What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field '$B$' at origin

For a circular coil of radius $R$ and $N$ turns carrying current $I$, the magnitude of the magnetic field at a point on its axis at a distance $x$ from its centre is given by,

$B=\frac{\mu_{0} I R^{2} N}{2\left(x^{2}+R^{2}\right)^{3 / 2}}$

$(a)$ Show that this reduces to the familiar result for field at the centre of the coil.

$(b)$ Consider two parallel co-axial circular coils of equal radius $R$ and number of turns $N,$ carrying equal currents in the same direction, and separated by a distance $R$. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to $R,$ and is given by,

$B=0.72 \frac{\mu_{0} N I}{R}, \quad \text { approximately }$

The electric current in a circular coil of four turns produces a magnetic induction $32\,T$ at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be $..........\,T$

Magnetic fields at two points on the axis of a circular coil at a distance of $0.05\,m$ and $0.2\,m$ from the centre are in the ratio $8 : 1$. The radius of the coil is.....$m$

The current of $5 \mathrm{~A}$ flows in a square loop of sides $1$ $\mathrm{m}$ is placed in air. The magnetic field at the centre of the loop is $\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}$. The value of $\mathrm{X}$ is____.

Give convection for electric or magnetic field emerging out of the plane of the paper and going into the plane of paper.