$B_X$ 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 $20 \mathrm{cm}$ radius and coil $Y$ has $400$ turns and $20 \mathrm{cm}$ radius, the ratio of $B_X$ and $B_Y$ is