The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1=2\pi \mathrm{m}$ and $R_2=4\pi \mathrm{m}$ carrying current $I=4 \mathrm{A}$ as per figure given below is $\alpha \times {10}^{-7} \mathrm{T}$. The value of $\alpha$ is _____. (Centre $\mathrm{O}$ is common for all segments)

An arrangements with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown.

The permeability of free space is ${\mu }_0$. The magnetic field at $C$ is

Two very long, straight, and insulated wires are kept at $90°$ angle from each other in $\mathrm{x}\mathrm{y}$ plane as shown in the figure.

These wires carry currents of equal magnitude $I$ , whose direction are shown in the figure. The net magnetic field at point $P$ will be:

Find the magnetic field at point $\mathrm{P}$ due to a straight line segment $\mathrm{A}\mathrm{B}$ of length $6 \mathrm{c}\mathrm{m}$ carrying a current of $5 \mathrm{A}.$ (See figure) $\left({\mu }_0=4\pi \times {10}^{-7} {\mathrm{NA}}^{-2}\right)$

A wire carrying current $\text{I}$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $\text{X}$ -axis while semicircular portion of radius $\text{R}$ is lying in $\text{Y}$ -$\text{Z}$ plane. Magnetic field at point $\text{O}$ is :

As shown in the figure, two infinitely long, identical wires are bent by ${90}^o$ and placed in such a way that the segments $LP$ and $QM$ are along the $x$ - axis, while segments $PS$ and $QN$ are parallel to the $y$ - axis. If $OP=OQ=4cm,$ and the magnitude of the magnetic field at $O$ is ${10}^{-4} T,$ and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at $O$ will be $\left({\mu }_0=4\pi \times {10}^{-7}N{A}^{-2}\right):$