Explanation

(c) The magnetic field at a point along the axis at distance $R$ from the centre of a circular coil of radius $R$ carrying $i$ is
$B_{A} = \frac{\mu_{0}2\pi iR^{2}}{4\pi\left( R^{2} + R^{2} \right)^{3/2}}$
$\ \ \ \ \ \ = \frac{\mu_{0}i}{2\sqrt{8}R} = \frac{B}{\sqrt{8}}\left\lbrack B_{centre} = B = \frac{\mu_{0}i}{2R} \right\rbrack$