For a circular coil of radius $\mathrm{R}$ and $\mathrm{N}$ turns carrying current $\mathrm{I}$, 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 $\mathbf{R}$, and number of turns $\mathbf{N}$, carrying equal currents in the same direction, and separated by a distance $\mathbf{R} .$ 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 $\mathbf{R}$, and is given by, $B=0.72 \frac{\mu_{0} N I}{R}$, approximately.