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:

$A$ straight wire of diameter $0.5\, mm$ carrying a current of $1\, A$ is replaced by another wire of $1\, mm$ diameter carrying the same current. The strength of the magnetic field at a point far away is

Two long parallel wires $X$ and $Y$,separated by a distance of $6 \text{ cm}$,carry currents of $5 \text{ A}$ and $4 \text{ A}$,respectively,in opposite directions as shown in the figure. The magnitude of the resultant magnetic field at point $P$,which is at a distance of $4 \text{ cm}$ from wire $Y$,is $x \times 10^{-5} \text{ T}$. The value of $x$ is . . . . . . .
Take the permeability of free space as $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.

$A$ 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 point $P$ is:

$A$ current $I$ flows through the loop as shown in the figure. The magnetic field at the centre $O$ is: