Q 12-04-171JEE MainJEE Main 2021 (26 Aug, Shift 1)Medium
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 $r < a$)
Answer: (C) $\frac{3}{2}\frac{r^2}{a^2}$
$B_{axis} = \dfrac{\mu_0Ia^2}{2(a^2 + r^2)^{3/2}} = B_0\left(1 + \dfrac{r^2}{a^2}\right)^{-3/2} \approx B_0\left(1 - \dfrac{3r^2}{2a^2}\right)$ for $r \ll a$.
$$\frac{|\Delta B|}{B_0} = \frac{3}{2}\frac{r^2}{a^2}$$
Solution by Sreeraj P, M.Sc Physics