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…

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