Thank you for reporting, we will resolve it shortly
Q.
The magnetic field at the centre of a circular coil of radius $r$, due to current $I$ flowing through it, is $B$. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is:
$B _{ C }=\frac{\mu_{0} I }{2 r },$
$ B _{ a }=\frac{\mu_{0} Ir ^{2}}{2\left( x ^{2}+ r ^{2}\right)^{3 / 2}}$
At $x=\frac{r}{2}$
$B _{ a }=\frac{\mu_{0} Ir ^{2}}{2\left(\frac{ r ^{2}}{4}+ r ^{2}\right)^{3 / 2}} $
$=\frac{\mu_{0} Ir ^{2}}{2\left(\frac{5}{4} r ^{2}\right)^{3 / 2}}=\frac{\mu_{0} I }{2 r }\left(\frac{4}{5}\right)^{3 / 2} $
$=\frac{\mu_{0} I }{2 r }\left(\frac{2}{\sqrt{5}}\right)^{3}$