Find the magnetic induction at point $O$ in the given figure.

$A$ straight wire of length $\pi^2 \, m$ carries a current of $2 \, A$. The magnetic field due to it is measured at a point $1 \, cm$ away from it. If the wire is bent into a circle and carries the same current,what is the ratio of the magnetic field at its centre to the magnetic field measured in the first case?

$A$ beam of neutrons performs circular motion of radius $r = 1 \, m$ under the influence of an inhomogeneous magnetic field with inhomogeneity extending over $\Delta r = 0.01 \, m$. The speed of the neutrons is $54 \, m/s$. The mass and magnetic moment of the neutrons are $1.67 \times 10^{-27} \, kg$ and $9.67 \times 10^{-27} \, J/T$ respectively. The average variation of the magnetic field over $\Delta r$ is approximately ....... $T$.

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{8}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is ($\mu_0 =$ permeability of free space).

Let $B_1$ be the magnitude of the magnetic field at the center of a circular coil of radius $R$ carrying current $I$. Let $B_2$ be the magnitude of the magnetic field at an axial distance $x$ from the center. For $x : R = 3 : 4$,the ratio $\frac{B_2}{B_1}$ is:

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have a common axis. The currents through $P$ and $Q$ are $I$ and $4I$ respectively in the clockwise direction as seen from $O$. The net magnetic field at $O$ is: