The unit of permeability of vacuum $(\mu_{0})$ is . . . . . . .

$A$ circular coil of wire consisting of $100$ turns,each of radius $8.0 \, cm$,carries a current of $0.40 \, A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?

$AB$ and $CD$ are long straight conductors,separated by a distance $d$,each carrying a current $I$. The magnetic field at the midpoint of $BC$ is

The ratio of the magnetic field at the centre of a circular ring of radius $R$ to the magnetic field at a point on its axis at a distance $2\sqrt{2}R$ from its centre 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 $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.

$A$ wire of resistance $R$ is bent in the form of a square of side $a$ as shown in the figure. Find the magnetic induction at the center of the square $O$ due to the current flowing through it.