Thank you for reporting, we will resolve it shortly
Q.
The fractional change in the magnetic field intensity at a distance ' $r$ ' from centre on the axis of current carrying coil of radius '$a$' to the magnetic field intensity at the centre of the same coil is: (Take $r < a$ )
$ B _{\text {axis }}=\frac{\mu_{0} i R ^{2}}{2\left( R ^{2}+ x ^{2}\right)^{3 / 2}} $
$B _{\text {centre }}=\frac{\mu_{0} i }{2 R } $
$\therefore B _{\text {centre }}=\frac{\mu_{0} i }{2 a }$
$\therefore B _{\text {axis }}=\frac{\mu_{0} ia ^{2}}{2\left( a ^{2}+ r ^{2}\right)^{3 / 2}}$
$\therefore $ fractional change in magnetic field =
$\frac{\frac{\mu_{0} i }{2 a }-\frac{\mu_{0} ia ^{2}}{2\left( a ^{2}+ r ^{2}\right)^{3 / 2}}}{\frac{\mu_{0} i }{2 a }}=1-\frac{1}{\left[1+\left(\frac{ r ^{2}}{ a ^{2}}\right)\right]^{3 / 2}} $
$\approx 1-\left[1-\frac{3}{2} \frac{ r ^{2}}{ a ^{2}}\right]=\frac{3}{2} \frac{ r ^{2}}{ a ^{2}}$
Note : $\left(1+\frac{r^{2}}{a^{2}}\right)^{-3 / 2} \approx\left(1-\frac{3}{2} \frac{r^{2}}{a^{2}}\right)$
[True only if $r << a$ ]