The magnetic field near a current-carrying conductor is given by

The magnetic field at the center of a current-carrying loop of radius $0.1 \ m$ is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the center of the loop is: (in $m$)

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

Magnetic field intensity at the centre of a coil of $50$ turns,radius $0.5\, m$ and carrying a current of $2\, A$ is:

$A$ current $i$ flows through a square loop of side $a$. What is the magnetic field at its center?

Which one of the following options represents the magnetic field $\vec{B}$ at the origin $O$ due to the current $I$ flowing in the given wire segments lying on the $xy$ plane?