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 $m$)

$A$ regular polygon of $6$ sides is formed by bending a wire of length $4 \pi \text{ m}$. If an electric current of $4 \pi \sqrt{3} \text{ A}$ is flowing through the sides of the polygon,the magnetic field at the centre of the polygon would be $x \times 10^{-7} \text{ T}$. The value of $x$ is . . . . . . .

The magnetic field at the centre $O$ due to the given structure is:

$A$ long straight wire in the horizontal plane carries a current of $50\, A$ in the north to south direction. Find the magnitude and direction of the magnetic field $B$ at a point $2.5\, m$ east of the wire.

Given below are two statements:
Statement $I:$ Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element $(Id\vec{l})$ of a current-carrying conductor only.
Statement $II:$ Biot-Savart's law is analogous to Coulomb's inverse square law of charge $q$,with the former being related to the field produced by a vector source,$Id\vec{l}$,while the latter is produced by a scalar source,$q$. In light of the above statements,choose the most appropriate answer from the options given below:

For a wire, as shown in the figure, carrying a current of $10 \,A$, find the magnetic induction field at the point $O$. (Given: $\mu_0 = 4 \pi \times 10^{-7} \,H/m$)