$B _{ X }$ and $B _{ Y }$ are the magnetic field at the centre of two coils of two coils $X$ and $Y$ respectively, each carrying equal current. If coil $X$ has $200$ turns and $20 cm$ radius and coil $Y$ has $400$ turns and $20 cm$ radius, the ratio of $B _{ X }$ and $B _{ Y }$ is
JEE MAIN 2022, Medium
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At centre $B=N\left(\frac{\mu_{0} i }{2 R}\right)$
$B_{x}=200\left(\frac{\mu_{0} \dot{i}}{2 \times 20 cm }\right)$
$B_{y}=400\left(\frac{\mu_{0} i}{2 \times 20 cm }\right)$
$\frac{ B _{x}}{ B _{y}}=\frac{1}{2}$
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