When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number of turns, area of the coil and radius of the coil wire are $\mathrm{N}, \mathrm{A}$ and r respectively. For a second coils number of turns, area of the coil and radius of the coil wire are $2 \mathrm{~N}, 2 \mathrm{~A}$ and 3 r respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt{2} \alpha P$. The value of $\alpha$ is $\_\_\_\_$。