dB$ due to a current element at any point on its axis is . . . . . . .