Math List $I$ with List $II$

Choose the correct answer from the option given below:

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,

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

Magnetic field at point $'M'$ of given current distribution

A current of $i$ ampere is flowing through each of the bent wires as shown the magnitude and direction of magnetic field at $O$ is 

For adjoining fig., The magnetic field at point, $P$ will be

A straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is